1. Vijay Mahadevan
  2. petsc

Commits

Vijay Mahadevan  committed b94ee70

Removing the ADR example and updating test output

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  • Parent commits 5fa2bd9
  • Branches master

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Files changed (6)

File src/dm/impls/moab/examples/tests/makefile

View file
 #requirespackage  'PETSC_HAVE_MOAB'
-#requireslanguage 'CXXONLY'
-#requiresprecision double
-#requiresscalar    real
 
 CFLAGS	        =
 FFLAGS	        =

File src/dm/impls/moab/examples/tutorials/ex2.cxx

View file
-static char help[] = "Solves C_t =  -D*C_xx + F(C) + R(C) + D(C) from Brian Wirth's SciDAC project.\n";
+/*T
+   Concepts: KSP^solving a system of linear equations using a MOAB based DM implementation.
+   Concepts: KSP^Laplacian, 2d
+   Processors: n
+T*/
 
 /*
-        C_t =  -D*C_xx + F(C) + R(C) + D(C) from Brian Wirth's SciDAC project. (A DMMoab fork of Barry's advection-diffusion-reaction/ex10.c)
+Inhomogeneous Laplacian in 2D. Modeled by the partial differential equation
 
-        D*C_xx  - diffusion of He[1-5] and V[1] and I[1]
-        F(C)  -   forcing function; He being created.
-        R(C)  -   reaction terms   (clusters combining)
-        D(C)  -   dissociation terms (cluster breaking up)
+   -div \rho grad u = f,  0 < x,y < 1,
 
-        Sample Options:
-          -ts_monitor_draw_solution               -- plot the solution for each concentration as a function of x each in a separate 1d graph
-              -draw_fields_by_name 1-He-2-V,1-He  -- only plot the solution for these two concentrations
-          -mymonitor                              -- plot the concentrations of He and V as a function of x and cluster size (2d contour plot)
-          -da_refine <n=1,2,...>                  -- run on a finer grid
-          -ts_max_steps maxsteps                  -- maximum number of time-steps to take
-          -ts_final_time time                     -- maximum time to compute to
+with forcing function
 
-    Rules for maximum number of He allowed for V in cluster
+   f = e^{-((x-xr)^2+(y-yr)^2)/\nu}
+
+with Dirichlet boundary conditions
+
+   u = f(x,y) for x = 0, x = 1, y = 0, y = 1
+
+or pure Neumman boundary conditions
+
+Usage:
+    mpiexec -n 2 ./ex2 -bc_type dirichlet -nu .01 -rho .01 -file input/quad_2p.h5m -dmmb_rw_dbg 0 -n 50
 
-    Usage: ./ex2 -n 10 -snes_mf -mymonitor -ts_monitor
-           ./ex2 -file <$XOLOTL_DIR/benchmarks/tungsten.txt> -snes_mf -mymonitor -ts_monitor
 */
 
+static char help[] = "\
+                      Solves 2D inhomogeneous Laplacian equation with a Gaussian source.\n \
+                      Usage: ./ex2 -bc_type dirichlet -nu .01 -n 10\n";
+
+
+/* PETSc includes */
+#include <petscksp.h>
 #include <petscdmmoab.h>
-#include <petscts.h>
-
-#define TINY_CLUSTER_CONFIG
-
-#ifndef TINY_CLUSTER_CONFIG
-/*    Hard wire the number of cluster sizes for He, V, and I, and He-V */
-#define  NHe          9
-#define  NV           10   /* 50 */
-#define  NI           2
-#define  MHeV         10   /* 50 */  /* maximum V size in He-V */
-PetscInt NHeV[MHeV+1];     /* maximum He size in an He-V with given V */
-#define  MNHeV        451  /* 6778 */
-#define  DOF          (NHe + NV + NI + MNHeV)
-#else
-/*    Hard wire the number of cluster sizes for He, V, and I, and He-V */
-#define  NHe          5
-#define  NV           1   /* 50 */
-#define  NI           2
-#define  MHeV         1   /* 50 */  /* maximum V size in He-V */
-PetscInt NHeV[MHeV+1];     /* maximum He size in an He-V with given V */
-#define  MNHeV        3  /* 6778 */
-#define  DOF          (NHe + NV + NI + MNHeV)
-#endif
 
-/*
-     Define all the concentrations (there is one of these unions at each grid point)
+#define LOCAL_ASSEMBLY
 
-      He[He] represents the clusters of pure Helium of size He
-      V[V] the Vacencies of size V,
-      I[I] represents the clusters of Interstials of size I,  and
-      HeV[He][V]  the mixed Helium-Vacancy clusters of size He and V
+const int NQPTS1D=2;
+const int NQPTS=NQPTS1D*NQPTS1D;
+const int VPERE=4;
 
-      The variables He, V, I are always used to index into the concentrations of He, V, and I respectively
-      Note that unlike in traditional C code the indices for He[], V[] and I[] run from 1 to N, NOT 0 to N-1
-      (the use of the union below "tricks" the C compiler to allow the indices to start at 1.)
+extern PetscErrorCode ComputeMatrix_MOAB(KSP,Mat,Mat,void*);
+extern PetscErrorCode ComputeRHS_MOAB(KSP,Vec,void*);
 
-*/
-typedef struct {
-  PetscScalar He[NHe];
-  PetscScalar V[NV];
-  PetscScalar I[NI];
-  PetscScalar HeV[MNHeV];
-} Concentrations;
+extern PetscErrorCode Compute_Quad4_Basis ( PetscScalar coords[3*4], int n, PetscScalar pts[], PetscScalar *phi, PetscScalar *dphidx, PetscScalar *dphidy );
+extern PetscErrorCode ComputeQuadraturePointsPhysical(const PetscScalar verts[VPERE*3], PetscScalar quad[NQPTS*3], PetscScalar jxw[NQPTS]);
+
+typedef enum {DIRICHLET, NEUMANN} BCType;
 
-/*
-     Holds problem specific options and data
-*/
 typedef struct {
-  PetscScalar HeDiffusion[6];
-  PetscScalar VDiffusion[2];
-  PetscScalar IDiffusion[2];
-  PetscScalar forcingScale;
-  PetscScalar reactionScale;
-  PetscScalar dissociationScale;
-  PetscInt    nelements;
-} AppCtx;
-
-extern PetscErrorCode RHSFunction(TS ts,PetscReal ftime,Vec C,Vec F,void *ptr);
-extern PetscErrorCode RHSJacobian(TS,PetscReal,Vec,Mat,Mat,void*);
-extern PetscErrorCode InitialConditions(DM,Vec);
-extern PetscErrorCode InitializeVariableSystem(DM);
-extern PetscErrorCode MyMonitorSetUp(TS);
-extern PetscErrorCode GetDfill(PetscInt*,void*);
-extern PetscErrorCode MyLoadData(MPI_Comm,const char*);
+  PetscInt  dim,n;
+  PetscReal rho;
+  PetscReal xref,yref;
+  PetscReal nu;
+  BCType    bcType;
+  char filename[PETSC_MAX_PATH_LEN];
+} UserContext;
 
 #undef __FUNCT__
 #define __FUNCT__ "main"
 int main(int argc,char **argv)
 {
-  TS             ts;                  /* nonlinear solver */
-  Vec            C;                   /* solution */
+  KSP            ksp;
+  DM             dm;
+  
+  UserContext    user;
+  const char     *bcTypes[2] = {"dirichlet","neumann"};
+  const char     *fields[1] = {"T-Variable"};
   PetscErrorCode ierr;
-  DM             dm;                  /* manages the grid data */
-  AppCtx         ctx;                 /* holds problem specific paramters */
-  /* PetscInt       He,*ofill,*dfill; */
-  char           filename[PETSC_MAX_PATH_LEN];
-  const PetscReal   bounds[2] = {0.0,8.0};
-  PetscBool      flg;
-
-  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-     Initialize program
-     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
+  PetscInt       bc,np;
+  Vec            b,x;
+  PetscBool      use_extfile;
+
   PetscInitialize(&argc,&argv,(char*)0,help);
 
-  PetscFunctionBeginUser;
-  ierr = PetscOptionsGetString(NULL,"-file",filename,PETSC_MAX_PATH_LEN,&flg);
-  if (flg) {
-    ierr = MyLoadData(PETSC_COMM_WORLD,filename);CHKERRQ(ierr);
+  MPI_Comm_size(PETSC_COMM_WORLD,&np);
+
+  ierr        = PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "ex2.c");
+  user.dim    = 2;
+  ierr        = PetscOptionsInt("-dim", "The dimension of the problem", "ex2.c", user.dim, &user.dim, NULL);CHKERRQ(ierr);
+  user.n      = 2;
+  ierr        = PetscOptionsInt("-n", "The elements in each direction", "ex2.c", user.n, &user.n, NULL);CHKERRQ(ierr);
+  user.rho    = 0.5;
+  ierr        = PetscOptionsReal("-rho", "The conductivity", "ex2.c", user.rho, &user.rho, NULL);CHKERRQ(ierr);
+  user.xref   = 0.5;
+  ierr        = PetscOptionsReal("-xref", "The x-coordinate of Gaussian center", "ex2.c", user.xref, &user.xref, NULL);CHKERRQ(ierr);
+  user.yref   = 0.5;
+  ierr        = PetscOptionsReal("-yref", "The y-coordinate of Gaussian center", "ex2.c", user.yref, &user.yref, NULL);CHKERRQ(ierr);
+  user.nu     = 0.05;
+  ierr        = PetscOptionsReal("-nu", "The width of the Gaussian source", "ex2.c", user.nu, &user.nu, NULL);CHKERRQ(ierr);
+  bc          = (PetscInt)DIRICHLET;
+  ierr        = PetscOptionsEList("-bc_type","Type of boundary condition","ex2.c",bcTypes,2,bcTypes[0],&bc,NULL);CHKERRQ(ierr);
+  user.bcType = (BCType)bc;
+  ierr        = PetscOptionsString("-file", "The mesh file for the problem", "ex2.c", "",user.filename,PETSC_MAX_PATH_LEN,&use_extfile);CHKERRQ(ierr);
+  ierr        = PetscOptionsEnd();
+
+  /* Create the DM object from either a mesh file or from in-memory structured grid */
+  if (use_extfile) {
+    ierr = DMMoabLoadFromFile(PETSC_COMM_WORLD, user.dim, user.filename, (np==1 ? "" : ""), &dm);CHKERRQ(ierr);
+  }
+  else {
+    ierr = DMMoabCreateBoxMesh(PETSC_COMM_WORLD, user.dim, PETSC_FALSE, NULL, user.n, 1, &dm);CHKERRQ(ierr);
   }
-
-  ctx.nelements      = 10;
-  ierr = PetscOptionsGetInt(NULL,"-n",&ctx.nelements,NULL);CHKERRQ(ierr);
-
-  ctx.HeDiffusion[1]    = 1000*2.95e-4; /* From Tibo's notes times 1,000 */
-  ctx.HeDiffusion[2]    = 1000*3.24e-4;
-  ctx.HeDiffusion[3]    = 1000*2.26e-4;
-  ctx.HeDiffusion[4]    = 1000*1.68e-4;
-  ctx.HeDiffusion[5]    = 1000*5.20e-5;
-  ctx.VDiffusion[1]     = 1000*2.71e-3;
-  ctx.IDiffusion[1]     = 1000*2.13e-4;
-  ctx.forcingScale      = 100.;         /* made up numbers */
-  ctx.reactionScale     = .001;
-  ctx.dissociationScale = .0001;
-
-  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-     Create distributed array (DMDA) to manage parallel grid and vectors
-  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
-  ierr = DMMoabCreateBoxMesh(PETSC_COMM_WORLD, 1, PETSC_FALSE, bounds, ctx.nelements, 1, &dm);CHKERRQ(ierr);
-  ierr = InitializeVariableSystem(dm);CHKERRQ(ierr);
   ierr = DMSetFromOptions(dm);CHKERRQ(ierr);
+  ierr = DMMoabSetFieldNames(dm, 1, fields);CHKERRQ(ierr);
 
   /* SetUp the data structures for DMMOAB */
   ierr = DMSetUp(dm);CHKERRQ(ierr);
 
