Actual source code: ex42.c
1: static const char help[] = "Simple libCEED test to calculate surface area using 1^T M 1";
3: /*
4: This is a recreation of libCeed Example 2: https://libceed.readthedocs.io/en/latest/examples/ceed/
5: */
7: #include <petscdmceed.h>
8: #include <petscdmplexceed.h>
9: #include <petscfeceed.h>
10: #include <petscdmplex.h>
11: #include <petscds.h>
13: typedef struct {
14: PetscReal areaExact;
15: CeedQFunctionUser setupgeo, apply;
16: const char *setupgeofname, *applyfname;
17: } AppCtx;
19: typedef struct {
20: CeedQFunction qf_apply;
21: CeedOperator op_apply;
22: CeedVector qdata, uceed, vceed;
23: } CeedData;
25: static PetscErrorCode CeedDataDestroy(CeedData *data)
26: {
28: CeedVectorDestroy(&data->qdata);
29: CeedVectorDestroy(&data->uceed);
30: CeedVectorDestroy(&data->vceed);
31: CeedQFunctionDestroy(&data->qf_apply);
32: CeedOperatorDestroy(&data->op_apply);
33: return 0;
34: }
36: CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out)
37: {
38: const CeedScalar *u = in[0], *qdata = in[1];
39: CeedScalar *v = out[0];
41: CeedPragmaSIMD for (CeedInt i = 0; i < Q; ++i) v[i] = qdata[i] * u[i];
43: return 0;
44: }
46: /*
47: // Reference (parent) 2D coordinates: X \in [-1, 1]^2
48: //
49: // Global physical coordinates given by the mesh (3D): xx \in [-l, l]^3
50: //
51: // Local physical coordinates on the manifold (2D): x \in [-l, l]^2
52: //
53: // Change of coordinates matrix computed by the library:
54: // (physical 3D coords relative to reference 2D coords)
55: // dxx_j/dX_i (indicial notation) [3 * 2]
56: //
57: // Change of coordinates x (physical 2D) relative to xx (phyisical 3D):
58: // dx_i/dxx_j (indicial notation) [2 * 3]
59: //
60: // Change of coordinates x (physical 2D) relative to X (reference 2D):
61: // (by chain rule)
62: // dx_i/dX_j = dx_i/dxx_k * dxx_k/dX_j
63: //
64: // The quadrature data is stored in the array qdata.
65: //
66: // We require the determinant of the Jacobian to properly compute integrals of the form: int(u v)
67: //
68: // Qdata: w * det(dx_i/dX_j)
69: */
70: CEED_QFUNCTION(SetupMassGeoCube)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out)
71: {
72: const CeedScalar *J = in[1], *w = in[2];
73: CeedScalar *qdata = out[0];
75: CeedPragmaSIMD for (CeedInt i = 0; i < Q; ++i)
76: {
77: // Read dxxdX Jacobian entries, stored as [[0 3], [1 4], [2 5]]
78: const CeedScalar dxxdX[3][2] = {
79: {J[i + Q * 0], J[i + Q * 3]},
80: {J[i + Q * 1], J[i + Q * 4]},
81: {J[i + Q * 2], J[i + Q * 5]}
82: };
83: // Modulus of dxxdX column vectors
84: const CeedScalar modg1 = PetscSqrtReal(dxxdX[0][0] * dxxdX[0][0] + dxxdX[1][0] * dxxdX[1][0] + dxxdX[2][0] * dxxdX[2][0]);
85: const CeedScalar modg2 = PetscSqrtReal(dxxdX[0][1] * dxxdX[0][1] + dxxdX[1][1] * dxxdX[1][1] + dxxdX[2][1] * dxxdX[2][1]);
86: // Use normalized column vectors of dxxdX as rows of dxdxx
87: const CeedScalar dxdxx[2][3] = {
88: {dxxdX[0][0] / modg1, dxxdX[1][0] / modg1, dxxdX[2][0] / modg1},
