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SWE: Initial implementation of generic restriction matrix
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This generic restriction matrix does not only have 1's but also the coordinate transformations needed from the coord system of the nodes that are on the panel edges (lat, long) to the local ones of the nodes on the adjacent panels
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@valeriabarra
valeriabarra committed Nov 9, 2020
1 parent ae889c7 commit d2f5d15
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Showing 4 changed files with 148 additions and 164 deletions.
4 changes: 2 additions & 2 deletions examples/fluids/shallow-water/shallowwater.c
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Original file line number Diff line number Diff line change
Expand Up @@ -374,8 +374,8 @@ int main(int argc, char **argv) {
// Setup transformation matrix different panels of the cube
Mat T;
EdgeNode edgenodes;
ierr = FindPanelEdgeNodes(dm, &physCtxData, ncompq, &nedgenodes, &edgenodes,
&T);
ierr = FindPanelEdgeNodes(dm, &physCtxData, ncompq, degree, topodim,
&nedgenodes, &edgenodes, &T);
CHKERRQ(ierr);

// Transform coordinate according to their panel systems
Expand Down
270 changes: 127 additions & 143 deletions examples/fluids/shallow-water/src/setup.c
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Original file line number Diff line number Diff line change
Expand Up @@ -76,7 +76,8 @@ problemData problemOptions[] = {
// -----------------------------------------------------------------------------

PetscErrorCode FindPanelEdgeNodes(DM dm, PhysicsContext phys_ctx,
PetscInt ncomp, PetscInt *edgenodecnt,
PetscInt ncomp, PetscInt degree,
PetscInt topodim, PetscInt *edgenodecnt,
EdgeNode *edgenodes, Mat *T) {

PetscInt ierr;
Expand Down Expand Up @@ -154,8 +155,8 @@ PetscErrorCode FindPanelEdgeNodes(DM dm, PhysicsContext phys_ctx,
(*edgenodecnt)++;
}
}
// ierr = SetupPanelCoordTransformations(dm, phys_ctx, ncomp, *edgenodes,
// *edgenodecnt, T); CHKERRQ(ierr);
ierr = SetupRestrictionMatrix(dm, phys_ctx, degree, ncomp, *edgenodes,
*edgenodecnt, T); CHKERRQ(ierr);

// Free heap
ierr = PetscFree2(bitmaploc, bitmap); CHKERRQ(ierr);
Expand All @@ -166,157 +167,147 @@ PetscErrorCode FindPanelEdgeNodes(DM dm, PhysicsContext phys_ctx,
// -----------------------------------------------------------------------------
// Auxiliary function that sets up all coordinate transformations between panels
// -----------------------------------------------------------------------------
PetscErrorCode SetupPanelCoordTransformations(DM dm, PhysicsContext phys_ctx,
PetscInt ncomp,
EdgeNode edgenodes,
PetscInt nedgenodes, Mat *T) {
PetscInt ierr;
PetscErrorCode SetupRestrictionMatrix(DM dm, PhysicsContext phys_ctx,
PetscInt degree, PetscInt ncomp,
EdgeNode edgenodes, PetscInt nedgenodes,
Mat *T) {
PetscInt ierr, nnodes, c, cStart, cEnd, nelem, numP, gdofs;
MPI_Comm comm;
Vec X;
PetscInt gdofs;
PetscSection section;
const PetscScalar *xarray;

PetscFunctionBeginUser;
ierr = PetscObjectGetComm((PetscObject)dm, &comm); CHKERRQ(ierr);
ierr = DMGetSection(dm, &section); CHKERRQ(ierr);

ierr = DMGetCoordinates(dm, &X); CHKERRQ(ierr);
ierr = VecGetSize(X, &gdofs); CHKERRQ(ierr);
nnodes = gdofs/ncomp;
ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd); CHKERRQ(ierr);
nelem = cEnd - cStart;
numP = degree + 1;

