Actual source code: ex28.c
1: static char help[] = "Example application of the Bhatnagar-Gross-Krook (BGK) collision operator.\n\
2: This example is a 0D-1V setting for the kinetic equation\n\
3: https://en.wikipedia.org/wiki/Bhatnagar%E2%80%93Gross%E2%80%93Krook_operator\n";
5: #include <petscdmplex.h>
6: #include <petscdmswarm.h>
7: #include <petscts.h>
8: #include <petscdraw.h>
9: #include <petscviewer.h>
11: typedef struct {
12: PetscInt particlesPerCell; /* The number of partices per cell */
13: PetscReal momentTol; /* Tolerance for checking moment conservation */
14: PetscBool monitorhg; /* Flag for using the TS histogram monitor */
15: PetscBool monitorsp; /* Flag for using the TS scatter monitor */
16: PetscBool monitorks; /* Monitor to perform KS test to the maxwellian */
17: PetscBool error; /* Flag for printing the error */
18: PetscInt ostep; /* print the energy at each ostep time steps */
19: PetscDraw draw; /* The draw object for histogram monitoring */
20: PetscDrawHG drawhg; /* The histogram draw context for monitoring */
21: PetscDrawSP drawsp; /* The scatter plot draw context for the monitor */
22: PetscDrawSP drawks; /* Scatterplot draw context for KS test */
23: } AppCtx;
25: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
26: {
27: PetscFunctionBeginUser;
28: options->monitorhg = PETSC_FALSE;
29: options->monitorsp = PETSC_FALSE;
30: options->monitorks = PETSC_FALSE;
31: options->particlesPerCell = 1;
32: options->momentTol = 100.0 * PETSC_MACHINE_EPSILON;
33: options->ostep = 100;
35: PetscOptionsBegin(comm, "", "Collision Options", "DMPLEX");
36: PetscCall(PetscOptionsBool("-monitorhg", "Flag to use the TS histogram monitor", "ex28.c", options->monitorhg, &options->monitorhg, NULL));
37: PetscCall(PetscOptionsBool("-monitorsp", "Flag to use the TS scatter plot monitor", "ex28.c", options->monitorsp, &options->monitorsp, NULL));
38: PetscCall(PetscOptionsBool("-monitorks", "Flag to plot KS test results", "ex28.c", options->monitorks, &options->monitorks, NULL));
39: PetscCall(PetscOptionsInt("-particles_per_cell", "Number of particles per cell", "ex28.c", options->particlesPerCell, &options->particlesPerCell, NULL));
40: PetscCall(PetscOptionsInt("-output_step", "Number of time steps between output", "ex28.c", options->ostep, &options->ostep, NULL));
41: PetscOptionsEnd();
42: PetscFunctionReturn(PETSC_SUCCESS);
43: }
45: /* Create the mesh for velocity space */
46: static PetscErrorCode CreateMesh(MPI_Comm comm, DM *dm, AppCtx *user)
47: {
48: PetscFunctionBeginUser;
49: PetscCall(DMCreate(comm, dm));
50: PetscCall(DMSetType(*dm, DMPLEX));
51: PetscCall(DMSetFromOptions(*dm));
52: PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
53: PetscFunctionReturn(PETSC_SUCCESS);
54: }
56: /* Since we are putting the same number of particles in each cell, this amounts to a uniform distribution of v */
57: static PetscErrorCode SetInitialCoordinates(DM sw)
58: {
59: AppCtx *user;
60: PetscRandom rnd;
61: DM dm;
62: DMPolytopeType ct;
63: PetscBool simplex;
64: PetscReal *centroid, *coords, *xi0, *v0, *J, *invJ, detJ, *vals;
65: PetscInt dim, d, cStart, cEnd, c, Np, p;
67: PetscFunctionBeginUser;
68: PetscCall(PetscRandomCreate(PetscObjectComm((PetscObject)sw), &rnd));
69: PetscCall(PetscRandomSetInterval(rnd, -1.0, 1.0));
70: PetscCall(PetscRandomSetFromOptions(rnd));