89: {dxxdX[0][1] / modg2, dxxdX[1][1] / modg2, dxxdX[2][1] / modg2}
90: };
92: CeedScalar dxdX[2][2];
93: for (int j = 0; j < 2; ++j)
94: for (int k = 0; k < 2; ++k) {
95: dxdX[j][k] = 0;
96: for (int l = 0; l < 3; ++l) dxdX[j][k] += dxdxx[j][l] * dxxdX[l][k];
97: }
98: qdata[i + Q * 0] = (dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]) * w[i]; /* det J * weight */
99: }
100: return 0;
101: }
103: /*
104: // Reference (parent) 2D coordinates: X \in [-1, 1]^2
105: //
106: // Global 3D physical coordinates given by the mesh: xx \in [-R, R]^3
107: // with R radius of the sphere
108: //
109: // Local 3D physical coordinates on the 2D manifold: x \in [-l, l]^3
110: // with l half edge of the cube inscribed in the sphere
111: //
112: // Change of coordinates matrix computed by the library:
113: // (physical 3D coords relative to reference 2D coords)
114: // dxx_j/dX_i (indicial notation) [3 * 2]
115: //
116: // Change of coordinates x (on the 2D manifold) relative to xx (phyisical 3D):
117: // dx_i/dxx_j (indicial notation) [3 * 3]
118: //
119: // Change of coordinates x (on the 2D manifold) relative to X (reference 2D):
120: // (by chain rule)
121: // dx_i/dX_j = dx_i/dxx_k * dxx_k/dX_j [3 * 2]
122: //
123: // modJ is given by the magnitude of the cross product of the columns of dx_i/dX_j
124: //
125: // The quadrature data is stored in the array qdata.
126: //
127: // We require the determinant of the Jacobian to properly compute integrals of
128: // the form: int(u v)
129: //
130: // Qdata: modJ * w
131: */
132: CEED_QFUNCTION(SetupMassGeoSphere)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out)
133: {
134: const CeedScalar *X = in[0], *J = in[1], *w = in[2];
135: CeedScalar *qdata = out[0];
137: CeedPragmaSIMD for (CeedInt i = 0; i < Q; ++i)
138: {
139: const CeedScalar xx[3][1] = {{X[i + 0 * Q]}, {X[i + 1 * Q]}, {X[i + 2 * Q]}};
140: // Read dxxdX Jacobian entries, stored as [[0 3], [1 4], [2 5]]
141: const CeedScalar dxxdX[3][2] = {
142: {J[i + Q * 0], J[i + Q * 3]},
143: {J[i + Q * 1], J[i + Q * 4]},
144: {J[i + Q * 2], J[i + Q * 5]}
145: };
146: // Setup
147: const CeedScalar modxxsq = xx[0][0] * xx[0][0] + xx[1][0] * xx[1][0] + xx[2][0] * xx[2][0];
148: CeedScalar xxsq[3][3];
149: for (int j = 0; j < 3; ++j)
150: for (int k = 0; k < 3; ++k) {
151: xxsq[j][k] = 0.;
152: for (int l = 0; l < 1; ++l) xxsq[j][k] += xx[j][l] * xx[k][l] / (sqrt(modxxsq) * modxxsq);
153: }
155: const CeedScalar dxdxx[3][3] = {
156: {1. / sqrt(modxxsq) - xxsq[0][0], -xxsq[0][1], -xxsq[0][2] },
157: {-xxsq[1][0], 1. / sqrt(modxxsq) - xxsq[1][1], -xxsq[1][2] },
158: {-xxsq[2][0], -xxsq[2][1], 1. / sqrt(modxxsq) - xxsq[2][2]}
159: };
161: CeedScalar dxdX[3][2];
162: for (int j = 0; j < 3; ++j)
163: for (int k = 0; k < 2; ++k) {
164: dxdX[j][k] = 0.;
165: for (int l = 0; l < 3; ++l) dxdX[j][k] += dxdxx[j][l] * dxxdX[l][k];
166: }
167: // J is given by the cross product of the columns of dxdX
168: const CeedScalar J[3][1] = {{dxdX[1][0] * dxdX[2][1] - dxdX[2][0] * dxdX[1][1]}, {dxdX[2][0] * dxdX[0][1] - dxdX[0][0] * dxdX[2][1]}, {dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]}};