-  /* The only spatial coupling in the Jacobian (diffusion) is for the first 5 He, the first V, and the first I.
-     The ofill (thought of as a DOF by DOF 2d (row-oriented) array) represents the nonzero coupling between degrees
-     of freedom at one point with degrees of freedom on the adjacent point to the left or right. A 1 at i,j in the
-     ofill array indicates that the degree of freedom i at a point is coupled to degree of freedom j at the
-     adjacent point. In this case ofill has only a few diagonal entries since the only spatial coupling is regular diffusion */
-  /* TODO: DMMoab does not have the capability to do DOF-Coupling as of now.. Assume full block coupling */
-  /*
-  ierr = PetscMalloc(DOF*DOF*sizeof(PetscInt),&ofill);CHKERRQ(ierr);
-  ierr = PetscMemzero(ofill,DOF*DOF*sizeof(PetscInt));CHKERRQ(ierr);
-  for (He=0; He<PetscMin(NHe,5); He++) ofill[He*DOF + He] = 1;
-  ofill[NHe*DOF + NHe] = ofill[(NHe+NV)*DOF + NHe + NV] = 1;
-  */
-
-  /*
-    dfil (thought of as a DOF by DOF 2d (row-oriented) array) repesents the nonzero coupling between degrees of
-   freedom within a single grid point, i.e. the reaction and dissassociation interactions. */
-  /*
-  ierr = PetscMalloc(DOF*DOF*sizeof(PetscInt),&dfill);CHKERRQ(ierr);
-  ierr = PetscMemzero(dfill,DOF*DOF*sizeof(PetscInt));CHKERRQ(ierr);
-  ierr = GetDfill(dfill,&ctx);CHKERRQ(ierr);
-  ierr = DMDASetBlockFills(da,dfill,ofill);CHKERRQ(ierr);
-  ierr = PetscFree(ofill);CHKERRQ(ierr);
-  ierr = PetscFree(dfill);CHKERRQ(ierr);
-  */
- 
-
-  /*  Extract global vector to hold solution */  
-  ierr = DMCreateGlobalVector(dm,&C);CHKERRQ(ierr);
-
-  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-     Create timestepping solver context
-     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
-  ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
-  ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr);
-  ierr = TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE);CHKERRQ(ierr);
-  ierr = TSSetDM(ts,dm);CHKERRQ(ierr);
-  ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
-  ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&ctx);CHKERRQ(ierr);
-  ierr = TSSetRHSJacobian(ts,NULL,NULL,RHSJacobian,&ctx);CHKERRQ(ierr);
-  ierr = TSSetSolution(ts,C);CHKERRQ(ierr);
-
-  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-     Set solver options
-   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
-  ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr);
-  ierr = TSSetDuration(ts,100,50.0);CHKERRQ(ierr);
-  ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
-  ierr = MyMonitorSetUp(ts);CHKERRQ(ierr);
-
-  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-     Set initial conditions
-   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
-  ierr = InitialConditions(dm,C);CHKERRQ(ierr);
-
-  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-     Solve the ODE system
-     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
-  ierr = TSSolve(ts,C);CHKERRQ(ierr);
-
-  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-     Free work space.
-   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
-  ierr = VecDestroy(&C);CHKERRQ(ierr);
-  ierr = TSDestroy(&ts);CHKERRQ(ierr);
-  ierr = DMDestroy(&dm);CHKERRQ(ierr);
-  ierr = PetscFinalize();
-  PetscFunctionReturn(0);
-}
+  ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
+  ierr = KSPSetComputeRHS(ksp,ComputeRHS_MOAB,&user);CHKERRQ(ierr);
+  ierr = KSPSetComputeOperators(ksp,ComputeMatrix_MOAB,&user);CHKERRQ(ierr);
+  ierr = KSPSetDM(ksp,dm);CHKERRQ(ierr);
 
-/*
-   cHeV is "trick" to allow easy accessing of the values in the HeV portion of the Concentrations.
-   cHeV[i] points to the beginning of each row of HeV[] with V indexing starting a 1.
+  ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
 
-*/
-#undef __FUNCT__
-#define __FUNCT__ "cHeVCreate"
-PetscErrorCode cHeVCreate(PetscReal ***cHeV)
-{
-  PetscErrorCode ierr;
+  /* Perform the actual solve */
+  ierr = KSPSolve(ksp,NULL,NULL);CHKERRQ(ierr);
+  ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
+  ierr = KSPGetRhs(ksp,&b);CHKERRQ(ierr);
 
-  PetscFunctionBegin;
-  ierr = PetscMalloc(MHeV*sizeof(PetscScalar),cHeV);CHKERRQ(ierr);
-  (*cHeV)--;
-  PetscFunctionReturn(0);
-}
+  ierr = DMMoabSetGlobalFieldVector(dm, x);CHKERRQ(ierr);
+  ierr = DMMoabOutput(dm, "ex2.h5m", "");CHKERRQ(ierr);
 
-#undef __FUNCT__
-#define __FUNCT__ "cHeVInitialize"
-PetscErrorCode cHeVInitialize(const PetscScalar *start,PetscReal **cHeV)
-{
-  PetscInt       i;
-
-  PetscFunctionBegin;
-  cHeV[1] = ((PetscScalar*) start) - 1 + NHe + NV + NI;
-  for (i=1; i<MHeV; i++) {
-    cHeV[i+1] = cHeV[i] + NHeV[i];
-  }
-  PetscFunctionReturn(0);
+  /* Cleanup objects */
+  ierr = DMDestroy(&dm);CHKERRQ(ierr);
+  ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
+  ierr = PetscFinalize();
+  return 0;
 }
 
-#undef __FUNCT__
-#define __FUNCT__ "cHeVDestroy"
-PetscErrorCode cHeVDestroy(PetscReal **cHeV)
-{
-  PetscErrorCode ierr;
-
-  PetscFunctionBegin;
-  cHeV++;
-  ierr = PetscFree(cHeV);CHKERRQ(ierr);
-  PetscFunctionReturn(0);
-}
 
-/* ------------------------------------------------------------------- */
 #undef __FUNCT__
-#define __FUNCT__ "InitializeVariableSystem"
-PetscErrorCode InitializeVariableSystem(DM dm)
+#define __FUNCT__ "ComputeRho_MOAB"
+PetscErrorCode ComputeRho_MOAB(PetscReal coords[3], PetscReal centerRho, PetscReal *rho)
 {
-  PetscErrorCode ierr;
-  PetscInt       I,He,V,cnt = 0;
-  char           field[PETSC_MAX_PATH_LEN];
-
   PetscFunctionBeginUser;
-  ierr = DMMoabSetFieldNames(dm, DOF, NULL);CHKERRQ(ierr);
-  ierr = DMMoabSetBlockSize(dm, DOF);CHKERRQ(ierr);
-
-  /* Name each of the concentrations */
-  for (He=1; He<NHe+1; He++) {
-    ierr = PetscSNPrintf(field,PETSC_MAX_PATH_LEN,"%d-He",He);CHKERRQ(ierr);
-    ierr = DMMoabSetFieldName(dm,cnt++,field);CHKERRQ(ierr);
-  }
-  for (V=1; V<NV+1; V++) {
-    ierr = PetscSNPrintf(field,PETSC_MAX_PATH_LEN,"%d-V",V);CHKERRQ(ierr);
-    ierr = DMMoabSetFieldName(dm,cnt++,field);CHKERRQ(ierr);
-  }
-  for (I=1; I<NI+1; I++) {
-    ierr = PetscSNPrintf(field,PETSC_MAX_PATH_LEN,"%d-I",I);CHKERRQ(ierr);
-    ierr = DMMoabSetFieldName(dm,cnt++,field);CHKERRQ(ierr);
-  }
-
-  for (He=1; He<MHeV+1; He++) {
-    for (V=1; V<NHeV[He]+1; V++) {
-      ierr = PetscSNPrintf(field,PETSC_MAX_PATH_LEN,"%d-He-%d-V",He,V);CHKERRQ(ierr);
-      ierr = DMMoabSetFieldName(dm,cnt++,field);CHKERRQ(ierr);
-    }
+  if ((coords[0] > 1.0/3.0) && (coords[0] < 2.0/3.0) && (coords[1] > 1.0/3.0) && (coords[1] < 2.0/3.0)) {
+    *rho = centerRho;
+  } else {
+    *rho = 1.0;
   }
   PetscFunctionReturn(0);
 }
 
-/* ------------------------------------------------------------------- */
-#undef __FUNCT__
-#define __FUNCT__ "InitialConditions"
-PetscErrorCode InitialConditions(DM dm,Vec C)
-{
-  PetscErrorCode    ierr;
-  PetscInt          i,I,He,V;
-  Concentrations    *c;
-  PetscReal         **cHeV;
-  const moab::Range *vowned;
-
-  PetscFunctionBeginUser;
-  /*
-     Get pointer to vector data
-  */
-  ierr = DMMoabVecGetArray(dm,C,&c);CHKERRQ(ierr);
-  /* Shift the c pointer to allow accessing with index of 1, instead of 0 */
-  c = (Concentrations*)(((PetscScalar*)c)-1);
-
-  /*
-     Get local grid vertices
-  */
-  ierr = DMMoabGetLocalVertices(dm, &vowned, NULL);CHKERRQ(ierr);
-
-  /*
-     Compute function over the locally owned part of the grid
-  */
-  ierr = cHeVCreate(&cHeV);CHKERRQ(ierr);
-  for(moab::Range::iterator iter = vowned->begin(); iter != vowned->end(); iter++) {
-    const moab::EntityHandle vhandle = *iter;
-    ierr = DMMoabGetDofsBlockedLocal(dm, 1, &vhandle, &i);CHKERRQ(ierr);
-
-    for (He=1; He<NHe+1; He++) c[i].He[He] = 0.0;
-    for (V=1;  V<NV+1;   V++)  c[i].V[V]   = 1.0;
-    for (I=1; I <NI+1;   I++)  c[i].I[I]   = 1.0;
-    ierr = cHeVInitialize(&c[i].He[1],cHeV);CHKERRQ(ierr);
-    for (V=1; V<MHeV+1; V++) {
-      for (He=1; He<NHeV[V]+1; He++)  cHeV[V][He] = 0.0;
-    }
-  }
-  ierr = cHeVDestroy(cHeV);CHKERRQ(ierr);
-
-  /*
-     Restore vectors
-  */
-  c    = (Concentrations*)(((PetscScalar*)c)+1);
-  ierr = DMMoabVecRestoreArray(dm,C,&c);CHKERRQ(ierr);
-  PetscFunctionReturn(0);
-}
 
-/* ------------------------------------------------------------------- */
 #undef __FUNCT__
-#define __FUNCT__ "RHSFunction"
-/*
-   RHSFunction - Evaluates nonlinear function that defines the ODE
-
-   Input Parameters:
-.  ts - the TS context
-.  U - input vector
-.  ptr - optional user-defined context
-
-   Output Parameter:
-.  F - function values
- */
-PetscErrorCode RHSFunction(TS ts,PetscReal ftime,Vec C,Vec F,void *ptr)
+#define __FUNCT__ "ComputeRHS_MOAB"
+PetscErrorCode ComputeRHS_MOAB(KSP ksp,Vec b,void *ptr)
 {
-  AppCtx            *ctx = (AppCtx*) ptr;
+  UserContext*      user = (UserContext*)ptr;
   DM                dm;
+  PetscInt          dof_indices[VPERE];
+  PetscBool         dbdry[VPERE];
+  PetscScalar       vpos[VPERE*3],quadrature[NQPTS*3],jxw[NQPTS];
+  PetscInt          i,q,num_conn;
+  const moab::EntityHandle *connect;
+  const moab::Range *elocal;
+  moab::Interface*  mbImpl;
+  PetscScalar       phi[VPERE*NQPTS],localv[VPERE];
+  PetscBool         elem_on_boundary;
   PetscErrorCode    ierr;
-  PetscInt          xi,Mx,He,he,V,v,I,i;
-  PetscReal         hx,sx,x,vpos[3],**cHeV,**fHeV;
-  Concentrations    *c,*f;
-  Vec               localC;
-  const moab::Range *vowned,*elocal;
 
-  PetscFunctionBeginUser;
-  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
-  ierr = DMGetLocalVector(dm,&localC);CHKERRQ(ierr);
-  ierr = DMMoabGetSize(dm,&Mx,PETSC_IGNORE);CHKERRQ(ierr);
-  hx   = 8.0/(PetscReal)(Mx); sx = 1.0/(hx*hx);
-  ierr = cHeVCreate(&cHeV);CHKERRQ(ierr);
-  ierr = cHeVCreate(&fHeV);CHKERRQ(ierr);
-
-  /*
-     Scatter ghost points to local vector,using the 2-step process
-        DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
-     By placing code between these two statements, computations can be
-     done while messages are in transition.
-  */
-  ierr = DMGlobalToLocalBegin(dm,C,INSERT_VALUES,localC);CHKERRQ(ierr);
-  ierr = DMGlobalToLocalEnd(dm,C,INSERT_VALUES,localC);CHKERRQ(ierr);
-
-  ierr = VecSet(F,0.0);CHKERRQ(ierr);
-
-  /*
-    Get pointers to vector data
-  */
-  ierr = DMMoabVecGetArrayRead(dm,localC,&c);CHKERRQ(ierr);
-  /* Shift the c pointer to allow accessing with index of 1, instead of 0 */
-  c    = (Concentrations*)(((PetscScalar*)c)-1);
-  ierr = DMMoabVecGetArray(dm,F,&f);CHKERRQ(ierr);
-  f    = (Concentrations*)(((PetscScalar*)f)-1);
-
-  /*
-     Get local grid boundaries
-  */
-  ierr = DMMoabGetLocalVertices(dm, &vowned, NULL);CHKERRQ(ierr);
-  ierr = DMMoabGetLocalElements(dm, &elocal);CHKERRQ(ierr);
+  PetscFunctionBegin;
+  ierr = KSPGetDM(ksp,&dm);CHKERRQ(ierr);
 
-  /*
-     Loop over grid points computing ODE terms for each grid point
-  */
-  for(moab::Range::iterator iter = vowned->begin(); iter != vowned->end(); iter++) {
-    const moab::EntityHandle vhandle = *iter;
-    ierr = DMMoabGetDofsBlockedLocal(dm, 1, &vhandle, &xi);CHKERRQ(ierr);
-
-    ierr = DMMoabGetVertexCoordinates(dm,1,&vhandle,vpos);CHKERRQ(ierr);
-    x = vpos[0];
-
-    /* -------------------------------------------------------------
-     ---- Compute diffusion over the locally owned part of the grid
-    */
-    /* He clusters larger than 5 do not diffuse -- are immobile */
-    for (He=1; He<PetscMin(NHe+1,6); He++) {
-      f[xi].He[He] +=  ctx->HeDiffusion[He]*(-2.0*c[xi].He[He] + c[xi-1].He[He] + c[xi+1].He[He])*sx;
-    }
+  /* reset the RHS */
+  ierr = VecSet(b, 0.0);CHKERRQ(ierr);
 
