PetIGA / demo / BoundaryIntegral.c

  This code solves the Laplace problem where the boundary conditions
  can be changed from Nuemann to Dirichlet via the commandline. While
  its primary use is in regression tests for PetIGA, it also
  demonstrates how boundary integrals may be performed to enforce
  things like Neumann conditions.

  keywords: steady, scalar, linear, testing, dimension independent,
  boundary integrals
#include "petiga.h"

#undef  __FUNCT__
#define __FUNCT__ "System"
PetscErrorCode System(IGAPoint p,PetscScalar *K,PetscScalar *F,void *ctx)
  PetscInt nen,dim;

  const PetscReal *N1;

  PetscInt a,b,i;
  for (a=0; a<nen; a++) {
    for (b=0; b<nen; b++) {
      PetscScalar Kab = 0.0;
      for (i=0; i<dim; i++)
        Kab += N1[a*dim+i]*N1[b*dim+i];
      K[a*nen+b] = Kab;
  return 0;

#undef  __FUNCT__
#define __FUNCT__ "Neumann"
PetscErrorCode Neumann(IGAPoint p,PetscScalar *K,PetscScalar *F,void *ctx)
  PetscReal *N0 = p->shape[0];
  PetscInt a,nen=p->nen;
  for (a=0; a<nen; a++) {
    PetscReal Na   = N0[a];
    F[a] = Na * 1.0;
  return 0;

typedef struct { 
  PetscInt dir;
  PetscInt side;
} AppCtx;

#undef  __FUNCT__
#define __FUNCT__ "Error"
PetscErrorCode Error(IGAPoint p,const PetscScalar *U,PetscInt n,PetscScalar *S,void *ctx)
  AppCtx *user = (AppCtx *)ctx;
  PetscScalar u;
  PetscReal x;
  if (user->side == 0)
    x = 1 - p->point[user->dir];
    x = p->point[user->dir];
  PetscReal e = u - x;
  S[0] = e*e;
  return 0;

#undef __FUNCT__
#define __FUNCT__ "main"
int main(int argc, char *argv[]) {

  PetscErrorCode  ierr;
  ierr = PetscInitialize(&argc,&argv,0,0);CHKERRQ(ierr);

  AppCtx user;
  user.dir  = 0;
  user.side = 1;

  ierr = PetscOptionsBegin(PETSC_COMM_WORLD,"","Options","IGA");CHKERRQ(ierr);
  ierr = PetscOptionsInt("-dir", "direction",__FILE__,user.dir, &user.dir, PETSC_NULL);CHKERRQ(ierr); 
  ierr = PetscOptionsInt("-side","side",     __FILE__,user.side,&user.side,PETSC_NULL);CHKERRQ(ierr); 
  ierr = PetscOptionsEnd();CHKERRQ(ierr);

  IGA iga;
  ierr = IGACreate(PETSC_COMM_WORLD,&iga);CHKERRQ(ierr);
  ierr = IGASetDof(iga,1);CHKERRQ(ierr);

  IGABoundary bnd;
  PetscInt d = !user.side; 
  PetscInt n = !!user.side;
  ierr = IGAGetBoundary(iga,user.dir,d,&bnd);CHKERRQ(ierr);
  ierr = IGABoundarySetValue(bnd,0,0.0);CHKERRQ(ierr);
  ierr = IGAGetBoundary(iga,user.dir,n,&bnd);CHKERRQ(ierr); 
  ierr = IGABoundarySetUserSystem(bnd,Neumann,PETSC_NULL);CHKERRQ(ierr);

  ierr = IGASetFromOptions(iga);CHKERRQ(ierr);
  ierr = IGASetUp(iga);CHKERRQ(ierr);

  Mat A;
  Vec x,b;
  ierr = IGACreateMat(iga,&A);CHKERRQ(ierr);
  ierr = IGACreateVec(iga,&x);CHKERRQ(ierr);
  ierr = IGACreateVec(iga,&b);CHKERRQ(ierr);
  ierr = IGASetUserSystem(iga,System,PETSC_NULL);CHKERRQ(ierr);
  ierr = IGAComputeSystem(iga,A,b);CHKERRQ(ierr);
  KSP ksp;
  ierr = IGACreateKSP(iga,&ksp);CHKERRQ(ierr);
  ierr = KSPSetOperators(ksp,A,A,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
  ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
  ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);

  PetscInt dim;
  ierr = IGAGetDim(iga,&dim);CHKERRQ(ierr);
  if (dim <= 2) {ierr = VecView(x,PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}

  PetscScalar error = 0;
  ierr = IGAFormScalar(iga,x,1,&error,Error,&user);CHKERRQ(ierr);
  error = PetscSqrtReal(PetscRealPart(error));
  ierr = PetscPrintf(PETSC_COMM_WORLD,"L2 error = %G\n",error);CHKERRQ(ierr);
  ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
  ierr = MatDestroy(&A);CHKERRQ(ierr);
  ierr = VecDestroy(&x);CHKERRQ(ierr);
  ierr = VecDestroy(&b);CHKERRQ(ierr);
  ierr = IGADestroy(&iga);CHKERRQ(ierr);

  PetscBool flag = PETSC_FALSE;
  PetscReal secs = -1;
  ierr = PetscOptionsHasName(0,"-sleep",&flag);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(0,"-sleep",&secs,0);CHKERRQ(ierr);
  if (flag) {ierr = PetscSleep(secs);CHKERRQ(ierr);}

  ierr = PetscFinalize();CHKERRQ(ierr);
  return 0;
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