72: PetscCall(DMGetApplicationContext(sw, &user));
73: Np = user->particlesPerCell;
74: PetscCall(DMGetDimension(sw, &dim));
75: PetscCall(DMSwarmGetCellDM(sw, &dm));
76: PetscCall(DMGetCoordinatesLocalSetUp(dm));
77: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
78: PetscCall(DMPlexGetCellType(dm, cStart, &ct));
79: simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct) + 1 ? PETSC_TRUE : PETSC_FALSE;
80: PetscCall(PetscMalloc5(dim, ¢roid, dim, &xi0, dim, &v0, dim * dim, &J, dim * dim, &invJ));
81: for (d = 0; d < dim; ++d) xi0[d] = -1.0;
82: PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
83: PetscCall(DMSwarmGetField(sw, "w_q", NULL, NULL, (void **)&vals));
84: for (c = cStart; c < cEnd; ++c) {
85: if (Np == 1) {
86: PetscCall(DMPlexComputeCellGeometryFVM(dm, c, NULL, centroid, NULL));
87: for (d = 0; d < dim; ++d) {
88: coords[c * dim + d] = centroid[d];
89: if ((coords[c * dim + d] >= -1) && (coords[c * dim + d] <= 1)) {
90: vals[c] = 1.0;
91: } else {
92: vals[c] = 0.;
93: }
94: }
95: } else {
96: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ)); /* affine */
97: for (p = 0; p < Np; ++p) {
98: const PetscInt n = c * Np + p;
99: PetscReal sum = 0.0, refcoords[3];
101: for (d = 0; d < dim; ++d) {
102: PetscCall(PetscRandomGetValueReal(rnd, &refcoords[d]));
103: sum += refcoords[d];
104: }
105: if (simplex && sum > 0.0)
106: for (d = 0; d < dim; ++d) refcoords[d] -= PetscSqrtReal(dim) * sum;
107: vals[n] = 1.0;
108: PetscCall(DMPlexReferenceToCoordinates(dm, c, 1, refcoords, &coords[n * dim]));
109: }
110: }
111: }
112: PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
113: PetscCall(DMSwarmRestoreField(sw, "w_q", NULL, NULL, (void **)&vals));
114: PetscCall(PetscFree5(centroid, xi0, v0, J, invJ));
115: PetscCall(PetscRandomDestroy(&rnd));
116: PetscFunctionReturn(PETSC_SUCCESS);
117: }
119: /* The initial conditions are just the initial particle weights */
120: static PetscErrorCode SetInitialConditions(DM dmSw, Vec u)
121: {
122: DM dm;
123: AppCtx *user;
124: PetscReal *vals;
125: PetscScalar *initialConditions;
126: PetscInt dim, d, cStart, cEnd, c, Np, p, n;
128: PetscFunctionBeginUser;
129: PetscCall(VecGetLocalSize(u, &n));
130: PetscCall(DMGetApplicationContext(dmSw, &user));
131: Np = user->particlesPerCell;
132: PetscCall(DMSwarmGetCellDM(dmSw, &dm));
133: PetscCall(DMGetDimension(dm, &dim));
134: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
135: PetscCheck(n == (cEnd - cStart) * Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "TS solution local size %" PetscInt_FMT " != %" PetscInt_FMT " nm particles", n, (cEnd - cStart) * Np);
136: PetscCall(DMSwarmGetField(dmSw, "w_q", NULL, NULL, (void **)&vals));
137: PetscCall(VecGetArray(u, &initialConditions));
138: for (c = cStart; c < cEnd; ++c) {
139: for (p = 0; p < Np; ++p) {
140: const PetscInt n = c * Np + p;
141: for (d = 0; d < dim; d++) initialConditions[n] = vals[n];
142: }
143: }
144: PetscCall(VecRestoreArray(u, &initialConditions));
145: PetscCall(DMSwarmRestoreField(dmSw, "w_q", NULL, NULL, (void **)&vals));
146: PetscFunctionReturn(PETSC_SUCCESS);
147: }
149: static PetscErrorCode CreateParticles(DM dm, DM *sw, AppCtx *user)
150: {
151: PetscInt *cellid;
152: PetscInt dim, cStart, cEnd, c, Np = user->particlesPerCell, p;
154: PetscFunctionBeginUser;
155: PetscCall(DMGetDimension(dm, &dim));