// Preallocate sparse matrix
ierr = MatCreateBAIJ(comm, 2, PETSC_DECIDE, PETSC_DECIDE, 4*gdofs/ncomp,
4*gdofs/ncomp, 2, NULL, 0, NULL, T); CHKERRQ(ierr);
for (PetscInt i=0; i < 4*gdofs/ncomp; i++) {
ierr = MatSetValue(*T, i, i, 1., INSERT_VALUES); CHKERRQ(ierr);
}
ierr = MatCreateAIJ(comm, nelem*numP*numP*ncomp, nnodes*ncomp,
PETSC_DETERMINE, PETSC_DETERMINE, 2, NULL,
nnodes*ncomp, NULL, T); CHKERRQ(ierr);

ierr = VecGetArrayRead(X, &xarray); CHKERRQ(ierr);
PetscScalar R = phys_ctx->R;
// Nodes loop
for (PetscInt i=0; i < gdofs; i += ncomp) {
// Read global Cartesian coordinates
PetscScalar x[3] = {xarray[i*ncomp + 0],
xarray[i*ncomp + 1],
xarray[i*ncomp + 2]
};
// Normalize quadrature point coordinates to sphere
PetscScalar rad = sqrt(x[0]*x[0] + x[1]*x[1] + x[2]*x[2]);
x[0] *= R / rad;
x[1] *= R / rad;
x[2] *= R / rad;
// Compute latitude and longitude
const PetscScalar theta = asin(x[2] / R); // latitude
const PetscScalar lambda = atan2(x[1], x[0]); // longitude

// For P_0 (front), P_1 (east), P_2 (back), P_3 (west):
PetscScalar T00 = cos(theta)*cos(lambda) * cos(lambda);
PetscScalar T01 = cos(theta)*cos(lambda) * 0.;
PetscScalar T10 = cos(theta)*cos(lambda) * -sin(theta)*sin(lambda);
PetscScalar T11 = cos(theta)*cos(lambda) * cos(theta);
const PetscScalar T_lateral[2][2] = {{T00,
T01},
{T10,
T11}
};
PetscScalar Tinv00 = 1./(cos(theta)*cos(lambda)) * (1./cos(lambda));
PetscScalar Tinv01 = 1./(cos(theta)*cos(lambda)) * 0.;
PetscScalar Tinv10 = 1./(cos(theta)*cos(lambda)) * tan(theta)*tan(lambda);
PetscScalar Tinv11 = 1./(cos(theta)*cos(lambda)) * (1./cos(theta));
const PetscScalar T_lateralinv[2][2] = {{Tinv00,
Tinv01},
{Tinv10,
Tinv11}
};
// For P4 (north):
T00 = sin(theta) * cos(lambda);
T01 = sin(theta) * sin(lambda);
T10 = sin(theta) * -sin(theta)*sin(lambda);
T11 = sin(theta) * sin(theta)*cos(lambda);
const PetscScalar T_top[2][2] = {{T00,
T01},
{T10,
T11}
};
Tinv00 = 1./(sin(theta)*sin(theta)) * sin(theta)*cos(lambda);
Tinv01 = 1./(sin(theta)*sin(theta)) * (-sin(lambda));
Tinv10 = 1./(sin(theta)*sin(theta)) * sin(theta)*sin(lambda);
Tinv11 = 1./(sin(theta)*sin(theta)) * cos(lambda);
const PetscScalar T_topinv[2][2] = {{Tinv00,
Tinv01},
{Tinv10,
Tinv11}
};

// For P5 (south):
T00 = sin(theta) * (-cos(theta));
T01 = sin(theta) * sin(lambda);
T10 = sin(theta) * sin(theta)*sin(lambda);
T11 = sin(theta) * sin(theta)*cos(lambda);
const PetscScalar T_bottom[2][2] = {{T00,
T01},
{T10,
T11}
};
Tinv00 = 1./(sin(theta)*sin(theta)) * (-sin(theta)*cos(lambda));
Tinv01 = 1./(sin(theta)*sin(theta)) * sin(lambda);
Tinv10 = 1./(sin(theta)*sin(theta)) * sin(theta)*sin(lambda);
Tinv11 = 1./(sin(theta)*sin(theta)) * cos(lambda);
const PetscScalar T_bottominv[2][2] = {{Tinv00,
Tinv01},
{Tinv10,
Tinv11}
};