-    /* V and I clusters ONLY of size 1 diffuse */
-    f[xi].V[1] +=  ctx->VDiffusion[1]*(-2.0*c[xi].V[1] + c[xi-1].V[1] + c[xi+1].V[1])*sx;
-    f[xi].I[1] +=  ctx->IDiffusion[1]*(-2.0*c[xi].I[1] + c[xi-1].I[1] + c[xi+1].I[1])*sx;
-
-    /* Mixed He - V clusters are immobile  */
-
-    /* ----------------------------------------------------------------
-     ---- Compute forcing that produces He of cluster size 1
-          Crude cubic approximation of graph from Tibo's notes
-    */
-    f[xi].He[1] +=  ctx->forcingScale*PetscMax(0.0,0.0006*x*x*x  - 0.0087*x*x + 0.0300*x);
-
-    ierr = cHeVInitialize(&c[xi].He[1],cHeV);CHKERRQ(ierr);
-    ierr = cHeVInitialize(&f[xi].He[1],fHeV);CHKERRQ(ierr);
-
-    /* -------------------------------------------------------------------------
-     ---- Compute dissociation terms that removes an item from a cluster
-          I assume dissociation means losing only a single item from a cluster
-          I cannot tell from the notes if clusters can break up into any sub-size.
-    */
-    /*   He[He] ->  He[He-1] + He[1] */
-    for (He=2; He<NHe+1; He++) {
-      f[xi].He[He-1] += ctx->dissociationScale*c[xi].He[He];
-      f[xi].He[1]    += ctx->dissociationScale*c[xi].He[He];
-      f[xi].He[He]   -= ctx->dissociationScale*c[xi].He[He];
-    }
+  /* get the essential MOAB mesh related quantities needed for FEM assembly */
+  ierr = DMMoabGetInterface(dm, &mbImpl);CHKERRQ(ierr);
+  ierr = DMMoabGetLocalElements(dm, &elocal);CHKERRQ(ierr);
 
-    /*   V[V] ->  V[V-1] + V[1] */
-    for (V=2; V<NV+1; V++) {
-      f[xi].V[V-1] += ctx->dissociationScale*c[xi].V[V];
-      f[xi].V[1]   += ctx->dissociationScale*c[xi].V[V];
-      f[xi].V[V]   -= ctx->dissociationScale*c[xi].V[V];
-    }
+  /* loop over local elements */
+  for(moab::Range::iterator iter = elocal->begin(); iter != elocal->end(); iter++) {
+    const moab::EntityHandle ehandle = *iter;
 
-    /*   I[I] ->  I[I-1] + I[1] */
-    for (I=2; I<NI+1; I++) {
-      f[xi].I[I-1] += ctx->dissociationScale*c[xi].I[I];
-      f[xi].I[1]   += ctx->dissociationScale*c[xi].I[I];
-      f[xi].I[I]   -= ctx->dissociationScale*c[xi].I[I];
-    }
+    ierr = PetscMemzero(localv,sizeof(PetscScalar)*VPERE);CHKERRQ(ierr);
 
-    /*   He[He]-V[1] ->  He[He] + V[1]  */
-    for (He=1; He<NHeV[1]+1; He++) {
-      f[xi].He[He] += 1000*ctx->dissociationScale*cHeV[1][He];
-      f[xi].V[1]   += 1000*ctx->dissociationScale*cHeV[1][He];
-      fHeV[1][He]  -= 1000*ctx->dissociationScale*cHeV[1][He];
-    }
+    // Get connectivity information:
+    ierr = DMMoabGetElementConnectivity(dm, ehandle, &num_conn, &connect);CHKERRQ(ierr);
+    if (num_conn != VPERE) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_WRONG, "Only QUAD4 element bases are supported in the current example. n(Connectivity)=%D.\n", num_conn);
 
-    /*   He[1]-V[V] ->  He[1] + V[V]  */
-    for (V=2; V<MHeV+1; V++) {
-      f[xi].He[1]  += 1000*ctx->dissociationScale*cHeV[V][1];
-      f[xi].V[V]   += 1000*ctx->dissociationScale*cHeV[V][1];
-      fHeV[V][1]   -= 1000*ctx->dissociationScale*cHeV[V][1];
-    }
+    /* compute the mid-point of the element and use a 1-point lumped quadrature */
+    ierr = DMMoabGetVertexCoordinates(dm,num_conn,connect,vpos);CHKERRQ(ierr);
 
-    /*   He[He]-V[V] ->  He[He-1]-V[V] + He[1]  */
-    for (V=2; V<MHeV+1; V++) {
-      for (He=2; He<NHeV[V]+1; He++) {
-        f[xi].He[1]   += 1000*ctx->dissociationScale*cHeV[V][He];
-        fHeV[V][He-1] += 1000*ctx->dissociationScale*cHeV[V][He];
-        fHeV[V][He]   -= 1000*ctx->dissociationScale*cHeV[V][He];
-      }
-    }
+    /* get the global DOF number to appropriately set the element contribution in the RHS vector */
+#ifdef LOCAL_ASSEMBLY
+    ierr = DMMoabGetFieldDofsLocal(dm, num_conn, connect, 0, dof_indices);CHKERRQ(ierr);
+#else
+    ierr = DMMoabGetFieldDofs(dm, num_conn, connect, 0, dof_indices);CHKERRQ(ierr);    
+#endif
 
-    /*   He[He]-V[V] ->  He[He]-V[V-1] + V[1]  */
-    for (V=2; V<MHeV+1; V++) {
-      for (He=2; He<NHeV[V-1]+1; He++) {
-        f[xi].V[1]    += 1000*ctx->dissociationScale*cHeV[V][He];
-        fHeV[V-1][He] += 1000*ctx->dissociationScale*cHeV[V][He];
-        fHeV[V][He]   -= 1000*ctx->dissociationScale*cHeV[V][He];
-      }
-    }
+    /* compute the quadrature points transformed to the physical space */
+    ierr = ComputeQuadraturePointsPhysical(vpos, quadrature, jxw);CHKERRQ(ierr);
 
-    /*   He[He]-V[V] ->  He[He]-V[V+1] + I[1]  */
-    for (V=1; V<MHeV; V++) {
-      for (He=1; He<NHeV[V]+1; He++) {
-        fHeV[V+1][He] += 1000*ctx->dissociationScale*cHeV[V][He];
-        f[xi].I[1]    += 1000*ctx->dissociationScale*cHeV[V][He];
-        fHeV[V][He]   -= 1000*ctx->dissociationScale*cHeV[V][He];
-      }
-    }
+    /* compute the basis functions and the derivatives wrt x and y directions */
+    ierr = Compute_Quad4_Basis(vpos, NQPTS, quadrature, phi,  0, 0);CHKERRQ(ierr);
 
-    /* ----------------------------------------------------------------
-     ---- Compute reaction terms that can create a cluster of given size
-    */
-    /*   He[He] + He[he] -> He[He+he]  */
-    for (He=2; He<NHe+1; He++) {
-      /* compute all pairs of clusters of smaller size that can combine to create a cluster of size He,
-         remove the upper half since they are symmetric to the lower half of the pairs. For example
-              when He = 5 (cluster size 5) the pairs are
-                 1   4
-                 2   2
-                 3   2  these last two are not needed in the sum since they repeat from above
-                 4   1  this is why he < (He/2) + 1            */
-      for (he=1; he<(He/2)+1; he++) {
-        f[xi].He[He] += ctx->reactionScale*c[xi].He[he]*c[xi].He[He-he];
-
-        /* remove the two clusters that merged to form the larger cluster */
-        f[xi].He[he]    -= ctx->reactionScale*c[xi].He[he]*c[xi].He[He-he];
-        f[xi].He[He-he] -= ctx->reactionScale*c[xi].He[he]*c[xi].He[He-he];
+    /* Compute function over the locally owned part of the grid */
+    for (q=0; q<NQPTS; ++q) {
+      const PetscScalar xx=(quadrature[3*q]-user->xref)*(quadrature[3*q]-user->xref);
+      const PetscScalar yy=(quadrature[3*q+1]-user->yref)*(quadrature[3*q+1]-user->yref);
+      for (i=0; i < VPERE; ++i) {
+        localv[i] += jxw[q] * phi[q*VPERE+i] * PetscExpScalar(-(xx+yy)/user->nu);
       }
     }
 
-    /*   V[V]  +  V[v] ->  V[V+v]  */
-    for (V=2; V<NV+1; V++) {
-      for (v=1; v<(V/2)+1; v++) {
-        f[xi].V[V]   += ctx->reactionScale*c[xi].V[v]*c[xi].V[V-v];
-        f[xi].V[v]   -= ctx->reactionScale*c[xi].V[v]*c[xi].V[V-v];
-        f[xi].V[V-v] -= ctx->reactionScale*c[xi].V[v]*c[xi].V[V-v];
-      }
-    }
+    /* check if element is on the boundary */
+    ierr = DMMoabIsEntityOnBoundary(dm,ehandle,&elem_on_boundary);CHKERRQ(ierr);
 
-    /*   I[I] +  I[i] -> I[I+i] */
-    for (I=2; I<NI+1; I++) {
-      for (i=1; i<(I/2)+1; i++) {
-        f[xi].I[I]   += ctx->reactionScale*c[xi].I[i]*c[xi].I[I-i];
-        f[xi].I[i]   -= ctx->reactionScale*c[xi].I[i]*c[xi].I[I-i];
-        f[xi].I[I-i] -= ctx->reactionScale*c[xi].I[i]*c[xi].I[I-i];
-      }
-    }
+    /* apply dirichlet boundary conditions */
+    if (elem_on_boundary && user->bcType == DIRICHLET) {
 
-    /* He[1] +  V[1]  ->  He[1]-V[1] */
-    fHeV[1][1]  += 1000*ctx->reactionScale*c[xi].He[1]*c[xi].V[1];
-    f[xi].He[1] -= 1000*ctx->reactionScale*c[xi].He[1]*c[xi].V[1];
-    f[xi].V[1]  -= 1000*ctx->reactionScale*c[xi].He[1]*c[xi].V[1];
-
-    /*  He[He]-V[V] + He[he] -> He[He+he]-V[V]  */
-    for (V=1; V<MHeV+1; V++) {
-      for (He=1; He<NHeV[V]; He++) {
-        for (he=1; he+He<NHeV[V]+1; he++) {
-          fHeV[V][He+he] += ctx->reactionScale*cHeV[V][He]*c[xi].He[he];
-          f[xi].He[he]   -= ctx->reactionScale*cHeV[V][He]*c[xi].He[he];
-          fHeV[V][He]    -= ctx->reactionScale*cHeV[V][He]*c[xi].He[he];
-        }
-      }
-    }
+      /* get the list of nodes on boundary so that we can enforce dirichlet conditions strongly */
+      ierr = DMMoabCheckBoundaryVertices(dm,num_conn,connect,dbdry);CHKERRQ(ierr);
 
-    /*  He[He]-V[V] + V[1] -> He[He][V+1] */
-    for (V=1; V<MHeV; V++) {
-      for (He=1; He<NHeV[V+1]; He++) {
-          fHeV[V+1][He] += ctx->reactionScale*cHeV[V][He]*c[xi].V[1];
-          /* remove the two clusters that merged to form the larger cluster */
-          f[xi].V[1]  -= ctx->reactionScale*cHeV[V][He]*c[xi].V[1];
-          fHeV[V][He] -= ctx->reactionScale*cHeV[V][He]*c[xi].V[1];
+      for (i=0; i < VPERE; ++i) {
+        if (dbdry[i]) {  /* dirichlet node */
+          /* think about strongly imposing dirichlet */
+          const PetscScalar xx=(vpos[3*i]-user->xref)*(vpos[3*i]-user->xref);
+          const PetscScalar yy=(vpos[3*i+1]-user->yref)*(vpos[3*i+1]-user->yref);
+          localv[i] = PetscExpScalar(-(xx+yy)/user->nu);
+        }
       }
     }
 
-    /*  He[He]-V[V]  + He[he]-V[v] -> He[He+he][V+v]  */
-    /*  Currently the reaction rates for this are zero */
+#ifdef LOCAL_ASSEMBLY
+    /* set the values directly into appropriate locations. Can alternately use VecSetValues */
+    ierr = VecSetValuesLocal(b, VPERE, dof_indices, localv, ADD_VALUES);CHKERRQ(ierr);
+#else
+    ierr = VecSetValues(b, VPERE, dof_indices, localv, ADD_VALUES);CHKERRQ(ierr);
+#endif
+  }
 
+  /* force right hand side to be consistent for singular matrix */
+  /* note this is really a hack, normally the model would provide you with a consistent right handside */
+  if (user->bcType == NEUMANN) {
+    MatNullSpace nullspace;
 