156: PetscCall(DMCreate(PetscObjectComm((PetscObject)dm), sw));
157: PetscCall(DMSetType(*sw, DMSWARM));
158: PetscCall(DMSetDimension(*sw, dim));
159: PetscCall(DMSwarmSetType(*sw, DMSWARM_PIC));
160: PetscCall(DMSwarmSetCellDM(*sw, dm));
161: PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "kinematics", dim, PETSC_REAL));
162: PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "w_q", 1, PETSC_SCALAR));
163: PetscCall(DMSwarmFinalizeFieldRegister(*sw));
164: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
165: PetscCall(DMSwarmSetLocalSizes(*sw, (cEnd - cStart) * Np, 0));
166: PetscCall(DMSetFromOptions(*sw));
167: PetscCall(DMSwarmGetField(*sw, DMSwarmPICField_cellid, NULL, NULL, (void **)&cellid));
168: for (c = cStart; c < cEnd; ++c) {
169: for (p = 0; p < Np; ++p) {
170: const PetscInt n = c * Np + p;
171: cellid[n] = c;
172: }
173: }
174: PetscCall(DMSwarmRestoreField(*sw, DMSwarmPICField_cellid, NULL, NULL, (void **)&cellid));
175: PetscCall(PetscObjectSetName((PetscObject)*sw, "Particles"));
176: PetscCall(DMViewFromOptions(*sw, NULL, "-sw_view"));
177: PetscFunctionReturn(PETSC_SUCCESS);
178: }
180: /*
181: f_t = 1/\tau \left( f_eq - f \right)
182: n_t = 1/\tau \left( \int f_eq - \int f \right) = 1/\tau (n - n) = 0
183: v_t = 1/\tau \left( \int v f_eq - \int v f \right) = 1/\tau (v - v) = 0
184: E_t = 1/\tau \left( \int v^2 f_eq - \int v^2 f \right) = 1/\tau (T - T) = 0
186: Let's look at a single cell:
188: \int_C f_t = 1/\tau \left( \int_C f_eq - \int_C f \right)
189: \sum_{x_i \in C} w^i_t = 1/\tau \left( F_eq(C) - \sum_{x_i \in C} w_i \right)
190: */
192: /* This computes the 1D Maxwellian distribution for given mass n, velocity v, and temperature T */
193: static PetscReal ComputePDF(PetscReal m, PetscReal n, PetscReal T, PetscReal v[])
194: {
195: return (n / PetscSqrtReal(2.0 * PETSC_PI * T / m)) * PetscExpReal(-0.5 * m * PetscSqr(v[0]) / T);
196: }
198: /*
199: erf z = \frac{2}{\sqrt\pi} \int^z_0 dt e^{-t^2} and erf \infty = 1
201: We begin with our distribution
203: \sqrt{\frac{m}{2 \pi T}} e^{-m v^2/2T}
205: Let t = \sqrt{m/2T} v, z = \sqrt{m/2T} w, so that we now have
207: \sqrt{\frac{m}{2 \pi T}} \int^w_0 dv e^{-m v^2/2T}
208: = \sqrt{\frac{m}{2 \pi T}} \int^{\sqrt{m/2T} w}_0 \sqrt{2T/m} dt e^{-t^2}
209: = 1/\sqrt{\pi} \int^{\sqrt{m/2T} w}_0 dt e^{-t^2}
210: = 1/2 erf(\sqrt{m/2T} w)
211: */
212: static PetscReal ComputeCDF(PetscReal m, PetscReal n, PetscReal T, PetscReal va, PetscReal vb)
213: {
214: PetscReal alpha = PetscSqrtReal(0.5 * m / T);
215: PetscReal za = alpha * va;
216: PetscReal zb = alpha * vb;
217: PetscReal sum = 0.0;
219: sum += zb >= 0 ? erf(zb) : -erf(-zb);
220: sum -= za >= 0 ? erf(za) : -erf(-za);
221: return 0.5 * n * sum;
222: }
224: static PetscErrorCode CheckDistribution(DM dm, PetscReal m, PetscReal n, PetscReal T, PetscReal v[])
225: {
226: PetscSection coordSection;
227: Vec coordsLocal;
228: PetscReal *xq, *wq;
229: PetscReal vmin, vmax, neq, veq, Teq;
230: PetscInt Nq = 100, q, cStart, cEnd, c;
232: PetscFunctionBeginUser;
233: PetscCall(DMGetBoundingBox(dm, &vmin, &vmax));
234: /* Check analytic over entire line */
235: neq = ComputeCDF(m, n, T, vmin, vmax);
236: PetscCheck(PetscAbsReal(neq - n) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Int f %g != %g mass (%g)", (double)neq, (double)n, (double)(neq - n));
237: /* Check analytic over cells */