169: // Use the magnitude of J as our detJ (volume scaling factor)
170: const CeedScalar modJ = sqrt(J[0][0] * J[0][0] + J[1][0] * J[1][0] + J[2][0] * J[2][0]);
171: qdata[i + Q * 0] = modJ * w[i];
172: }
173: return 0;
174: }
176: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *ctx)
177: {
178: DMPlexShape shape = DM_SHAPE_UNKNOWN;
181: PetscOptionsBegin(comm, "", "libCEED Test Options", "DMPLEX");
182: PetscOptionsEnd();
183: PetscOptionsGetEnum(NULL, NULL, "-dm_plex_shape", DMPlexShapes, (PetscEnum *)&shape, NULL);
184: ctx->setupgeo = NULL;
185: ctx->setupgeofname = NULL;
186: ctx->apply = Mass;
187: ctx->applyfname = Mass_loc;
188: ctx->areaExact = 0.0;
189: switch (shape) {
190: case DM_SHAPE_BOX_SURFACE:
191: ctx->setupgeo = SetupMassGeoCube;
192: ctx->setupgeofname = SetupMassGeoCube_loc;
193: ctx->areaExact = 6.0;
194: break;
195: case DM_SHAPE_SPHERE:
196: ctx->setupgeo = SetupMassGeoSphere;
197: ctx->setupgeofname = SetupMassGeoSphere_loc;
198: ctx->areaExact = 4.0 * M_PI;
199: break;
200: default:
201: break;
202: }
203: return 0;
204: }
206: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *ctx, DM *dm)
207: {
208: DMCreate(comm, dm);
209: DMSetType(*dm, DMPLEX);
210: DMSetFromOptions(*dm);
211: DMViewFromOptions(*dm, NULL, "-dm_view");
212: #ifdef PETSC_HAVE_LIBCEED
213: {
214: Ceed ceed;
215: const char *usedresource;
217: DMGetCeed(*dm, &ceed);
218: CeedGetResource(ceed, &usedresource);
219: PetscPrintf(PetscObjectComm((PetscObject)*dm), "libCEED Backend: %s\n", usedresource);
220: }
221: #endif
222: return 0;
223: }
225: static PetscErrorCode SetupDiscretization(DM dm)
226: {
227: DM cdm;
228: PetscFE fe, cfe;
229: PetscInt dim, cnc;
230: PetscBool simplex;
233: DMGetDimension(dm, &dim);
234: DMPlexIsSimplex(dm, &simplex);
235: PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, NULL, PETSC_DETERMINE, &fe);
236: PetscFESetName(fe, "indicator");
237: DMAddField(dm, NULL, (PetscObject)fe);
238: PetscFEDestroy(&fe);
239: DMCreateDS(dm);
240: DMPlexSetClosurePermutationTensor(dm, PETSC_DETERMINE, NULL);
241: DMGetCoordinateDim(dm, &cnc);
242: PetscFECreateDefault(PETSC_COMM_SELF, dim, cnc, simplex, NULL, PETSC_DETERMINE, &cfe);
243: DMProjectCoordinates(dm, cfe);
244: PetscFEDestroy(&cfe);
245: DMGetCoordinateDM(dm, &cdm);
246: DMPlexSetClosurePermutationTensor(cdm, PETSC_DETERMINE, NULL);
247: return 0;
248: }
250: static PetscErrorCode LibCeedSetupByDegree(DM dm, AppCtx *ctx, CeedData *data)
251: {
252: PetscDS ds;
253: PetscFE fe, cfe;
254: Ceed ceed;
255: CeedElemRestriction Erestrictx, Erestrictu, Erestrictq;
256: CeedQFunction qf_setupgeo;
257: CeedOperator op_setupgeo;
258: CeedVector xcoord;
259: CeedBasis basisu, basisx;
260: CeedInt Nqdata = 1;
261: CeedInt nqpts, nqptsx;
262: DM cdm;
263: Vec coords;
264: const PetscScalar *coordArray;
265: PetscInt dim, cdim, cStart, cEnd, Ncell;
268: DMGetCeed(dm, &ceed);
269: DMGetDimension(dm, &dim);