-    /*  V[V] + I[I]  ->   V[V-I] if V > I else I[I-V] */
-    for (V=1; V<NV+1; V++) {
-      for (I=1; I<PetscMin(V,NI); I++) {
-        f[xi].V[V-I] += ctx->reactionScale*c[xi].V[V]*c[xi].I[I];
-        f[xi].V[V]   -= ctx->reactionScale*c[xi].V[V]*c[xi].I[I];
-        f[xi].I[I]   -= ctx->reactionScale*c[xi].V[V]*c[xi].I[I];
-      }
-      for (I=V+1; I<NI+1; I++) {
-          f[xi].I[I-V] += ctx->reactionScale*c[xi].V[V]*c[xi].I[I];
-          f[xi].V[V]   -= ctx->reactionScale*c[xi].V[V]*c[xi].I[I];
-          f[xi].I[I]   -= ctx->reactionScale*c[xi].V[V]*c[xi].I[I];
-      }
-    }
+    ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr);
+    ierr = MatNullSpaceRemove(nullspace,b);CHKERRQ(ierr);
+    ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr);
   }
 
-  /*
-     Restore vectors
-  */
-  c    = (Concentrations*)(((PetscScalar*)c)+1);
-  ierr = DMMoabVecRestoreArrayRead(dm,localC,&c);CHKERRQ(ierr);
-  f    = (Concentrations*)(((PetscScalar*)f)+1);
-  ierr = DMMoabVecRestoreArray(dm,F,&f);CHKERRQ(ierr);
-  ierr = DMRestoreLocalVector(dm,&localC);CHKERRQ(ierr);
-  ierr = cHeVDestroy(cHeV);CHKERRQ(ierr);
-  ierr = cHeVDestroy(fHeV);CHKERRQ(ierr);
-//  VecView(F,0);
-//  std::cin.get();
+  /* Restore vectors */
+  ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
+  ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
   PetscFunctionReturn(0);
 }
-/* ------------------------------------------------------------------- */
 
-#define BARRY_IMPL
 
 #undef __FUNCT__
-#define __FUNCT__ "RHSJacobian"
-/*
-    Compute the Jacobian entries based on IFuction() and insert them into the matrix
-*/
-PetscErrorCode RHSJacobian(TS ts,PetscReal ftime,Vec C,Mat A,Mat J,void *ptr)
+#define __FUNCT__ "ComputeMatrix_MOAB"
+PetscErrorCode ComputeMatrix_MOAB(KSP ksp,Mat J,Mat jac,void *ctx)
 {
-  AppCtx               *ctx = (AppCtx*) ptr;
-  DM                   dm;
-  PetscErrorCode       ierr;
-  PetscInt             xi,Mx,/*xs,xm,*/He,he,V,v,I,i;
-  PetscInt             row[3],col[3],dof_indices[2*DOF],lcols[2],rcols[2],left,right;
-  PetscReal            hx,sx,x,val[6],vpos[3],lvals[2],rvals[2];
-  const Concentrations *c,*f;
-  Vec                  localC;
+  UserContext       *user = (UserContext*)ctx;
+  DM                dm;
+  PetscInt          i,j,q,num_conn;
+  PetscInt          dof_indices[VPERE];
+  PetscScalar       vpos[VPERE*3],quadrature[NQPTS*3],jxw[NQPTS];
+  PetscBool         dbdry[VPERE];
   const moab::EntityHandle *connect;
-  PetscInt             vpere=2;
-  const moab::Range    *elocal;
-  const PetscReal      *rowstart,*colstart;
-  const PetscReal      **cHeV,**fHeV;
-  static PetscBool     initialized = PETSC_FALSE;
-
+  const moab::Range *elocal;
+  moab::Interface*  mbImpl;
+  PetscBool         elem_on_boundary;
+  PetscScalar       array[VPERE*VPERE];
+  PetscScalar       phi[VPERE*NQPTS], dphidx[VPERE*NQPTS], dphidy[VPERE*NQPTS];
+  PetscReal         rho;
+  PetscErrorCode    ierr;
+ 
   PetscFunctionBeginUser;
-  ierr = cHeVCreate((PetscScalar***)&cHeV);CHKERRQ(ierr);
-  ierr = cHeVCreate((PetscScalar***)&fHeV);CHKERRQ(ierr);
-  ierr = MatZeroEntries(J);CHKERRQ(ierr);
-  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
-  ierr = DMGetLocalVector(dm,&localC);CHKERRQ(ierr);
-  ierr = DMMoabGetSize(dm,&Mx,PETSC_IGNORE);CHKERRQ(ierr);
-  hx   = 8.0/(PetscReal)(Mx); sx = 1.0/(hx*hx);
-
-  /*
-     Scatter ghost points to local vector,using the 2-step process
-        DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
-     By placing code between these two statements, computations can be
-     done while messages are in transition.
-  */
-  ierr = DMGlobalToLocalBegin(dm,C,INSERT_VALUES,localC);CHKERRQ(ierr);
-  ierr = DMGlobalToLocalEnd(dm,C,INSERT_VALUES,localC);CHKERRQ(ierr);
-
-  /*
-    Get pointers to vector data
-
-    The f[] is dummy, values are never set into it. It is only used to determine the 
-    local row for the entries in the Jacobian
-  */
-  ierr = DMMoabVecGetArrayRead(dm,localC,&c);CHKERRQ(ierr);
-  /* Shift the c pointer to allow accessing with index of 1, instead of 0 */
-  c    = (Concentrations*)(((PetscScalar*)c)-1);
-  ierr = DMMoabVecGetArray(dm,C,&f);CHKERRQ(ierr);
-  f    = (Concentrations*)(((PetscScalar*)f)-1);
-
-  /*
-     Get local grid boundaries
-  */
+  ierr      = KSPGetDM(ksp,&dm);CHKERRQ(ierr);
+
+  /* get the essential MOAB mesh related quantities needed for FEM assembly */  
+  ierr = DMMoabGetInterface(dm, &mbImpl);CHKERRQ(ierr);
   ierr = DMMoabGetLocalElements(dm, &elocal);CHKERRQ(ierr);
-//  ierr = DMMoabGetLocalVertices(dm, &vowned, NULL);CHKERRQ(ierr);
-//  ierr = DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
-//  rowstart = &f[xs].He[1] -  N*N - 3*N;
-//  colstart = &c[xs-1].He[1];
-
-#ifdef BARRY_IMPL
-  rowstart = &f[1].He[1] - DOF;
-  colstart = &c[0].He[1];
-#else
-  rowstart = &f[-1].He[1] - DOF*0;
-  colstart = &c[-1].He[1];
-#endif
 
-  if (!initialized) {
-    /* Compute ODE terms over the locally owned part of the grid 
-      Assemble the operator by looping over edges and computing
-      contribution for each vertex dof                         */
-    for(moab::Range::iterator iter = elocal->begin(); iter != elocal->end(); iter++) {
-      const moab::EntityHandle ehandle = *iter;
-
-      // Get connectivity information in canonical order
-      ierr = DMMoabGetElementConnectivity(dm, ehandle, &vpere, &connect);CHKERRQ(ierr);
-      if (vpere != 2) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_WRONG, "Only EDGE2 element bases are supported in the current example. n(Connectivity)=%D.\n", vpere);
-
-      ierr = DMMoabGetDofsBlockedLocal(dm, 1, &connect[0], &xi);CHKERRQ(ierr);
-      ierr = DMMoabGetDofsBlockedLocal(dm, vpere, connect, dof_indices);CHKERRQ(ierr);
-//      ierr = DMMoabGetDofsLocal(dm, vpere, connect, dof_indices);CHKERRQ(ierr);
-
-//      const PetscInt lcols[] = {idl,idr}, rcols[] = {idr, idl};
-
-//      const PetscInt lcols[] = {idl,idr}, rcols[] = {idr, idl};
-//      ierr = MatSetValuesLocal(*Jpre,1,&idr,2,rcols,&e_vals[0][0][0],ADD_VALUES);CHKERRQ(ierr);
-//      ierr = MatSetValuesLocal(*Jpre,1,&idl,2,lcols,&e_vals[0][0][0],ADD_VALUES);CHKERRQ(ierr);
-
-      const int& idl = dof_indices[0]-1;
-      const int& idr = dof_indices[1]-1;
-      PetscPrintf(PETSC_COMM_WORLD,"\t [%D, %D] dof_indices [%D %D]\n", idl,idr,dof_indices[0],dof_indices[1]);
-
-      ierr = cHeVInitialize(&c[xi].He[1],(PetscScalar**)cHeV);CHKERRQ(ierr);
-      ierr = cHeVInitialize(&f[xi].He[1],(PetscScalar**)fHeV);CHKERRQ(ierr);
-
-      /* -------------------------------------------------------------
-         ---- Compute diffusion over the locally owned part of the grid
-       */
-      /* He clusters larger than 5 do not diffuse -- are immobile */
-      for (He=1; He<PetscMin(NHe+1,6); He++) {
-#ifdef BARRY_IMPL
-        row[0] = &f[xi].He[He] - rowstart;
-        col[0] = &c[xi-1].He[He] - colstart;
-        col[1] = &c[xi].He[He] - colstart;
-        col[2] = &c[xi+1].He[He] - colstart;
-        val[0] = ctx->HeDiffusion[He]*sx;
-        val[1] = -2.0*ctx->HeDiffusion[He]*sx;
-        val[2] = ctx->HeDiffusion[He]*sx;
-        PetscPrintf(PETSC_COMM_WORLD,"[1] Setting row %D: Col = [%D, %D, %D]\n", row[0],col[0],col[1],col[2]);
-        ierr = MatSetValuesLocal(J,1,row,3,col,val,ADD_VALUES);CHKERRQ(ierr);
-#else
-        left = &f[idl].He[He] - rowstart; right = &f[idr].He[He] - rowstart;
-        lcols[0] = &c[idl].He[He] - colstart; lcols[1] = &c[idr].He[He] - colstart;
-        rcols[0] = lcols[1]; rcols[1] = lcols[0];
-        lvals[0] = ctx->HeDiffusion[He]*sx; lvals[1] = -ctx->HeDiffusion[He]*sx;
-        rvals[0] = lvals[1]; rvals[1] = lvals[0];
-        PetscPrintf(PETSC_COMM_WORLD,"\t [1] row [%D %D]: Left Cols = [%D, %D]  Right Cols = [%D, %D]\n", left,right,lcols[0],lcols[1],rcols[0],rcols[1]);
-        ierr = MatSetValuesLocal(J,1,&left,2,lcols,lvals,ADD_VALUES);CHKERRQ(ierr);
-        ierr = MatSetValuesLocal(J,1,&right,2,rcols,rvals,ADD_VALUES);CHKERRQ(ierr);
-#endif
-      }
+  /* loop over local elements */
+  for(moab::Range::iterator iter = elocal->begin(); iter != elocal->end(); iter++) {
+    const moab::EntityHandle ehandle = *iter;
 
-      /* V and I clusters ONLY of size 1 diffuse */
-#ifdef BARRY_IMPL
-      row[0] = &f[xi].V[1] - rowstart;
-      col[0] = &c[xi-1].V[1] - colstart;
-      col[1] = &c[xi].V[1] - colstart;
-      col[2] = &c[xi+1].V[1] - colstart;
-      val[0] = ctx->VDiffusion[1]*sx;
-      val[1] = -2.0*ctx->VDiffusion[1]*sx;
-      val[2] = ctx->VDiffusion[1]*sx;
-      PetscPrintf(PETSC_COMM_WORLD,"[2] Setting row %D: Col = [%D, %D, %D]\n", row[0],col[0],col[1],col[2]);
-      ierr = MatSetValuesLocal(J,1,row,3,col,val,ADD_VALUES);CHKERRQ(ierr);
-#else
-      left = &f[idl].V[1] - rowstart; right = &f[idr].V[1] - rowstart;
-      lcols[0] = &c[idl].V[1] - colstart; lcols[1] = &c[idr].V[1] - colstart;
-      rcols[0] = lcols[1]; rcols[1] = lcols[0];
-      lvals[0] = ctx->VDiffusion[1]*sx; lvals[1] = -ctx->VDiffusion[1]*sx;
-      rvals[0] = lvals[1]; rvals[1] = lvals[0];
-      PetscPrintf(PETSC_COMM_WORLD,"\t [2] row [%D %D]: Left Cols = [%D, %D]  Right Cols = [%D, %D]\n", left,right,lcols[0],lcols[1],rcols[0],rcols[1]);
-      ierr = MatSetValuesLocal(J,1,&left,2,lcols,lvals,ADD_VALUES);CHKERRQ(ierr);
-      //ierr = MatSetValuesLocal(*J,1,&right,2,rcols,rvals,ADD_VALUES);CHKERRQ(ierr);
-#endif
+    // Get connectivity information:
+    ierr = DMMoabGetElementConnectivity(dm, ehandle, &num_conn, &connect);CHKERRQ(ierr);
+    if (num_conn != VPERE) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_WRONG, "Only QUAD4 element bases are supported in the current example. Connectivity=%D.\n", num_conn);
+
+    /* compute the mid-point of the element and use a 1-point lumped quadrature */
+    ierr = DMMoabGetVertexCoordinates(dm,num_conn,connect,vpos);CHKERRQ(ierr);
 