238: PetscCall(DMGetCoordinatesLocal(dm, &coordsLocal));
239: PetscCall(DMGetCoordinateSection(dm, &coordSection));
240: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
241: neq = 0.0;
242: for (c = cStart; c < cEnd; ++c) {
243: PetscScalar *vcoords = NULL;
245: PetscCall(DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &vcoords));
246: neq += ComputeCDF(m, n, T, vcoords[0], vcoords[1]);
247: PetscCall(DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &vcoords));
248: }
249: PetscCheck(PetscAbsReal(neq - n) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell Int f %g != %g mass (%g)", (double)neq, (double)n, (double)(neq - n));
250: /* Check quadrature over entire line */
251: PetscCall(PetscMalloc2(Nq, &xq, Nq, &wq));
252: PetscCall(PetscDTGaussQuadrature(100, vmin, vmax, xq, wq));
253: neq = 0.0;
254: for (q = 0; q < Nq; ++q) neq += ComputePDF(m, n, T, &xq[q]) * wq[q];
255: PetscCheck(PetscAbsReal(neq - n) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Int f %g != %g mass (%g)", (double)neq, (double)n, (double)(neq - n));
256: /* Check omemnts with quadrature */
257: veq = 0.0;
258: for (q = 0; q < Nq; ++q) veq += xq[q] * ComputePDF(m, n, T, &xq[q]) * wq[q];
259: veq /= neq;
260: PetscCheck(PetscAbsReal(veq - v[0]) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Int v f %g != %g velocity (%g)", (double)veq, (double)v[0], (double)(veq - v[0]));
261: Teq = 0.0;
262: for (q = 0; q < Nq; ++q) Teq += PetscSqr(xq[q]) * ComputePDF(m, n, T, &xq[q]) * wq[q];
263: Teq = Teq * m / neq - PetscSqr(veq);
264: PetscCheck(PetscAbsReal(Teq - T) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Int v^2 f %g != %g temperature (%g)", (double)Teq, (double)T, (double)(Teq - T));
265: PetscCall(PetscFree2(xq, wq));
266: PetscFunctionReturn(PETSC_SUCCESS);
267: }
269: static PetscErrorCode RHSFunctionParticles(TS ts, PetscReal t, Vec U, Vec R, void *ctx)
270: {
271: const PetscScalar *u;
272: PetscSection coordSection;
273: Vec coordsLocal;
274: PetscScalar *r, *coords;
275: PetscReal n = 0.0, v = 0.0, E = 0.0, T = 0.0, m = 1.0, cn = 0.0, cv = 0.0, cE = 0.0, pE = 0.0, eqE = 0.0;
276: PetscInt dim, d, Np, Ncp, p, cStart, cEnd, c;
277: DM dmSw, plex;
279: PetscFunctionBeginUser;
280: PetscCall(VecGetLocalSize(U, &Np));
281: PetscCall(VecGetArrayRead(U, &u));
282: PetscCall(VecGetArray(R, &r));
283: PetscCall(TSGetDM(ts, &dmSw));
284: PetscCall(DMSwarmGetCellDM(dmSw, &plex));
285: PetscCall(DMGetDimension(dmSw, &dim));
286: PetscCall(DMGetCoordinatesLocal(plex, &coordsLocal));
287: PetscCall(DMGetCoordinateSection(plex, &coordSection));
288: PetscCall(DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd));
289: Np /= dim;
290: Ncp = Np / (cEnd - cStart);
291: /* Calculate moments of particle distribution, note that velocity is in the coordinate */
292: PetscCall(DMSwarmGetField(dmSw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
293: for (p = 0; p < Np; ++p) {
294: PetscReal m1 = 0.0, m2 = 0.0;
296: for (d = 0; d < dim; ++d) {
297: m1 += PetscRealPart(coords[p * dim + d]);
298: m2 += PetscSqr(PetscRealPart(coords[p * dim + d]));
299: }
300: n += u[p];
301: v += u[p] * m1;
302: E += u[p] * m2;
303: }
304: v /= n;
305: T = E * m / n - v * v;
306: PetscCall(PetscInfo(ts, "Time %.2f: mass %.4f velocity: %+.4f temperature: %.4f\n", (double)t, (double)n, (double)v, (double)T));
307: PetscCall(CheckDistribution(plex, m, n, T, &v));