270: DMGetCoordinateDim(dm, &cdim);
271: DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
272: Ncell = cEnd - cStart;
273: // CEED bases
274: DMGetDS(dm, &ds);
275: PetscDSGetDiscretization(ds, 0, (PetscObject *)&fe);
276: PetscFEGetCeedBasis(fe, &basisu);
277: DMGetCoordinateDM(dm, &cdm);
278: DMGetDS(cdm, &ds);
279: PetscDSGetDiscretization(ds, 0, (PetscObject *)&cfe);
280: PetscFEGetCeedBasis(cfe, &basisx);
282: DMPlexGetCeedRestriction(cdm, NULL, 0, 0, 0, &Erestrictx);
283: DMPlexGetCeedRestriction(dm, NULL, 0, 0, 0, &Erestrictu);
284: CeedBasisGetNumQuadraturePoints(basisu, &nqpts);
285: CeedBasisGetNumQuadraturePoints(basisx, &nqptsx);
287: CeedElemRestrictionCreateStrided(ceed, Ncell, nqpts, Nqdata, Nqdata * Ncell * nqpts, CEED_STRIDES_BACKEND, &Erestrictq);
289: DMGetCoordinatesLocal(dm, &coords);
290: VecGetArrayRead(coords, &coordArray);
291: CeedElemRestrictionCreateVector(Erestrictx, &xcoord, NULL);
292: CeedVectorSetArray(xcoord, CEED_MEM_HOST, CEED_COPY_VALUES, (PetscScalar *)coordArray);
293: VecRestoreArrayRead(coords, &coordArray);
295: // Create the vectors that will be needed in setup and apply
296: CeedElemRestrictionCreateVector(Erestrictu, &data->uceed, NULL);
297: CeedElemRestrictionCreateVector(Erestrictu, &data->vceed, NULL);
298: CeedElemRestrictionCreateVector(Erestrictq, &data->qdata, NULL);
300: // Create the Q-function that builds the operator (i.e. computes its quadrature data) and set its context data
301: CeedQFunctionCreateInterior(ceed, 1, ctx->setupgeo, ctx->setupgeofname, &qf_setupgeo);
302: CeedQFunctionAddInput(qf_setupgeo, "x", cdim, CEED_EVAL_INTERP);
303: CeedQFunctionAddInput(qf_setupgeo, "dx", cdim * dim, CEED_EVAL_GRAD);
304: CeedQFunctionAddInput(qf_setupgeo, "weight", 1, CEED_EVAL_WEIGHT);
305: CeedQFunctionAddOutput(qf_setupgeo, "qdata", Nqdata, CEED_EVAL_NONE);
307: // Set up the mass operator
308: CeedQFunctionCreateInterior(ceed, 1, ctx->apply, ctx->applyfname, &data->qf_apply);
309: CeedQFunctionAddInput(data->qf_apply, "u", 1, CEED_EVAL_INTERP);
310: CeedQFunctionAddInput(data->qf_apply, "qdata", Nqdata, CEED_EVAL_NONE);
311: CeedQFunctionAddOutput(data->qf_apply, "v", 1, CEED_EVAL_INTERP);
313: // Create the operator that builds the quadrature data for the operator
314: CeedOperatorCreate(ceed, qf_setupgeo, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_setupgeo);
315: CeedOperatorSetField(op_setupgeo, "x", Erestrictx, basisx, CEED_VECTOR_ACTIVE);
316: CeedOperatorSetField(op_setupgeo, "dx", Erestrictx, basisx, CEED_VECTOR_ACTIVE);
317: CeedOperatorSetField(op_setupgeo, "weight", CEED_ELEMRESTRICTION_NONE, basisx, CEED_VECTOR_NONE);
318: CeedOperatorSetField(op_setupgeo, "qdata", Erestrictq, CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
320: // Create the mass operator
321: CeedOperatorCreate(ceed, data->qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &data->op_apply);
322: CeedOperatorSetField(data->op_apply, "u", Erestrictu, basisu, CEED_VECTOR_ACTIVE);