-#ifdef BARRY_IMPL
-      row[0] = &f[xi].I[1] - rowstart;
-      col[0] = &c[xi-1].I[1] - colstart;
-      col[1] = &c[xi].I[1] - colstart;
-      col[2] = &c[xi+1].I[1] - colstart;
-      val[0] = ctx->IDiffusion[1]*sx;
-      val[1] = -2.0*ctx->IDiffusion[1]*sx;
-      val[2] = ctx->IDiffusion[1]*sx;
-      PetscPrintf(PETSC_COMM_WORLD,"[3] Setting row %D: Col = [%D, %D, %D]\n", row[0],col[0],col[1],col[2]);
-      ierr = MatSetValuesLocal(J,1,row,3,col,val,ADD_VALUES);CHKERRQ(ierr);
+    /* get the global DOF number to appropriately set the element contribution in the RHS vector */
+#ifdef LOCAL_ASSEMBLY
+    ierr = DMMoabGetFieldDofsLocal(dm, num_conn, connect, 0, dof_indices);CHKERRQ(ierr);
 #else
-      left = &f[idl].I[1] - rowstart; right = &f[idr].I[1] - rowstart;
-      lcols[0] = &c[idl].I[1] - colstart; lcols[1] = &c[idr].I[1] - colstart;
-      rcols[0] = lcols[1]; rcols[1] = lcols[0];
-      lvals[0] = ctx->IDiffusion[1]*sx; lvals[1] = -ctx->IDiffusion[1]*sx;
-      rvals[0] = lvals[1]; rvals[1] = lvals[0];
-      PetscPrintf(PETSC_COMM_WORLD,"\t [3] row [%D %D]: Left Cols = [%D, %D]  Right Cols = [%D, %D]\n", left,right,lcols[0],lcols[1],rcols[0],rcols[1]);
-      ierr = MatSetValuesLocal(J,1,&left,2,lcols,lvals,ADD_VALUES);CHKERRQ(ierr);
-      //ierr = MatSetValuesLocal(J,1,&right,2,rcols,rvals,ADD_VALUES);CHKERRQ(ierr);
+    ierr = DMMoabGetFieldDofs(dm, num_conn, connect, 0, dof_indices);CHKERRQ(ierr);
 #endif
 
-      /* Mixed He - V clusters are immobile  */
-      
-      /* -------------------------------------------------------------------------
-       ---- Compute dissociation terms that removes an item from a cluster
-       I assume dissociation means losing only a single item from a cluster
-       I cannot tell from the notes if clusters can break up into any sub-size.
-       */
-      
-      /*   He[He] ->  He[He-1] + He[1] */
-      for (He=2; He<NHe+1; He++) {
-        row[0] = &f[xi].He[He-1] - rowstart;
-        row[1] = &f[xi].He[1] - rowstart;
-        row[2] = &f[xi].He[He] - rowstart;
-        col[0] = &c[xi].He[He] - colstart;
-        val[0] = ctx->dissociationScale;
-        val[1] = ctx->dissociationScale;
-        val[2] = -ctx->dissociationScale;
-        ierr = MatSetValuesLocal(J,3,row,1,col,val,ADD_VALUES);CHKERRQ(ierr);
-      }
-      
-      /*   V[V] ->  V[V-1] + V[1] */
-      for (V=2; V<NV+1; V++) {
-        row[0] = &f[xi].V[V-1] - rowstart;
-        row[1] = &f[xi].V[1] - rowstart;
-        row[2] = &f[xi].V[V] - rowstart;
-        col[0] = &c[xi].V[V] - colstart;
-        val[0] = ctx->dissociationScale;
-        val[1] = ctx->dissociationScale;
-        val[2] = -ctx->dissociationScale;
-        ierr = MatSetValuesLocal(J,3,row,1,col,val,ADD_VALUES);CHKERRQ(ierr);
-      }
-      
-      /*   I[I] ->  I[I-1] + I[1] */
-      for (I=2; I<NI+1; I++) {
-        row[0] = &f[xi].I[I-1] - rowstart;
-        row[1] = &f[xi].I[1] - rowstart;
-        row[2] = &f[xi].I[I] - rowstart;
-        col[0] = &c[xi].I[I] - colstart;
-        val[0] = ctx->dissociationScale;
-        val[1] = ctx->dissociationScale;
-        val[2] = -ctx->dissociationScale;
-        ierr = MatSetValuesLocal(J,3,row,1,col,val,ADD_VALUES);CHKERRQ(ierr);
-      }
-      
-      /*   He[He]-V[1] ->  He[He] + V[1]  */
-      for (He=1; He<NHeV[1]+1; He++) {
-        row[0] = &f[xi].He[He] - rowstart;
-        row[1] = &f[xi].V[1] - rowstart;
-        row[2] = &fHeV[1][He] - rowstart;
-        col[0] = &cHeV[1][He] - colstart;
-        val[0] = 1000*ctx->dissociationScale;
-        val[1] = 1000*ctx->dissociationScale;
-        val[2] = -1000*ctx->dissociationScale;
-        ierr = MatSetValuesLocal(J,3,row,1,col,val,ADD_VALUES);CHKERRQ(ierr);
-      }
-      
-
-      /*   He[1]-V[V] ->  He[1] + V[V]  */
-      for (V=2; V<MHeV+1; V++) {
-        row[0] = &f[xi].He[1] - rowstart;
-        row[1] = &f[xi].V[V] - rowstart;
-        row[2] = &fHeV[V][1] - rowstart;
-        col[0] = &cHeV[V][1] - colstart;
-        val[0] = 1000*ctx->dissociationScale;
-        val[1] = 1000*ctx->dissociationScale;
-        val[2] = -1000*ctx->dissociationScale;
-        ierr = MatSetValuesLocal(J,3,row,1,col,val,ADD_VALUES);CHKERRQ(ierr);
-      }
-      
-      /*   He[He]-V[V] ->  He[He-1]-V[V] + He[1]  */
-      for (V=2; V<MHeV+1; V++) {
-        for (He=2; He<NHeV[V]+1; He++) {
-          row[0] = &f[xi].He[1] - rowstart;
-          row[1] = &fHeV[V][He-1] - rowstart;
-          row[2] = &fHeV[V][He] - rowstart;
-          col[0] = &cHeV[V][He] - colstart;
-          val[0] = 1000*ctx->dissociationScale;
-          val[1] = 1000*ctx->dissociationScale;
-          val[2] = -1000*ctx->dissociationScale;
-          ierr = MatSetValuesLocal(J,3,row,1,col,val,ADD_VALUES);CHKERRQ(ierr);
-        }
-      }
-      
-      /*   He[He]-V[V] ->  He[He]-V[V-1] + V[1]  */
-      for (V=2; V<MHeV+1; V++) {
-        for (He=2; He<NHeV[V-1]+1; He++) {
-          row[0] = &f[xi].V[1] - rowstart;
-          row[1] = &fHeV[V-1][He] - rowstart;
-          row[2] = &fHeV[V][He] - rowstart;
-          col[0] = &cHeV[V][He] - colstart;
-          val[0] = 1000*ctx->dissociationScale;
-          val[1] = 1000*ctx->dissociationScale;
-          val[2] = -1000*ctx->dissociationScale;
-          ierr = MatSetValuesLocal(J,3,row,1,col,val,ADD_VALUES);CHKERRQ(ierr);
-        }
-      }
-      
-      /*   He[He]-V[V] ->  He[He]-V[V+1] + I[1]  */
-      for (V=1; V<MHeV; V++) {
-        for (He=1; He<NHeV[V]+1; He++) {
-          row[0] = &fHeV[V+1][He] - rowstart;
-          row[1] = &f[xi].I[1] - rowstart;
-          row[2] = &fHeV[V][He] - rowstart;
-          col[0] = &cHeV[V][He] - colstart;
-          val[0] = 1000*ctx->dissociationScale;
-          val[1] = 1000*ctx->dissociationScale;
-          val[2] = -1000*ctx->dissociationScale;
-          ierr = MatSetValuesLocal(J,3,row,1,col,val,ADD_VALUES);CHKERRQ(ierr);
-        }
-      }
-    }
-    ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
-    ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
-    ierr = MatSetOption(J,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);CHKERRQ(ierr);
-    ierr = MatStoreValues(J);CHKERRQ(ierr);
-    MatSetFromOptions(J);
-    initialized = PETSC_TRUE;
-  } else {
-    ierr = MatRetrieveValues(J);CHKERRQ(ierr);
-  }
+    /* compute the quadrature points transformed to the physical space */
+    ierr = ComputeQuadraturePointsPhysical(vpos, quadrature, jxw);CHKERRQ(ierr);
 
+    /* compute the basis functions and the derivatives wrt x and y directions */
+    ierr = Compute_Quad4_Basis(vpos, NQPTS, quadrature, phi,  dphidx, dphidy);CHKERRQ(ierr);
 
-  /*
-     Loop over grid points computing Jacobian terms for each grid point for reaction terms
-  */
-  for(moab::Range::iterator iter = elocal->begin(); iter != elocal->end(); iter++) {
-    const moab::EntityHandle ehandle = *iter;
+    /* compute the inhomogeneous diffusion coefficient at the first quadrature point 
+        -- for large spatial variations, embed this property evaluation inside quadrature loop */
+    ierr  = ComputeRho_MOAB(quadrature, user->rho, &rho);CHKERRQ(ierr);
 
-    // Get connectivity information in canonical order
-    ierr = DMMoabGetElementConnectivity(dm, ehandle, &vpere, &connect);CHKERRQ(ierr);
-    if (vpere != 2) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_WRONG, "Only EDGE2 element bases are supported in the current example. n(Connectivity)=%D.\n", vpere);
-
-//      ierr = DMMoabGetDofsBlockedLocal(dm, 1, &vhandle, &xi);CHKERRQ(ierr);
-    ierr = DMMoabGetDofsLocal(dm, vpere, connect, dof_indices);CHKERRQ(ierr);
-
-    ierr = cHeVInitialize(&c[xi].He[1],(PetscScalar**)cHeV);CHKERRQ(ierr);
-    ierr = cHeVInitialize(&f[xi].He[1],(PetscScalar**)fHeV);CHKERRQ(ierr);
-    /* ----------------------------------------------------------------
-     ---- Compute reaction terms that can create a cluster of given size
-    */
-    /*   He[He] + He[he] -> He[He+he]  */
-    for (He=2; He<NHe+1; He++) {
-      /* compute all pairs of clusters of smaller size that can combine to create a cluster of size He,
-         remove the upper half since they are symmetric to the lower half of the pairs. For example
-              when He = 5 (cluster size 5) the pairs are
-                 1   4
-                 2   2
-                 3   2  these last two are not needed in the sum since they repeat from above
-                 4   1  this is why he < (He/2) + 1            */
-      for (he=1; he<(He/2)+1; he++) {
-        row[0] = &f[xi].He[He] - rowstart;
-        row[1] = &f[xi].He[he] - rowstart;
-        row[2] = &f[xi].He[He-he] - rowstart;
-        col[0] = &c[xi].He[he] - colstart;
-        col[1] = &c[xi].He[He-he] - colstart;
-        val[0] = ctx->reactionScale*c[xi].He[He-he];
-        val[1] = ctx->reactionScale*c[xi].He[he];
-        val[2] = -ctx->reactionScale*c[xi].He[He-he];
-        val[3] = -ctx->reactionScale*c[xi].He[he];
-        val[4] = -ctx->reactionScale*c[xi].He[He-he];
-        val[5] = -ctx->reactionScale*c[xi].He[he];
-        ierr = MatSetValuesLocal(J,3,row,2,col,val,ADD_VALUES);CHKERRQ(ierr);
-      }
-    }
+    ierr = PetscMemzero(array, VPERE*VPERE*sizeof(PetscScalar));
 
-    /*   V[V]  +  V[v] ->  V[V+v]  */
-    for (V=2; V<NV+1; V++) {
-      for (v=1; v<(V/2)+1; v++) {
-        row[0] = &f[xi].V[V] - rowstart;
-        row[1] = &f[xi].V[v] - rowstart;
-        row[2] = &f[xi].V[V-v] - rowstart;
-        col[0] = &c[xi].V[v] - colstart;
-        col[1] = &c[xi].V[V-v] - colstart;
-        val[0] = ctx->reactionScale*c[xi].V[V-v];
-        val[1] = ctx->reactionScale*c[xi].V[v];
-        val[2] = -ctx->reactionScale*c[xi].V[V-v];
-        val[3] = -ctx->reactionScale*c[xi].V[v];
-        val[4] = -ctx->reactionScale*c[xi].V[V-v];
-        val[5] = -ctx->reactionScale*c[xi].V[v];
-        ierr = MatSetValuesLocal(J,3,row,2,col,val,ADD_VALUES);CHKERRQ(ierr);
+    /* Compute function over the locally owned part of the grid */
+    for (q=0; q<NQPTS; ++q) {
+      for (i=0; i < VPERE; ++i) {
+        for (j=0; j < VPERE; ++j) {
+          array[i*VPERE+j] += jxw[q] * rho * ( dphidx[q*VPERE+i]*dphidx[q*VPERE+j] + 
+                                               dphidy[q*VPERE+i]*dphidy[q*VPERE+j] );
+        }
       }
     }
 
