/*@C
PetscDTGaussJacobiQuadrature - create Gauss-Jacobi quadrature for a simplex
Not Collective
Input Arguments:
+ dim - The simplex dimension
. order - The number of points in one dimension
. a - left end of interval (often-1)
- b - right end of interval (often +1)
Output Argument:
. q - A PetscQuadrature object
Level: intermediate
References:
Karniadakis and Sherwin.
FIAT
.seealso: PetscDTGaussTensorQuadrature(), PetscDTGaussQuadrature()
@*/
PetscErrorCode PetscDTGaussJacobiQuadrature(PetscInt dim, PetscInt order, PetscReal a, PetscReal b, PetscQuadrature *q)
{
PetscInt npoints = dim > 1 ? dim > 2 ? order*PetscSqr(order) : PetscSqr(order) : order;
PetscReal *px, *wx, *py, *wy, *pz, *wz, *x, *w;
PetscInt i, j, k;
PetscErrorCode ierr;
PetscFunctionBegin;
if ((a != -1.0) || (b != 1.0)) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must use default internal right now");
ierr = PetscMalloc1(npoints*dim, &x);CHKERRQ(ierr);
ierr = PetscMalloc1(npoints, &w);CHKERRQ(ierr);
switch (dim) {
case 0:
ierr = PetscFree(x);CHKERRQ(ierr);
ierr = PetscFree(w);CHKERRQ(ierr);
ierr = PetscMalloc1(1, &x);CHKERRQ(ierr);
ierr = PetscMalloc1(1, &w);CHKERRQ(ierr);
x[0] = 0.0;
w[0] = 1.0;
break;
case 1:
ierr = PetscDTGaussJacobiQuadrature1D_Internal(order, 0.0, 0.0, x, w);CHKERRQ(ierr);
break;
case 2:
ierr = PetscMalloc4(order,&px,order,&wx,order,&py,order,&wy);CHKERRQ(ierr);
ierr = PetscDTGaussJacobiQuadrature1D_Internal(order, 0.0, 0.0, px, wx);CHKERRQ(ierr);
ierr = PetscDTGaussJacobiQuadrature1D_Internal(order, 1.0, 0.0, py, wy);CHKERRQ(ierr);
for (i = 0; i < order; ++i) {
for (j = 0; j < order; ++j) {
ierr = PetscDTMapSquareToTriangle_Internal(px[i], py[j], &x[(i*order+j)*2+0], &x[(i*order+j)*2+1]);CHKERRQ(ierr);
w[i*order+j] = 0.5 * wx[i] * wy[j];
}
}
ierr = PetscFree4(px,wx,py,wy);CHKERRQ(ierr);
break;
case 3:
ierr = PetscMalloc6(order,&px,order,&wx,order,&py,order,&wy,order,&pz,order,&wz);CHKERRQ(ierr);
ierr = PetscDTGaussJacobiQuadrature1D_Internal(order, 0.0, 0.0, px, wx);CHKERRQ(ierr);
ierr = PetscDTGaussJacobiQuadrature1D_Internal(order, 1.0, 0.0, py, wy);CHKERRQ(ierr);
ierr = PetscDTGaussJacobiQuadrature1D_Internal(order, 2.0, 0.0, pz, wz);CHKERRQ(ierr);
for (i = 0; i < order; ++i) {
for (j = 0; j < order; ++j) {
for (k = 0; k < order; ++k) {
ierr = PetscDTMapCubeToTetrahedron_Internal(px[i], py[j], pz[k], &x[((i*order+j)*order+k)*3+0], &x[((i*order+j)*order+k)*3+1], &x[((i*order+j)*order+k)*3+2]);CHKERRQ(ierr);
w[(i*order+j)*order+k] = 0.125 * wx[i] * wy[j] * wz[k];
}
}
}
ierr = PetscFree6(px,wx,py,wy,pz,wz);CHKERRQ(ierr);
break;
default:
SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot construct quadrature rule for dimension %d", dim);
}
ierr = PetscQuadratureCreate(PETSC_COMM_SELF, q);CHKERRQ(ierr);
ierr = PetscQuadratureSetData(*q, dim, npoints, x, w);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@C
PetscDTGaussJacobiQuadrature - create Gauss-Jacobi quadrature for a simplex
Not Collective
Input Arguments:
+ dim - The simplex dimension
. npoints - number of points
. a - left end of interval (often-1)
- b - right end of interval (often +1)
Output Arguments:
+ points - quadrature points
- weights - quadrature weights
Level: intermediate
References:
Karniadakis and Sherwin.