308: /*
309: Begin cellwise evaluation of the collision operator. Essentially, penalize the weights of the particles
310: in that cell against the maxwellian for the number of particles expected to be in that cell
311: */
312: for (c = cStart; c < cEnd; ++c) {
313: PetscScalar *vcoords = NULL;
314: PetscReal relaxation = 1.0, neq;
315: PetscInt sp = c * Ncp, q;
317: /* Calculate equilibrium occupation for this velocity cell */
318: PetscCall(DMPlexVecGetClosure(plex, coordSection, coordsLocal, c, NULL, &vcoords));
319: neq = ComputeCDF(m, n, T, vcoords[0], vcoords[1]);
320: PetscCall(DMPlexVecRestoreClosure(plex, coordSection, coordsLocal, c, NULL, &vcoords));
321: for (q = 0; q < Ncp; ++q) r[sp + q] = (1.0 / relaxation) * (neq - u[sp + q]);
322: }
323: /* Check update */
324: for (p = 0; p < Np; ++p) {
325: PetscReal m1 = 0.0, m2 = 0.0;
326: PetscScalar *vcoords = NULL;
328: for (d = 0; d < dim; ++d) {
329: m1 += PetscRealPart(coords[p * dim + d]);
330: m2 += PetscSqr(PetscRealPart(coords[p * dim + d]));
331: }
332: cn += r[p];
333: cv += r[p] * m1;
334: cE += r[p] * m2;
335: pE += u[p] * m2;
336: PetscCall(DMPlexVecGetClosure(plex, coordSection, coordsLocal, p, NULL, &vcoords));
337: eqE += ComputeCDF(m, n, T, vcoords[0], vcoords[1]) * m2;
338: PetscCall(DMPlexVecRestoreClosure(plex, coordSection, coordsLocal, p, NULL, &vcoords));
339: }
340: PetscCall(PetscInfo(ts, "Time %.2f: mass update %.8f velocity update: %+.8f energy update: %.8f (%.8f, %.8f)\n", (double)t, (double)cn, (double)cv, (double)cE, (double)pE, (double)eqE));
341: PetscCall(DMSwarmRestoreField(dmSw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
342: PetscCall(VecRestoreArrayRead(U, &u));
343: PetscCall(VecRestoreArray(R, &r));
344: PetscFunctionReturn(PETSC_SUCCESS);
345: }
347: static PetscErrorCode HGMonitor(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
348: {
349: AppCtx *user = (AppCtx *)ctx;
350: const PetscScalar *u;
351: DM sw, dm;
352: PetscInt dim, Np, p;
354: PetscFunctionBeginUser;
355: if (step < 0) PetscFunctionReturn(PETSC_SUCCESS);
356: if ((user->ostep > 0) && (!(step % user->ostep))) {
357: PetscDrawAxis axis;
359: PetscCall(TSGetDM(ts, &sw));
360: PetscCall(DMSwarmGetCellDM(sw, &dm));
361: PetscCall(DMGetDimension(dm, &dim));
362: PetscCall(PetscDrawHGReset(user->drawhg));
363: PetscCall(PetscDrawHGGetAxis(user->drawhg, &axis));
364: PetscCall(PetscDrawAxisSetLabels(axis, "Particles", "V", "f(V)"));
365: PetscCall(PetscDrawAxisSetLimits(axis, -3, 3, 0, 100));
366: PetscCall(PetscDrawHGSetLimits(user->drawhg, -3.0, 3.0, 0, 10));
367: PetscCall(VecGetLocalSize(U, &Np));
368: Np /= dim;
369: PetscCall(VecGetArrayRead(U, &u));
370: /* get points from solution vector */
371: for (p = 0; p < Np; ++p) PetscCall(PetscDrawHGAddValue(user->drawhg, u[p]));
372: PetscCall(PetscDrawHGDraw(user->drawhg));
373: PetscCall(VecRestoreArrayRead(U, &u));
374: }
375: PetscFunctionReturn(PETSC_SUCCESS);
376: }
378: static PetscErrorCode SPMonitor(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
379: {
380: AppCtx *user = (AppCtx *)ctx;
381: const PetscScalar *u;
382: PetscReal *v, *coords;
383: PetscInt Np, p;
384: DM dmSw;
386: PetscFunctionBeginUser;
387: if (step < 0) PetscFunctionReturn(PETSC_SUCCESS);
388: if ((user->ostep > 0) && (!(step % user->ostep))) {
389: PetscDrawAxis axis;
391: PetscCall(TSGetDM(ts, &dmSw));