const PetscScalar (*transforms[6])[2][2] = {&T_lateral,
&T_lateral,
&T_lateral,
&T_lateral,
&T_top,
&T_bottom
};

const PetscScalar (*inv_transforms[6])[2][2] = {&T_lateralinv,
&T_lateralinv,
&T_lateralinv,
&T_lateralinv,
&T_topinv,
&T_bottominv
};
// Loop over elements
for (c = cStart; c < cEnd; c++) {
PetscInt numindices, *indices, i;
ierr = DMPlexGetClosureIndices(dm, section, section, c, PETSC_TRUE,
&numindices, &indices, NULL, NULL);
CHKERRQ(ierr);
for (i = 0; i < numindices; i += ncomp) {
for (PetscInt j = 0; j < ncomp; j++) {
if (indices[i+j] != indices[i] + (PetscInt)(copysign(j, indices[i])))
SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP,
"Cell %D closure indices not interlaced", c);
}
// NO BC on closed surfaces
PetscInt loc = indices[i];

for (PetscInt e = 0; e < nedgenodes; e++) {
if (edgenodes[e].idx == i) {
const PetscScalar (*matrixA)[2][2] = inv_transforms[edgenodes[e].panelA];
const PetscScalar (*matrixB)[2][2] = transforms[edgenodes[e].panelB];

// inv_transform * transform (A^{-1}*B)
// This product represents the mapping from coordinate system A
// to spherical coordinates and then to coordinate system B. Vice versa
// for transform * inv_transform (B^{-1}*A)
PetscScalar matrixAB[2][2], matrixBA[2][2];
for (int j=0; j<2; j++) {
for (int k=0; k<2; k++) {
matrixAB[j][k] = matrixBA[j][k] = 0;
for (int l=0; l<2; l++) {
matrixAB[j][k] += (*matrixA)[j][l] * (*matrixB)[l][k];
matrixBA[j][k] += (*matrixB)[j][l] * (*matrixA)[l][k];
}
}
// Query element panel
PetscInt panel;
ierr = DMGetLabelValue(dm, "panel", c, &panel); CHKERRQ(ierr);

// Query if edge node
PetscBool isEdgeNode = PETSC_FALSE;

for (PetscInt e = 0; e < nedgenodes; e++) {
if (edgenodes[e].idx == loc) {
isEdgeNode = PETSC_TRUE;
break;
}
PetscInt idxAB[2] = {4*i/ncomp + 0, 4*i/ncomp +1};
PetscInt idxBA[2] = {4*i/ncomp + 2, 4*i/ncomp +3};
ierr = MatSetValues(*T, 2, idxAB, 2, idxAB, (PetscScalar *)matrixAB,
INSERT_VALUES); CHKERRQ(ierr);
ierr = MatSetValues(*T, 2, idxBA, 2, idxBA, (PetscScalar *)matrixBA,
INSERT_VALUES); CHKERRQ(ierr);
}

PetscScalar entries[9];
if (isEdgeNode) {
ierr = VecGetArrayRead(X, &xarray); CHKERRQ(ierr);
PetscScalar R = phys_ctx->R;
// Read global Cartesian coordinates
PetscScalar x[3] = {xarray[loc + 0],
xarray[loc + 1],
xarray[loc + 2]
};
// Restore array read
ierr = VecRestoreArrayRead(X, &xarray); CHKERRQ(ierr);

// Normalize quadrature point coordinates to sphere
PetscScalar rad = sqrt(x[0]*x[0] + x[1]*x[1] + x[2]*x[2]);
x[0] *= R / rad;
x[1] *= R / rad;
x[2] *= R / rad;
// Compute latitude and longitude
const PetscScalar theta = asin(x[2] / R); // latitude
const PetscScalar lambda = atan2(x[1], x[0]); // longitude