FIAT
.seealso: PetscDTGaussQuadrature()
@*/
PetscErrorCode PetscDTGaussJacobiQuadrature(PetscInt dim, PetscInt npoints, PetscReal a, PetscReal b, PetscReal *points[], PetscReal *weights[])
{
PetscReal *px, *wx, *py, *wy, *pz, *wz, *x, *w;
PetscInt i, j, k;
PetscErrorCode ierr;
PetscFunctionBegin;
if ((a != -1.0) || (b != 1.0)) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must use default internal right now");
switch (dim) {
case 1:
ierr = PetscMalloc(npoints * sizeof(PetscReal), &x);CHKERRQ(ierr);
ierr = PetscMalloc(npoints * sizeof(PetscReal), &w);CHKERRQ(ierr);
ierr = PetscDTGaussJacobiQuadrature1D_Internal(npoints, 0.0, 0.0, x, w);CHKERRQ(ierr);
break;
case 2:
ierr = PetscMalloc(npoints*npoints*2 * sizeof(PetscReal), &x);CHKERRQ(ierr);
ierr = PetscMalloc(npoints*npoints * sizeof(PetscReal), &w);CHKERRQ(ierr);
ierr = PetscMalloc4(npoints,PetscReal,&px,npoints,PetscReal,&wx,npoints,PetscReal,&py,npoints,PetscReal,&wy);CHKERRQ(ierr);
ierr = PetscDTGaussJacobiQuadrature1D_Internal(npoints, 0.0, 0.0, px, wx);CHKERRQ(ierr);
ierr = PetscDTGaussJacobiQuadrature1D_Internal(npoints, 1.0, 0.0, py, wy);CHKERRQ(ierr);
for (i = 0; i < npoints; ++i) {
for (j = 0; j < npoints; ++j) {
ierr = PetscDTMapSquareToTriangle_Internal(px[i], py[j], &x[(i*npoints+j)*2+0], &x[(i*npoints+j)*2+1]);CHKERRQ(ierr);
w[i*npoints+j] = 0.5 * wx[i] * wy[j];
}
}
ierr = PetscFree4(px,wx,py,wy);CHKERRQ(ierr);
break;
case 3:
ierr = PetscMalloc(npoints*npoints*3 * sizeof(PetscReal), &x);CHKERRQ(ierr);
ierr = PetscMalloc(npoints*npoints * sizeof(PetscReal), &w);CHKERRQ(ierr);
ierr = PetscMalloc6(npoints,PetscReal,&px,npoints,PetscReal,&wx,npoints,PetscReal,&py,npoints,PetscReal,&wy,npoints,PetscReal,&pz,npoints,PetscReal,&wz);CHKERRQ(ierr);
ierr = PetscDTGaussJacobiQuadrature1D_Internal(npoints, 0.0, 0.0, px, wx);CHKERRQ(ierr);
ierr = PetscDTGaussJacobiQuadrature1D_Internal(npoints, 1.0, 0.0, py, wy);CHKERRQ(ierr);
ierr = PetscDTGaussJacobiQuadrature1D_Internal(npoints, 2.0, 0.0, pz, wz);CHKERRQ(ierr);
for (i = 0; i < npoints; ++i) {
for (j = 0; j < npoints; ++j) {
for (k = 0; k < npoints; ++k) {
ierr = PetscDTMapCubeToTetrahedron_Internal(px[i], py[j], pz[k], &x[((i*npoints+j)*npoints+k)*3+0], &x[((i*npoints+j)*npoints+k)*3+1], &x[((i*npoints+j)*npoints+k)*3+2]);CHKERRQ(ierr);
w[(i*npoints+j)*npoints+k] = 0.125 * wx[i] * wy[j] * wz[k];
}
}
}
ierr = PetscFree6(px,wx,py,wy,pz,wz);CHKERRQ(ierr);
break;
default:
SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot construct quadrature rule for dimension %d", dim);
}
if (points) *points = x;
if (weights) *weights = w;
PetscFunctionReturn(0);
}