392: PetscCall(PetscDrawSPReset(user->drawsp));
393: PetscCall(PetscDrawSPGetAxis(user->drawsp, &axis));
394: PetscCall(PetscDrawAxisSetLabels(axis, "Particles", "V", "w"));
395: PetscCall(VecGetLocalSize(U, &Np));
396: PetscCall(VecGetArrayRead(U, &u));
397: /* get points from solution vector */
398: PetscCall(PetscMalloc1(Np, &v));
399: for (p = 0; p < Np; ++p) v[p] = PetscRealPart(u[p]);
400: PetscCall(DMSwarmGetField(dmSw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
401: for (p = 0; p < Np - 1; ++p) PetscCall(PetscDrawSPAddPoint(user->drawsp, &coords[p], &v[p]));
402: PetscCall(PetscDrawSPDraw(user->drawsp, PETSC_TRUE));
403: PetscCall(VecRestoreArrayRead(U, &u));
404: PetscCall(DMSwarmRestoreField(dmSw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
405: PetscCall(PetscFree(v));
406: }
407: PetscFunctionReturn(PETSC_SUCCESS);
408: }
410: static PetscErrorCode KSConv(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
411: {
412: AppCtx *user = (AppCtx *)ctx;
413: const PetscScalar *u;
414: PetscScalar sup;
415: PetscReal *v, *coords, T = 0., vel = 0., step_cast, w_sum;
416: PetscInt dim, Np, p, cStart, cEnd;
417: DM sw, plex;
419: PetscFunctionBeginUser;
420: if (step < 0) PetscFunctionReturn(PETSC_SUCCESS);
421: if ((user->ostep > 0) && (!(step % user->ostep))) {
422: PetscDrawAxis axis;
423: PetscCall(PetscDrawSPGetAxis(user->drawks, &axis));
424: PetscCall(PetscDrawAxisSetLabels(axis, "Particles", "t", "D_n"));
425: PetscCall(PetscDrawSPSetLimits(user->drawks, 0., 100, 0., 3.5));
426: PetscCall(TSGetDM(ts, &sw));
427: PetscCall(VecGetLocalSize(U, &Np));
428: PetscCall(VecGetArrayRead(U, &u));
429: /* get points from solution vector */
430: PetscCall(PetscMalloc1(Np, &v));
431: PetscCall(DMSwarmGetCellDM(sw, &plex));
432: PetscCall(DMGetDimension(sw, &dim));
433: PetscCall(DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd));
434: for (p = 0; p < Np; ++p) v[p] = PetscRealPart(u[p]);
435: PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
436: w_sum = 0.;
437: for (p = 0; p < Np; ++p) {
438: w_sum += u[p];
439: T += u[p] * coords[p] * coords[p];
440: vel += u[p] * coords[p];
441: }
442: vel /= w_sum;
443: T = T / w_sum - vel * vel;
444: sup = 0.0;
445: for (p = 0; p < Np; ++p) {
446: PetscReal tmp = 0.;
447: tmp = PetscAbs(u[p] - ComputePDF(1.0, w_sum, T, &coords[p * dim]));
448: if (tmp > sup) sup = tmp;
449: }
450: step_cast = (PetscReal)step;
451: PetscCall(PetscDrawSPAddPoint(user->drawks, &step_cast, &sup));
452: PetscCall(PetscDrawSPDraw(user->drawks, PETSC_TRUE));
453: PetscCall(VecRestoreArrayRead(U, &u));
454: PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
455: PetscCall(PetscFree(v));
456: }
457: PetscFunctionReturn(PETSC_SUCCESS);
458: }
460: static PetscErrorCode InitializeSolve(TS ts, Vec u)
461: {
462: DM dm;
463: AppCtx *user;
465: PetscFunctionBeginUser;
466: PetscCall(TSGetDM(ts, &dm));
467: PetscCall(DMGetApplicationContext(dm, &user));
468: PetscCall(SetInitialCoordinates(dm));
469: PetscCall(SetInitialConditions(dm, u));
470: PetscFunctionReturn(PETSC_SUCCESS);
471: }
472: /*
473: A single particle is generated for each velocity space cell using the dmswarmpicfield_coor and is used to evaluate collisions in that cell.
474: 0 weight ghost particles are initialized outside of a small velocity domain to ensure the tails of the amxwellian are resolved.