-    /*   I[I] +  I[i] -> I[I+i] */
-    for (I=2; I<NI+1; I++) {
-      for (i=1; i<(I/2)+1; i++) {
-        row[0] = &f[xi].I[I] - rowstart;
-        row[1] = &f[xi].I[i] - rowstart;
-        row[2] = &f[xi].I[I-i] - rowstart;
-        col[0] = &c[xi].I[i] - colstart;
-        col[1] = &c[xi].I[I-i] - colstart;
-        val[0] = ctx->reactionScale*c[xi].I[I-i];
-        val[1] = ctx->reactionScale*c[xi].I[i];
-        val[2] = -ctx->reactionScale*c[xi].I[I-i];
-        val[3] = -ctx->reactionScale*c[xi].I[i];
-        val[4] = -ctx->reactionScale*c[xi].I[I-i];
-        val[5] = -ctx->reactionScale*c[xi].I[i];
-        ierr = MatSetValuesLocal(J,3,row,2,col,val,ADD_VALUES);CHKERRQ(ierr);
-      }
-    }
+    /* check if element is on the boundary */
+    ierr = DMMoabIsEntityOnBoundary(dm,ehandle,&elem_on_boundary);CHKERRQ(ierr);
 
-    /* He[1] +  V[1]  ->  He[1]-V[1] */
-    row[0] = &fHeV[1][1] - rowstart;
-    row[1] = &f[xi].He[1] - rowstart;
-    row[2] = &f[xi].V[1] - rowstart;
-    col[0] = &c[xi].He[1] - colstart;
-    col[1] = &c[xi].V[1] - colstart;
-    val[0] = 1000*ctx->reactionScale*c[xi].V[1];
-    val[1] = 1000*ctx->reactionScale*c[xi].He[1];
-    val[2] = -1000*ctx->reactionScale*c[xi].V[1];
-    val[3] = -1000*ctx->reactionScale*c[xi].He[1];
-    val[4] = -1000*ctx->reactionScale*c[xi].V[1];
-    val[5] = -1000*ctx->reactionScale*c[xi].He[1];
-    ierr = MatSetValuesLocal(J,3,row,2,col,val,ADD_VALUES);CHKERRQ(ierr);
-
-    /*  He[He]-V[V] + He[he] -> He[He+he]-V[V]  */
-   for (V=1; V<MHeV+1; V++) {
-      for (He=1; He<NHeV[V]; He++) {
-         for (he=1; he+He<NHeV[V]+1; he++) {
-          row[0] = &fHeV[V][He+he] - rowstart;
-          row[1] = &f[xi].He[he] - rowstart;
-          row[2] = &fHeV[V][He] - rowstart;
-          col[0] = &c[xi].He[he] - colstart;
-          col[1] = &cHeV[V][He] - colstart;
-          val[0] = ctx->reactionScale*cHeV[V][He];
-          val[1] = ctx->reactionScale*c[xi].He[he];
-          val[2] = -ctx->reactionScale*cHeV[V][He];
-          val[3] = -ctx->reactionScale*c[xi].He[he];
-          val[4] = -ctx->reactionScale*cHeV[V][He];
-          val[5] = -ctx->reactionScale*c[xi].He[he];
-          ierr = MatSetValuesLocal(J,3,row,2,col,val,ADD_VALUES);CHKERRQ(ierr);
+    /* apply dirichlet boundary conditions */
+    if (elem_on_boundary && user->bcType == DIRICHLET) {
+
+      /* get the list of nodes on boundary so that we can enforce dirichlet conditions strongly */
+      ierr = DMMoabCheckBoundaryVertices(dm,num_conn,connect,dbdry);CHKERRQ(ierr);
+
+      for (i=0; i < VPERE; ++i) {
+        if (dbdry[i]) {  /* dirichlet node */
+          /* think about strongly imposing dirichlet */
+          for (j=0; j < VPERE; ++j) {
+            /* TODO: symmetrize the system - need the RHS */
+            array[i*VPERE+j] = 0.0;
+          }
+          array[i*VPERE+i] = 1.0;
         }
       }
     }
 
+#ifdef LOCAL_ASSEMBLY
+    /* set the values directly into appropriate locations. Can alternately use VecSetValues */
+    ierr = MatSetValuesLocal(jac, VPERE, dof_indices, VPERE, dof_indices, array, ADD_VALUES);CHKERRQ(ierr);
+#else
+    ierr = MatSetValues(jac, VPERE, dof_indices, VPERE, dof_indices, array, ADD_VALUES);CHKERRQ(ierr);
+#endif
+  }
 
-    /*  He[He]-V[V] + V[1] -> He[He][V+1] */
-    for (V=1; V<MHeV; V++) {
-      for (He=1; He<NHeV[V+1]; He++) {
-        row[0] = &fHeV[V+1][He] - rowstart;
-        row[1] = &f[xi].V[1] - rowstart;
-        row[2] = &fHeV[V][He] - rowstart;
-        col[0] = &c[xi].V[1] - colstart;
-        col[1] = &cHeV[V][He] - colstart;
-        val[0] = ctx->reactionScale*cHeV[V][He];
-        val[1] = ctx->reactionScale*c[xi].V[1];
-        val[2] = -ctx->reactionScale*cHeV[V][He];
-        val[3] = -ctx->reactionScale*c[xi].V[1];
-        val[4] = -ctx->reactionScale*cHeV[V][He];
-        val[5] = -ctx->reactionScale*c[xi].V[1];
-        ierr = MatSetValuesLocal(J,3,row,2,col,val,ADD_VALUES);CHKERRQ(ierr);
-     }
-    }
+  ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
+  ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
 
-    /*  He[He]-V[V]  + He[he]-V[v] -> He[He+he][V+v]  */
-    /*  Currently the reaction rates for this are zero */
-
-
-    /*  V[V] + I[I]  ->   V[V-I] if V > I else I[I-V] */
-    for (V=1; V<NV+1; V++) {
-      for (I=1; I<PetscMin(V,NI); I++) {
-        row[0] = &f[xi].V[V-I] - rowstart;
-        row[1] = &f[xi].V[V] - rowstart;
-        row[2] = &f[xi].I[I] - rowstart;
-        col[0] = &c[xi].V[V] - colstart;
-        col[1] = &c[xi].I[I]  - colstart;
-        val[0] = ctx->reactionScale*c[xi].I[I];
-        val[1] = ctx->reactionScale*c[xi].V[V];
-        val[2] = -ctx->reactionScale*c[xi].I[I];
-        val[3] = -ctx->reactionScale*c[xi].V[V];
-        val[4] = -ctx->reactionScale*c[xi].I[I];
-        val[5] = -ctx->reactionScale*c[xi].V[V];
-        ierr = MatSetValuesLocal(J,3,row,2,col,val,ADD_VALUES);CHKERRQ(ierr);
-      }
-      for (I=V+1; I<NI+1; I++) {
-        row[0] = &f[xi].I[I-V] - rowstart;
-        row[1] = &f[xi].V[V] - rowstart;
-        row[2] = &f[xi].I[I] - rowstart;
-        col[0] = &c[xi].V[V] - colstart;
-        col[1] = &c[xi].I[I] - colstart;
-        val[0] = ctx->reactionScale*c[xi].I[I];
-        val[1] = ctx->reactionScale*c[xi].V[V];
-        val[2] = -ctx->reactionScale*c[xi].I[I];
-        val[3] = -ctx->reactionScale*c[xi].V[V];
-        val[4] = -ctx->reactionScale*c[xi].I[I];
-        val[5] = -ctx->reactionScale*c[xi].V[V];
-        ierr = MatSetValuesLocal(J,3,row,2,col,val,ADD_VALUES);CHKERRQ(ierr);
-      }
-    }
-  }
+  if (user->bcType == NEUMANN) {
+    MatNullSpace nullspace;
 
-  /*
-     Restore vectors
-  */
-  c    = (Concentrations*)(((PetscScalar*)c)+1);
-  ierr = DMMoabVecRestoreArrayRead(dm,localC,&c);CHKERRQ(ierr);
-  f    = (Concentrations*)(((PetscScalar*)f)+1);
-  ierr = DMMoabVecRestoreArray(dm,C,&f);CHKERRQ(ierr);
-  ierr = DMRestoreLocalVector(dm,&localC);CHKERRQ(ierr);
-  ierr = cHeVDestroy((PetscScalar**)cHeV);CHKERRQ(ierr);
-  ierr = cHeVDestroy((PetscScalar**)fHeV);CHKERRQ(ierr);
-
-  ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
-  ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
-  if (A != J) {
-    ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
-    ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
+    ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr);
+    ierr = MatSetNullSpace(jac,nullspace);CHKERRQ(ierr);
+    ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr);
   }
   PetscFunctionReturn(0);
 }
-/* ------------------------------------------------------------------- */
 
-#undef __FUNCT__
-#define __FUNCT__ "GetDfill"
+
 /*
-    Determines the nonzero structure within the diagonal blocks of the Jacobian that represent coupling resulting from reactions and
-    dissasociations of the clusters
+*  Purpose: BASIS_MN_Q4: all bases at N points for a Q4 element.
+*
+*  Discussion:
+*
+*    The routine is given the coordinates of the vertices of a quadrilateral.
+*    It works directly with these coordinates, and does not refer to a 
+*    reference element.
+*
+*    The sides of the element are presumed to lie along coordinate axes.
+*
+*    The routine evaluates the basis functions associated with each corner,
+*    and their derivatives with respect to X and Y.
+*
+*  Physical Element Q4:
+*
+*    |
+*    |  4-------3
+*    |  |       |
+*    Y  |       |
+*    |  |       |
+*    |  1-------2
+*    |
+*    +-----X------>
+*
+*  Parameters:
+*
+*    Input, PetscScalar Q[3*4], the coordinates of the vertices.
+*    It is common to list these points in counter clockwise order.
+*
+*    Input, int N, the number of evaluation points.
+*
+*    Input, PetscScalar P[3*N], the evaluation points.
+*
+*    Output, PetscScalar PHI[4*N], the bases at the evaluation points.
+*
+*    Output, PetscScalar DPHIDX[4*N], DPHIDY[4*N], the derivatives of the
+*    bases at the evaluation points.
+*
+*  Original Author: John Burkardt (http://people.sc.fsu.edu/~jburkardt/cpp_src/fem2d_pack/fem2d_pack.cpp)
+*  Modified by Vijay Mahadevan
 */
-PetscErrorCode GetDfill(PetscInt *dfill, void *ptr)
+#undef __FUNCT__
+#define __FUNCT__ "Compute_Quad4_Basis"
+PetscErrorCode Compute_Quad4_Basis ( PetscScalar coords[VPERE*3], PetscInt n, PetscScalar *pts, PetscScalar *phi, PetscScalar *dphidx, PetscScalar *dphidy)
 {
-  PetscInt       He,he,V,v,I,i,j,k,rows[3],cols[2];
-  Concentrations *c;
-  PetscScalar    *idxstart,**cHeV;
-  PetscErrorCode ierr;
+  PetscScalar ejac;
+  int i,j;
 
-  /* ensure fill for the diagonal of matrix */
-  for (i=0; i<(DOF); i++) {
-    dfill[i*DOF + i] = 1;
-  }
+  PetscFunctionBegin;
+  ejac = ( coords[0+2*3] - coords[0+0*3] ) * ( coords[1+2*3] - coords[1+0*3] );
+  ejac = 1.0/(ejac);
 
-  /*
-   c is never used except for computing offsets between variables which are used to fill the non-zero
-   structure of the matrix
-   */
-  ierr     = PetscMalloc(sizeof(Concentrations),&c);CHKERRQ(ierr);
-  c        = (Concentrations*)(((PetscScalar*)c)-1);
-  ierr     = cHeVCreate(&cHeV);CHKERRQ(ierr);
-  ierr     = cHeVInitialize(&c->He[1],cHeV);CHKERRQ(ierr);
-  idxstart = (PetscScalar*)&c->He[1];
-
-  /* -------------------------------------------------------------------------
-   ---- Compute dissociation terms that removes an item from a cluster
-   I assume dissociation means losing only a single item from a cluster
-   I cannot tell from the notes if clusters can break up into any sub-size.
-   */
-  /*   He[He] ->  He[He-1] + He[1] */
-  for (He=2; He<NHe+1; He++) {
-    rows[0] = &c->He[He-1] - idxstart;
-    rows[1] = &c->He[1] - idxstart;
-    rows[2] = &c->He[He] - idxstart;
-    cols[0] = &c->He[He] - idxstart;
-    for (j=0; j<3; j++) {
-      dfill[rows[j]*DOF + cols[0]] = 1;
-    }
-  }
+  for (j=0;j<n;j++)
+  {
+    phi[0+j*4] =      ( coords[0+2*3] - pts[0+j*3]  ) * ( coords[1+2*3] - pts[1+j*3]  );
+    phi[1+j*4] =      ( pts[0+j*3]  - coords[0+0*3] ) * ( coords[1+2*3] - pts[1+j*3]  );
+    phi[2+j*4] =      ( pts[0+j*3]  - coords[0+0*3] ) * ( pts[1+j*3]  - coords[1+0*3] );
+    phi[3+j*4] =      ( coords[0+2*3] - pts[0+j*3]  ) * ( pts[1+j*3]  - coords[1+0*3] );
 