323: CeedOperatorSetField(data->op_apply, "qdata", Erestrictq, CEED_BASIS_COLLOCATED, data->qdata);
324: CeedOperatorSetField(data->op_apply, "v", Erestrictu, basisu, CEED_VECTOR_ACTIVE);
326: // Setup qdata
327: CeedOperatorApply(op_setupgeo, xcoord, data->qdata, CEED_REQUEST_IMMEDIATE);
329: CeedElemRestrictionDestroy(&Erestrictq);
330: CeedQFunctionDestroy(&qf_setupgeo);
331: CeedOperatorDestroy(&op_setupgeo);
332: CeedVectorDestroy(&xcoord);
333: return 0;
334: }
336: int main(int argc, char **argv)
337: {
338: MPI_Comm comm;
339: DM dm;
340: AppCtx ctx;
341: Vec U, Uloc, V, Vloc;
342: PetscScalar *v;
343: PetscScalar area;
344: CeedData ceeddata;
347: PetscInitialize(&argc, &argv, NULL, help);
348: comm = PETSC_COMM_WORLD;
349: ProcessOptions(comm, &ctx);
350: CreateMesh(comm, &ctx, &dm);
351: SetupDiscretization(dm);
353: LibCeedSetupByDegree(dm, &ctx, &ceeddata);
355: DMCreateGlobalVector(dm, &U);
356: DMCreateLocalVector(dm, &Uloc);
357: VecDuplicate(U, &V);
358: VecDuplicate(Uloc, &Vloc);
360: /**/
361: VecSet(Uloc, 1.);
362: VecZeroEntries(V);
363: VecZeroEntries(Vloc);
364: VecGetArray(Vloc, &v);
365: CeedVectorSetArray(ceeddata.vceed, CEED_MEM_HOST, CEED_USE_POINTER, v);
366: CeedVectorSetValue(ceeddata.uceed, 1.0);
367: CeedOperatorApply(ceeddata.op_apply, ceeddata.uceed, ceeddata.vceed, CEED_REQUEST_IMMEDIATE);
368: CeedVectorTakeArray(ceeddata.vceed, CEED_MEM_HOST, NULL);
369: VecRestoreArray(Vloc, &v);
370: DMLocalToGlobalBegin(dm, Vloc, ADD_VALUES, V);
371: DMLocalToGlobalEnd(dm, Vloc, ADD_VALUES, V);
373: VecSum(V, &area);
374: if (ctx.areaExact > 0.) {
375: PetscReal error = PetscAbsReal(area - ctx.areaExact);
376: PetscReal tol = PETSC_SMALL;
378: PetscPrintf(comm, "Exact mesh surface area : % .*f\n", PetscAbsReal(ctx.areaExact - round(ctx.areaExact)) > 1E-15 ? 14 : 1, (double)ctx.areaExact);
379: PetscPrintf(comm, "Computed mesh surface area : % .*f\n", PetscAbsScalar(area - round(area)) > 1E-15 ? 14 : 1, (double)PetscRealPart(area));
380: if (error > tol) {
381: PetscPrintf(comm, "Area error : % .14g\n", (double)error);
382: } else {
383: PetscPrintf(comm, "Area verifies!\n");
384: }
385: }
387: CeedDataDestroy(&ceeddata);
388: VecDestroy(&U);
389: VecDestroy(&Uloc);
390: VecDestroy(&V);
391: VecDestroy(&Vloc);
392: DMDestroy(&dm);
393: return PetscFinalize();
394: }
396: /*TEST
398: build:
399: requires: libceed
401: testset:
402: args: -dm_plex_simplex 0 -petscspace_degree 3 -dm_view -dm_petscds_view \
403: -petscfe_default_quadrature_order 4 -coord_dm_default_quadrature_order 4
405: test:
406: suffix: cube_3
407: args: -dm_plex_shape box_surface -dm_refine 2
409: test:
410: suffix: cube_3_p4
411: nsize: 4
412: args: -petscpartitioner_type simple -dm_refine_pre 1 -dm_plex_shape box_surface -dm_refine 1
414: test:
415: suffix: sphere_3
416: args: -dm_plex_shape sphere -dm_refine 3
418: test:
419: suffix: sphere_3_p4
420: nsize: 4
421: args: -petscpartitioner_type simple -dm_refine_pre 1 -dm_plex_shape sphere -dm_refine 2
423: TEST*/