475: */
476: int main(int argc, char **argv)
477: {
478: TS ts; /* nonlinear solver */
479: DM dm, sw; /* Velocity space mesh and Particle Swarm */
480: Vec u, w; /* swarm vector */
481: MPI_Comm comm;
482: AppCtx user;
484: PetscFunctionBeginUser;
485: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
486: comm = PETSC_COMM_WORLD;
487: PetscCall(ProcessOptions(comm, &user));
488: PetscCall(CreateMesh(comm, &dm, &user));
489: PetscCall(CreateParticles(dm, &sw, &user));
490: PetscCall(DMSetApplicationContext(sw, &user));
491: PetscCall(TSCreate(comm, &ts));
492: PetscCall(TSSetDM(ts, sw));
493: PetscCall(TSSetMaxTime(ts, 10.0));
494: PetscCall(TSSetTimeStep(ts, 0.01));
495: PetscCall(TSSetMaxSteps(ts, 100000));
496: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
497: if (user.monitorhg) {
498: PetscCall(PetscDrawCreate(comm, NULL, "monitor", 0, 0, 400, 300, &user.draw));
499: PetscCall(PetscDrawSetFromOptions(user.draw));
500: PetscCall(PetscDrawHGCreate(user.draw, 20, &user.drawhg));
501: PetscCall(PetscDrawHGSetColor(user.drawhg, 3));
502: PetscCall(TSMonitorSet(ts, HGMonitor, &user, NULL));
503: } else if (user.monitorsp) {
504: PetscCall(PetscDrawCreate(comm, NULL, "monitor", 0, 0, 400, 300, &user.draw));
505: PetscCall(PetscDrawSetFromOptions(user.draw));
506: PetscCall(PetscDrawSPCreate(user.draw, 1, &user.drawsp));
507: PetscCall(TSMonitorSet(ts, SPMonitor, &user, NULL));
508: } else if (user.monitorks) {
509: PetscCall(PetscDrawCreate(comm, NULL, "monitor", 0, 0, 400, 300, &user.draw));
510: PetscCall(PetscDrawSetFromOptions(user.draw));
511: PetscCall(PetscDrawSPCreate(user.draw, 1, &user.drawks));
512: PetscCall(TSMonitorSet(ts, KSConv, &user, NULL));
513: }
514: PetscCall(TSSetRHSFunction(ts, NULL, RHSFunctionParticles, &user));
515: PetscCall(TSSetFromOptions(ts));
516: PetscCall(TSSetComputeInitialCondition(ts, InitializeSolve));
517: PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "w_q", &w));
518: PetscCall(VecDuplicate(w, &u));
519: PetscCall(VecCopy(w, u));
520: PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "w_q", &w));
521: PetscCall(TSComputeInitialCondition(ts, u));
522: PetscCall(TSSolve(ts, u));
523: if (user.monitorhg) {
524: PetscCall(PetscDrawSave(user.draw));
525: PetscCall(PetscDrawHGDestroy(&user.drawhg));
526: PetscCall(PetscDrawDestroy(&user.draw));
527: }
528: if (user.monitorsp) {
529: PetscCall(PetscDrawSave(user.draw));
530: PetscCall(PetscDrawSPDestroy(&user.drawsp));
531: PetscCall(PetscDrawDestroy(&user.draw));
532: }
533: if (user.monitorks) {
534: PetscCall(PetscDrawSave(user.draw));
535: PetscCall(PetscDrawSPDestroy(&user.drawks));
536: PetscCall(PetscDrawDestroy(&user.draw));
537: }
538: PetscCall(VecDestroy(&u));
539: PetscCall(TSDestroy(&ts));
540: PetscCall(DMDestroy(&sw));
541: PetscCall(DMDestroy(&dm));
542: PetscCall(PetscFinalize());
543: return 0;
544: }
546: /*TEST
547: build:
548: requires: double !complex
549: test:
550: suffix: 1
551: args: -particles_per_cell 1 -output_step 10 -ts_type euler -dm_plex_dim 1 -dm_plex_box_faces 200 -dm_plex_box_lower -10 -dm_plex_box_upper 10 -dm_view -monitorsp
552: test:
553: suffix: 2
554: args: -particles_per_cell 1 -output_step 50 -ts_type euler -dm_plex_dim 1 -dm_plex_box_faces 200 -dm_plex_box_lower -10 -dm_plex_box_upper 10 -dm_view -monitorks
555: TEST*/