-  /*   V[V] ->  V[V-1] + V[1] */
-  for (V=2; V<NV+1; V++) {
-    rows[0] = &c->V[V] - idxstart;
-    rows[1] = &c->V[1] - idxstart;
-    rows[2] = &c->V[V-1] - idxstart;
-    cols[0] = &c->V[V] - idxstart;
-    for (j=0; j<3; j++) {
-      dfill[rows[j]*DOF + cols[0]] = 1;
+    if (dphidx) {
+      dphidx[0+j*4] = - ( coords[1+2*3] - pts[1+j*3] );
+      dphidx[1+j*4] =   ( coords[1+2*3] - pts[1+j*3] );
+      dphidx[2+j*4] =   ( pts[1+j*3]  - coords[1+0*3] );
+      dphidx[3+j*4] = - ( pts[1+j*3]  - coords[1+0*3] );
     }
-  }
-  
-  /*   I[I] ->  I[I-1] + I[1] */
-  for (I=2; I<NI+1; I++) {
-    rows[0] = &c->I[I] - idxstart;
-    rows[1] = &c->I[1] - idxstart;
-    rows[2] = &c->I[I-1] - idxstart;
-    cols[0] = &c->I[I] - idxstart;
-    for (j=0; j<3; j++) {
-      dfill[rows[j]*DOF + cols[0]] = 1;
-    }
-  }
-  
-  /*   He[He]-V[1] ->  He[He] + V[1]  */
-  for (He=1; He<NHeV[1]+1; He++) {
-    rows[0] = &c->He[He] - idxstart;
-    rows[1] = &c->V[1] - idxstart;
-    rows[2] = &cHeV[1][He] - idxstart;
-    cols[0] = &cHeV[1][He] - idxstart;
-    for (j=0; j<3; j++) {
-      dfill[rows[j]*DOF + cols[0]] = 1;
-    }
-  }
-  
-  /*   He[1]-V[V] ->  He[1] + V[V]  */
-  for (V=2; V<MHeV+1; V++) {
-    rows[0] = &c->He[1] - idxstart;
-    rows[1] = &c->V[V] - idxstart;
-    rows[2] = &cHeV[V][1] - idxstart;
-    cols[0] = &cHeV[V][1] - idxstart;
-    for (j=0; j<3; j++) {
-      dfill[rows[j]*DOF + cols[0]] = 1;
-    }
-  }
-  
-  /*   He[He]-V[V] ->  He[He-1]-V[V] + He[1]  */
-  for (V=2; V<MHeV+1; V++) {
-    for (He=2; He<NHeV[V]+1; He++) {
-      rows[0] = &c->He[1] - idxstart;
-      rows[1] = &cHeV[V][He] - idxstart;
-      rows[2] = &cHeV[V][He-1] - idxstart;
-      cols[0] = &cHeV[V][He] - idxstart;
-      for (j=0; j<3; j++) {
-        dfill[rows[j]*DOF + cols[0]] = 1;
-      }
-    }
-  }
-  
-  /*   He[He]-V[V] ->  He[He]-V[V-1] + V[1]  */
-  for (V=2; V<MHeV+1; V++) {
-    for (He=2; He<NHeV[V-1]+1; He++) {
-      rows[0] = &c->V[1] - idxstart;
-      rows[1] = &cHeV[V][He] - idxstart;
-      rows[2] = &cHeV[V-1][He] - idxstart;
-      cols[0] = &cHeV[V][He] - idxstart;
-      for (j=0; j<3; j++) {
-        dfill[rows[j]*DOF + cols[0]] = 1;
-      }
-    }
-  }
-  
-  /*   He[He]-V[V] ->  He[He]-V[V+1] + I[1]  */
-  for (V=1; V<MHeV; V++) {
-    for (He=1; He<NHeV[V]+1; He++) {
-      rows[0] = &c->I[1] - idxstart;
-      rows[1] = &cHeV[V+1][He] - idxstart;
-      rows[2] = &cHeV[V][He] - idxstart;
-      cols[0] = &cHeV[V][He] - idxstart;
-      for (j=0; j<3; j++) {
-        dfill[rows[j]*DOF + cols[0]] = 1;
-      }
-    }
-  }
 
-  /* These are the reaction terms in the diagonal block */
-  for (He=2; He<NHe+1; He++) {
-    for (he=1; he<(He/2)+1; he++) {
-      rows[0] = &c->He[He] - idxstart;
-      rows[1] = &c->He[he] - idxstart;
-      rows[2] = &c->He[He-he] - idxstart;
-      cols[0] = &c->He[he] - idxstart;
-      cols[1] = &c->He[He-he] - idxstart;
-      for (j=0; j<3; j++) {
-        for (k=0; k<2; k++) {
-          dfill[rows[j]*DOF + cols[k]] = 1;
-        }
-      }
+    if (dphidy) {
+      dphidy[0+j*4] = - ( coords[0+2*3] - pts[0+j*3] );
+      dphidy[1+j*4] = - ( pts[0+j*3]  - coords[0+0*3] );
+      dphidy[2+j*4] =   ( pts[0+j*3]  - coords[0+0*3] );
+      dphidy[3+j*4] =   ( coords[0+2*3] - pts[0+j*3] );
     }
   }
 
-  /*   V[V]  +  V[v] ->  V[V+v]  */
-  for (V=2; V<NV+1; V++) {
-    for (v=1; v<(V/2)+1; v++) {
-      rows[0] = &c->V[V] - idxstart;
-      rows[1] = &c->V[v] - idxstart;
-      rows[2] = &c->V[V-v] - idxstart;
-      cols[0] = &c->V[v] - idxstart;
-      cols[1] = &c->V[V-v] - idxstart;
-      for (j=0; j<3; j++) {
-        for (k=0; k<2; k++) {
-          dfill[rows[j]*DOF + cols[k]] = 1;
-        }
-      }
-    }
-  }
-  
-  /*   I[I] +  I[i] -> I[I+i] */
-  for (I=2; I<NI+1; I++) {
-    for (i=1; i<(I/2)+1; i++) {
-      rows[0] = &c->I[I] - idxstart;
-      rows[1] = &c->I[i] - idxstart;
-      rows[2] = &c->I[I-i] - idxstart;
-      cols[0] = &c->I[i] - idxstart;
-      cols[1] = &c->I[I-i] - idxstart;
-      for (j=0; j<3; j++) {
-        for (k=0; k<2; k++) {
-          dfill[rows[j]*DOF + cols[k]] = 1;
-        }
-      }
+  /*  Divide by element jacobian. */
+  for ( j = 0; j < n; j++ ) {
+    for ( i = 0; i < VPERE; i++ ) {
+      phi[i+j*4]    *= ejac;
+      if (dphidx) dphidx[i+j*4] *= ejac;
+      if (dphidy) dphidy[i+j*4] *= ejac;
     }
   }
-  
-  /* He[1] +  V[1]  ->  He[1]-V[1] */
-  rows[0] = &cHeV[1][1] - idxstart;
-  rows[1] = &c->He[1] - idxstart;
-  rows[2] = &c->V[1] - idxstart;
-  cols[0] = &c->He[1] - idxstart;
-  cols[1] = &c->V[1] - idxstart;
-  for (j=0; j<3; j++) {
-    for (k=0; k<2; k++) {
-      dfill[rows[j]*DOF + cols[k]] = 1;
-    }
+#if 0
+  /* verify if the computed basis functions are consistent */
+  for ( j = 0; j < n; j++ ) {
+    PetscScalar phisum=0,dphixsum=0,dphiysum=0;
+    for ( i = 0; i < 4; i++ ) {
+      phisum += phi[i+j*4];
+      if (dphidx) dphixsum += dphidx[i+j*4];
+      if (dphidy) dphiysum += dphidy[i+j*4];
+    }
+    PetscPrintf(PETSC_COMM_WORLD, "Sum of basis at quadrature point %D = %G, %G, %G\n", j, phisum, dphixsum, dphiysum);
   }
-  
-  /*  He[He]-V[V] + He[he] -> He[He+he]-V[V]  */
-  for (V=1; V<MHeV+1; V++) {
-    for (He=1; He<NHeV[V]; He++) {
-      for (he=1; he+He<NHeV[V]+1; he++) {
-        rows[0] = &cHeV[V][He+he] - idxstart;
-        rows[1] = &c->He[he] - idxstart;
-        rows[2] = &cHeV[V][He] - idxstart;
-        cols[0] = &cHeV[V][He] - idxstart;
-        cols[1] = &c->He[he] - idxstart;
-        for (j=0; j<3; j++) {
-          for (k=0; k<2; k++) {
-            dfill[rows[j]*DOF + cols[k]] = 1;
-          }
-        }
-      }
-    }
-  }
-  /*  He[He]-V[V] + V[1] -> He[He][V+1] */
-  for (V=1; V<MHeV; V++) {
-    for (He=1; He<NHeV[V+1]; He++) {
-      rows[0] = &cHeV[V+1][He] - idxstart;
-      rows[1] = &c->V[1] - idxstart;
-      rows[2] = &cHeV[V][He] - idxstart;
-      cols[0] = &cHeV[V][He] - idxstart;
-      cols[1] = &c->V[1] - idxstart;
-      for (j=0; j<3; j++) {
-        for (k=0; k<2; k++) {
-          dfill[rows[j]*DOF + cols[k]] = 1;
-        }
-      }
-    }
-  }
-
-  /*  He[He]-V[V]  + He[he]-V[v] -> He[He+he][V+v]  */
-  /*  Currently the reaction rates for this are zero */
-  
-  /*  V[V] + I[I]  ->   V[V-I] if V > I else I[I-V] */
-  for (V=1; V<NV+1; V++) {
-    for (I=1; I<PetscMin(V,NI); I++) {
-      rows[0] = &c->V[V-I] - idxstart;
-      rows[1] = &c->V[V] - idxstart;
-      rows[2] = &c->I[I] - idxstart;
-      cols[0] = &c->V[V] - idxstart;
-      cols[1] = &c->I[I] - idxstart;
-      for (j=0; j<3; j++) {
-        for (k=0; k<2; k++) {
-          dfill[rows[j]*DOF + cols[k]] = 1;
-        }
-      }
-    }
-    for (I=V+1; I<NI+1; I++) {
-      rows[0] = &c->I[I-V] - idxstart;
-      rows[1] = &c->V[V] - idxstart;
-      rows[2] = &c->I[I] - idxstart;
-      cols[0] = &c->V[V] - idxstart;
-      cols[1] = &c->I[I] - idxstart;
-      for (j=0; j<3; j++) {
-        for (k=0; k<2; k++) {
-          dfill[rows[j]*DOF + cols[k]] = 1;
-        }
-      }
-    }
-  }
-
-  c    = (Concentrations*)(((PetscScalar*)c)+1);
-  ierr = cHeVDestroy(cHeV);CHKERRQ(ierr);
-  ierr = PetscFree(c);CHKERRQ(ierr);
+#endif
   PetscFunctionReturn(0);
 }
-/* ------------------------------------------------------------------- */
-
-typedef struct {
-  DM          Heda,Vda,HeVda;       /* defines the 2d layout of the He subvector */
-  Vec         He,V,HeV;
-  VecScatter  Hescatter,Vscatter,HeVscatter;
-  PetscViewer Heviewer,Vviewer,HeVviewer;
-} MyMonitorCtx;
-
-#undef __FUNCT__
-#define __FUNCT__ "MyMonitorMonitor"
-/*
-   Display He as a function of space and cluster size for each time step
-*/
-PetscErrorCode MyMonitorMonitor(TS ts,PetscInt timestep,PetscReal time,Vec solution, void *ictx)
-{
-  MyMonitorCtx   *ctx = (MyMonitorCtx*)ictx;
-  PetscErrorCode ierr;
-
-  PetscFunctionBeginUser;
-  ierr = VecScatterBegin(ctx->Hescatter,solution,ctx->He,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
-  ierr = VecScatterEnd(ctx->Hescatter,solution,ctx->He,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
-  ierr = VecView(ctx->He,ctx->Heviewer);CHKERRQ(ierr);
-
-  ierr = VecScatterBegin(ctx->Vscatter,solution,ctx->V,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
-  ierr = VecScatterEnd(ctx->Vscatter,solution,ctx->V,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
-  ierr = VecView(ctx->V,ctx->Vviewer);CHKERRQ(ierr);
 
-  ierr = VecScatterBegin(ctx->HeVscatter,solution,ctx->HeV,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
-  ierr = VecScatterEnd(ctx->HeVscatter,solution,ctx->HeV,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
-  ierr = VecView(ctx->HeV,ctx->HeVviewer);CHKERRQ(ierr);
-  PetscFunctionReturn(0);
-}
 