PetscScalar T00, T01, T10, T11;

switch (panel) {
case 0:
case 1:
case 2:
case 3:
// For P_0 (front), P_1 (east), P_2 (back), P_3 (west):
T00 = cos(theta)*cos(lambda) * cos(lambda);
T01 = cos(theta)*cos(lambda) * 0.;
T10 = cos(theta)*cos(lambda) * -sin(theta)*sin(lambda);
T11 = cos(theta)*cos(lambda) * cos(theta);
break;
case 4:
// For P4 (north):
T00 = sin(theta) * cos(lambda);
T01 = sin(theta) * sin(lambda);
T10 = sin(theta) * -sin(theta)*sin(lambda);
T11 = sin(theta) * sin(theta)*cos(lambda);
break;
case 5:
// For P5 (south):
T00 = sin(theta) * (-cos(theta));
T01 = sin(theta) * sin(lambda);
T10 = sin(theta) * sin(theta)*sin(lambda);
T11 = sin(theta) * sin(theta)*cos(lambda);
break;
}

entries[0] = T00;
entries[1] = T01;
entries[2] = 0.;
entries[3] = T10;
entries[4] = T11;
entries[5] = 0.;
entries[6] = 0.;
entries[7] = 0.;
entries[8] = 1.;

} else {
entries[0] = 1.;
entries[1] = 0.;
entries[2] = 0.;
entries[3] = 0.;
entries[4] = 1.;
entries[5] = 0.;
entries[6] = 0.;
entries[7] = 0.;
entries[8] = 1.;
}
PetscInt elem = c - cStart;
PetscInt idxrow[3] = {elem*loc + 0, elem*loc + 1, elem*loc + 2};
PetscInt idxcol[3] = {loc + 0, loc + 1, loc + 2};
ierr = MatSetValues(*T, ncomp, idxrow, ncomp, idxcol, entries,
INSERT_VALUES); CHKERRQ(ierr);
}
ierr = DMPlexRestoreClosureIndices(dm, section, section, c, PETSC_TRUE,
&numindices, &indices, NULL, NULL);
CHKERRQ(ierr);
}

// Assemble matrix for all node transformations
ierr = MatAssemblyBegin(*T, MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
ierr = MatAssemblyEnd(*T, MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);

// Restore array read
ierr = VecRestoreArrayRead(X, &xarray); CHKERRQ(ierr);

PetscFunctionReturn(0);
}

Expand Down Expand Up @@ -377,9 +368,7 @@ PetscErrorCode TransformCoords(DM dm, Vec Xloc, const PetscInt ncompx,
xpanelslocarray[n*ncompx+1] = lambda;
xpanelslocarray[n*ncompx+2] = -1;
}

else {

switch (panel) {
case 0:
x = l * (Y / X);
Expand Down Expand Up @@ -680,9 +669,6 @@ PetscErrorCode SetupLibceed(DM dm, Ceed ceed, CeedInt degree, CeedInt qextra,
CHKERRQ(ierr);

// CEED restrictions
// TODO: After the resitrction matrix is implemented comment the following line
ierr = CreateRestrictionPlex(ceed, dmcoord, numP, ncompq, &Erestrictq);
CHKERRQ(ierr);
ierr = CreateRestrictionPlex(ceed, dmcoord, 2, ncompx, &Erestrictx);
CHKERRQ(ierr);

Expand All @@ -693,11 +679,9 @@ PetscErrorCode SetupLibceed(DM dm, Ceed ceed, CeedInt degree, CeedInt qextra,
CEED_STRIDES_BACKEND, &Erestrictqdi);
// Solution vec restriction is a strided (identity) because we use a user
// mat mult before and after operator apply
// TODO: After the restriction matrix for the solution vector is implemented,
// decomment the following line
// CeedElemRestrictionCreateStrided(ceed, nelem, numP*numP, ncompq,
// ncompq*nelem*numP*numP,
// CEED_STRIDES_BACKEND, &Erestrictq);
CeedElemRestrictionCreateStrided(ceed, nelem, numP*numP, ncompq,
ncompq*nelem*numP*numP,
CEED_STRIDES_BACKEND, &Erestrictq);

// Element coordinates
ierr = DMGetCoordinatesLocal(dm, &Xloc); CHKERRQ(ierr);
Expand Down
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