-#undef __FUNCT__
-#define __FUNCT__ "MyMonitorDestroy"
 /*
-   Frees all data structures associated with the monitor
+*  Purpose: Compute the quadrature points in the physical space with appropriate transformation for QUAD4 elements.
+*
+*  Parameters:
+*
+*    Input, PetscScalar verts[VPERE*4], the coordinates of the vertices.
+*    It is common to list these points in counter clockwise order.
+*
+*    Output, PetscScalar quad[3*NQPTS], the physical quadrature evaluation point.
+*
+*    Output, PetscScalar jxw[NQPTS], the product of Jacobian of the physical element times the weights at the quadrature points.
 */
-PetscErrorCode MyMonitorDestroy(void **ictx)
-{
-  MyMonitorCtx   **ctx = (MyMonitorCtx**)ictx;
-  PetscErrorCode ierr;
-
-  PetscFunctionBeginUser;
-  ierr = VecScatterDestroy(&(*ctx)->Hescatter);CHKERRQ(ierr);
-  ierr = VecDestroy(&(*ctx)->He);CHKERRQ(ierr);
-  ierr = DMDestroy(&(*ctx)->Heda);CHKERRQ(ierr);
-  ierr = PetscViewerDestroy(&(*ctx)->Heviewer);CHKERRQ(ierr);
-
-  ierr = VecScatterDestroy(&(*ctx)->Vscatter);CHKERRQ(ierr);
-  ierr = VecDestroy(&(*ctx)->V);CHKERRQ(ierr);
-  ierr = DMDestroy(&(*ctx)->Vda);CHKERRQ(ierr);
-  ierr = PetscViewerDestroy(&(*ctx)->Vviewer);CHKERRQ(ierr);
-
-  ierr = VecScatterDestroy(&(*ctx)->HeVscatter);CHKERRQ(ierr);
-  ierr = VecDestroy(&(*ctx)->HeV);CHKERRQ(ierr);
-  ierr = DMDestroy(&(*ctx)->HeVda);CHKERRQ(ierr);
-  ierr = PetscViewerDestroy(&(*ctx)->HeVviewer);CHKERRQ(ierr);
-  ierr = PetscFree(*ctx);CHKERRQ(ierr);
-  PetscFunctionReturn(0);
-}
-
-#if 1
-#include <petscdmda.h>
-
 #undef __FUNCT__
-#define __FUNCT__ "MyMonitorSetUp"
-/*
-   Sets up a monitor that will display He as a function of space and cluster size for each time step
-*/
-PetscErrorCode MyMonitorSetUp(TS ts)
+#define __FUNCT__ "ComputeQuadraturePointsPhysical"
+PetscErrorCode ComputeQuadraturePointsPhysical(const PetscScalar verts[VPERE*3], PetscScalar quad[NQPTS*3], PetscScalar jxw[NQPTS])
 {
-  DM             dm,da;
-  PetscErrorCode ierr;
-  PetscInt       xi,xs,xm,*idx,M,xj,cnt = 0;
-  const PetscInt *lx;
-  Vec            C;
-  MyMonitorCtx   *ctx;
-  PetscBool      flg;
-  IS             is;
-  char           ycoor[32];
-  PetscReal      valuebounds[4] = {0, 1.2, 0, 1.2};
-
-  PetscFunctionBeginUser;
-  ierr = PetscOptionsHasName(NULL,"-mymonitor",&flg);CHKERRQ(ierr);
-  if (!flg) PetscFunctionReturn(0);
-
-  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
-  ierr = PetscNew(&ctx);CHKERRQ(ierr);
-
-  /* create the replica 1-D DMDA object */
-  ierr = DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC,-8,DOF,1,NULL,&da);CHKERRQ(ierr);
-
-  /* setup visualization for He */
-  ierr = PetscViewerDrawOpen(PetscObjectComm((PetscObject)da),NULL,"",PETSC_DECIDE,PETSC_DECIDE,600,400,&ctx->Heviewer);CHKERRQ(ierr);
-  ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
-  ierr = DMDAGetInfo(da,PETSC_IGNORE,&M,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
-  ierr = DMDAGetOwnershipRanges(da,&lx,NULL,NULL);CHKERRQ(ierr);
-  ierr = DMDACreate2d(PetscObjectComm((PetscObject)da),DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,M,NHe,PETSC_DETERMINE,1,1,1,lx,NULL,&ctx->Heda);CHKERRQ(ierr);
-  ierr = DMDASetFieldName(ctx->Heda,0,"He");CHKERRQ(ierr);
-  ierr = DMDASetCoordinateName(ctx->Heda,0,"X coordinate direction");CHKERRQ(ierr);
-  ierr = PetscSNPrintf(ycoor,32,"%D ... Cluster size ... 1",NHe);CHKERRQ(ierr);
-  ierr = DMDASetCoordinateName(ctx->Heda,1,ycoor);CHKERRQ(ierr);
-  ierr = DMCreateGlobalVector(ctx->Heda,&ctx->He);CHKERRQ(ierr);
-  ierr = PetscMalloc(NHe*xm*sizeof(PetscInt),&idx);CHKERRQ(ierr);
-  cnt  = 0;
-  for (xj=0; xj<NHe; xj++) {
-    for (xi=xs; xi<xs+xm; xi++) {
-      idx[cnt++] = DOF*xi + xj;
-    }
-  }
-  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)ts),NHe*xm,idx,PETSC_OWN_POINTER,&is);CHKERRQ(ierr);
-  ierr = TSGetSolution(ts,&C);CHKERRQ(ierr);
-  ierr = VecScatterCreate(C,is,ctx->He,NULL,&ctx->Hescatter);CHKERRQ(ierr);
-  ierr = ISDestroy(&is);CHKERRQ(ierr);
-  /* sets the bounds on the contour plot values so the colors mean the same thing for different timesteps */
-  ierr = PetscViewerDrawSetBounds(ctx->Heviewer,2,valuebounds);CHKERRQ(ierr);
-
-  /* setup visualization for V */
-  ierr = PetscViewerDrawOpen(PetscObjectComm((PetscObject)da),NULL,"",PETSC_DECIDE,PETSC_DECIDE,600,400,&ctx->Vviewer);CHKERRQ(ierr);
-  ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
-  ierr = DMDAGetInfo(da,PETSC_IGNORE,&M,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
-  ierr = DMDAGetOwnershipRanges(da,&lx,NULL,NULL);CHKERRQ(ierr);
-  ierr = DMDACreate2d(PetscObjectComm((PetscObject)da),DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,M,NV,PETSC_DETERMINE,1,1,1,lx,NULL,&ctx->Vda);CHKERRQ(ierr);
-  ierr = DMDASetFieldName(ctx->Vda,0,"V");CHKERRQ(ierr);
-  ierr = DMDASetCoordinateName(ctx->Vda,0,"X coordinate direction");CHKERRQ(ierr);
-  ierr = PetscSNPrintf(ycoor,32,"%D ... Cluster size ... 1",NV);CHKERRQ(ierr);
-  ierr = DMDASetCoordinateName(ctx->Vda,1,ycoor);CHKERRQ(ierr);
-  ierr = DMCreateGlobalVector(ctx->Vda,&ctx->V);CHKERRQ(ierr);
-  ierr = PetscMalloc(NV*xm*sizeof(PetscInt),&idx);CHKERRQ(ierr);
-  cnt  = 0;
-  for (xj=0; xj<NV; xj++) {
-    for (xi=xs; xi<xs+xm; xi++) {
-      idx[cnt++] = NHe + DOF*xi + xj;
-    }
-  }
-  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)ts),NV*xm,idx,PETSC_OWN_POINTER,&is);CHKERRQ(ierr);
-  ierr = TSGetSolution(ts,&C);CHKERRQ(ierr);
-  ierr = VecScatterCreate(C,is,ctx->V,NULL,&ctx->Vscatter);CHKERRQ(ierr);
-  ierr = ISDestroy(&is);CHKERRQ(ierr);
-  /* sets the bounds on the contour plot values so the colors mean the same thing for different timesteps */
-  ierr = PetscViewerDrawSetBounds(ctx->Vviewer,2,valuebounds);CHKERRQ(ierr);
-
-  /* setup visualization for HeV[1][] */
-  ierr = PetscViewerDrawOpen(PetscObjectComm((PetscObject)da),NULL,"",PETSC_DECIDE,PETSC_DECIDE,600,400,&ctx->HeVviewer);CHKERRQ(ierr);
-  ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
-  ierr = DMDAGetInfo(da,PETSC_IGNORE,&M,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
-  ierr = DMDAGetOwnershipRanges(da,&lx,NULL,NULL);CHKERRQ(ierr);
-  ierr = DMDACreate2d(PetscObjectComm((PetscObject)da),DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,M,NHeV[1],PETSC_DETERMINE,1,1,1,lx,NULL,&ctx->HeVda);CHKERRQ(ierr);
-  ierr = DMDASetFieldName(ctx->HeVda,0,"HeV[1][]");CHKERRQ(ierr);
-  ierr = DMDASetCoordinateName(ctx->HeVda,0,"X coordinate direction");CHKERRQ(ierr);
-  ierr = PetscSNPrintf(ycoor,32,"%D ... Cluster size ... 1",NHeV[1]);CHKERRQ(ierr);
-  ierr = DMDASetCoordinateName(ctx->HeVda,1,ycoor);CHKERRQ(ierr);
-  ierr = DMCreateGlobalVector(ctx->HeVda,&ctx->HeV);CHKERRQ(ierr);
-  ierr = PetscMalloc(NHeV[1]*xm*sizeof(PetscInt),&idx);CHKERRQ(ierr);
-  cnt  = 0;
-  for (xj=0; xj<NHeV[1]; xj++) {
-    for (xi=xs; xi<xs+xm; xi++) {
-      idx[cnt++] = NHe + NV + NI + DOF*xi + xj;
-    }
+  int i,j;
+  PetscScalar centroid[3];
+  const PetscScalar GLG_QUAD[3] = {-0.577350269189625764509148780502, 0.577350269189625764509148780502, 1.0};
+  PetscScalar dx = fabs(verts[0+2*3] - verts[0+0*3])/2, dy = fabs( verts[1+2*3] - verts[1+0*3] )/2;
+  PetscScalar ejac = dx*dy;
+  
+  centroid[0] = centroid[1] = centroid[2] = 0.0;
+  for (i=0; i<VPERE; ++i) {
+    centroid[0] += verts[i*3+0];
+    centroid[1] += verts[i*3+1];
+    centroid[2] += verts[i*3+2];
   }
-  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)ts),NHeV[1]*xm,idx,PETSC_OWN_POINTER,&is);CHKERRQ(ierr);
-  ierr = TSGetSolution(ts,&C);CHKERRQ(ierr);
-  ierr = VecScatterCreate(C,is,ctx->HeV,NULL,&ctx->HeVscatter);CHKERRQ(ierr);
-  ierr = ISDestroy(&is);CHKERRQ(ierr);
-  /* sets the bounds on the contour plot values so the colors mean the same thing for different timesteps */
-  ierr = PetscViewerDrawSetBounds(ctx->HeVviewer,2,valuebounds);CHKERRQ(ierr);
-
-  ierr = TSMonitorSet(ts,MyMonitorMonitor,ctx,MyMonitorDestroy);CHKERRQ(ierr);
-  ierr = DMDestroy(&da);CHKERRQ(ierr);
-  PetscFunctionReturn(0);
-}
-#endif
-
-#undef __FUNCT__
-#define __FUNCT__ "MyLoadData"
-PetscErrorCode MyLoadData(MPI_Comm comm,const char *filename)
-{
-  PetscErrorCode ierr;
-  FILE           *fp;
-  char           buff[256];
-  PetscInt       He,V,I,lc = 0;
-  char           Hebindstr[32],Vbindstr[32],Ibindstr[32],trapbindstr[32],*sharp;
-  PetscReal      Hebind,Vbind,Ibind,trapbind;
+  centroid[0] /= 4;
+  centroid[1] /= 4;
+  centroid[2] /= 4;
 
-  PetscFunctionBegin;
-  ierr = PetscFOpen(comm,filename,"r",&fp);CHKERRQ(ierr);
-  ierr = PetscMemzero(buff,sizeof(char)*256);CHKERRQ(ierr);
-  ierr = PetscSynchronizedFGets(comm,fp,256,buff);CHKERRQ(ierr);
-  while (buff[0]) {
-    ierr = PetscStrchr(buff,'#',&sharp);CHKERRQ(ierr);
-    if (!sharp) {
-      sscanf(buff,"%d %d %d %s %s %s %s",&He,&V,&I,Hebindstr,Vbindstr,Ibindstr,trapbindstr);
-      Hebind = strtod(Hebindstr,NULL);
-      Vbind = strtod(Vbindstr,NULL);
-      Ibind = strtod(Ibindstr,NULL);
-      trapbind = strtod(trapbindstr,NULL);
-      if (V <= NV) {
-        if (He > NHe && V == 0 && I == 0) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Recompile with correct NHe %d %d",He,NHe);
-        if (He == 0  && V > NV && I == 0) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Recompile with correct V %d %d",V,NV);
-        if (He == 0  && V == 0 && I > NI) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Recompile with correct NI %d %d",I,NI);
-        if (lc++ > DOF) SETERRQ6(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Recompile with correct NHe %d NV %d NI %d MNHeV % lc=%D and DOF=%D",NHe,NV,NI,MNHeV,lc,DOF);
-        if (He > 0 && V > 0) {  /* assumes the He are sorted in increasing order */
-          NHeV[V] = He;
-        }
-      }
+  for (i=0; i<NQPTS1D; ++i) {
+    for (j=0; j<NQPTS1D; ++j) {
+      quad[(i*NQPTS1D+j)*3] = centroid[0]+dx*(GLG_QUAD[i]);
+      quad[(i*NQPTS1D+j)*3+1] = centroid[1]+dy*(GLG_QUAD[j]);
+      quad[(i*NQPTS1D+j)*3+2] = centroid[2];
+      jxw[i*NQPTS1D+j] = GLG_QUAD[NQPTS1D]*ejac;
     }
-    ierr = PetscMemzero(buff,sizeof(char)*256);CHKERRQ(ierr);
-    ierr = PetscSynchronizedFGets(comm,fp,256,buff);CHKERRQ(ierr);
   }
-  if (lc != DOF) SETERRQ6(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Recompile with correct NHe %d NV %d NI %d MNHeV %d Actual DOF %d User DOF %d",NHe,NV,NI,MNHeV,lc,DOF);
   PetscFunctionReturn(0);
 }
 

File src/dm/impls/moab/examples/tutorials/ex3.cxx

-/*T
-   Concepts: KSP^solving a system of linear equations using a MOAB based DM implementation.
-   Concepts: KSP^Laplacian, 2d
-   Processors: n
-T*/
-