/* ******************************************************* * ( (u.\grad) phi_j, phi_i ) * return 1 value * */ FLOAT phgQuadDofDotGradBasBas(ELEMENT *e, DOF *u, DOF *v, int m, int n, int order) { int i; const FLOAT *g1, *g2, *gu, *w, *lambda; FLOAT d, d0; QUAD *quad; assert(u->dim == 3); if (order < 0) order = DofTypeOrder(u, e) + BasisOrder(v, e, m) - 1 + BasisOrder(v, e, n); if (order < 0) order = 0; quad = phgQuadGetQuad3D(order); gu = phgQuadGetDofValues(e, u, quad); g1 = phgQuadGetBasisGradient(e, v, m, quad); g2 = phgQuadGetBasisValues(e, v, n, quad); d = 0.; lambda = quad->points; w = quad->weights; for (i = 0; i < quad->npoints; i++) { d0 = 0.; d0 += (*(gu++)) * (*(g1++)) * (*(g2)); /* u dphi_m/dx phi_n */ d0 += (*(gu++)) * (*(g1++)) * (*(g2)); /* v dphi_m/dy phi_n */ d0 += (*(gu++)) * (*(g1++)) * (*(g2)); /* w dphi_m/dz phi_n */ g2++; d += d0 * (*(w++)); lambda += Dim + 1; } return d * phgGeomGetVolume(u->g, e); }
/* Dof norm for curved elements */ FLOAT dofNormL2(DOF *dof) { GRID *g = dof->g; SIMPLEX *e; FLOAT norm = 0; FLOAT a = 0, b = 0; int i, dim = DofDim(dof); ForAllElements(g, e) { QUAD *quad = phgQuadGetQuad3D(2*DofTypeOrder(dof, e)); FLOAT vol, det, v[dim]; const FLOAT *p, *w; int q; p = quad->points; w = quad->weights; for (q = 0; q < quad->npoints; q++) { phgGeomGetCurvedJacobianAtLambda(g, e, p, &det); vol = fabs(det / 6.); phgDofEval(dof, e, p, v); for (i = 0; i < dim; i++) norm += vol*(*w) * (v[i] * v[i]); w++; p += Dim+1; } }
/* *************************** * ( (u.\grad) u, phi_i ) * return 3 values. * */ void phgQuadDofDotGradDofBas(ELEMENT *e, DOF *u, DOF *gradu, int n, int order, FLOAT *values) { int i; const FLOAT *g2, *gu, *ggu, *w, *lambda; FLOAT d1, d2, d3, dd1, dd2, dd3, vol; QUAD *quad; assert(gradu->dim == 9 && u->dim == 3); if (order < 0) order = DofTypeOrder(u, e) + DofTypeOrder(gradu, e) + BasisOrder(u, e, n); if (order < 0) order = 0; quad = phgQuadGetQuad3D(order); gu = phgQuadGetDofValues(e, u, quad); ggu = phgQuadGetDofValues(e, gradu, quad); g2 = phgQuadGetBasisValues(e, u, n, quad); dd1 = dd2 = dd3 = 0.; lambda = quad->points; w = quad->weights; for (i = 0; i < quad->npoints; i++) { d1 = d2 = d3 = 0.; d1 += *(gu) * (*(ggu++)) * (*(g2)); /* u du/dx phi_n */ d1 += *(gu + 1) * (*(ggu++)) * (*(g2)); /* v du/dy phi_n */ d1 += *(gu + 2) * (*(ggu++)) * (*(g2)); /* w du/dz phi_n */ d2 += *(gu) * (*(ggu++)) * (*(g2)); /* u dv/dx phi_n */ d2 += *(gu + 1) * (*(ggu++)) * (*(g2)); /* v dv/dy phi_n */ d2 += *(gu + 2) * (*(ggu++)) * (*(g2)); /* w dv/dz phi_n */ d3 += *(gu) * (*(ggu++)) * (*(g2)); /* u dw/dx phi_n */ d3 += *(gu + 1) * (*(ggu++)) * (*(g2)); /* v dw/dy phi_n */ d3 += *(gu + 2) * (*(ggu++)) * (*(g2)); /* w dw/dz phi_n */ dd1 += d1 * (*w); dd2 += d2 * (*w); dd3 += d3 * (*w); gu += 3; g2++; w++; lambda += Dim + 1; } vol = phgGeomGetVolume(u->g, e); values[0] = dd1 * vol; values[1] = dd2 * vol; values[2] = dd3 * vol; return; }
/* ***************************** * (grad(u_3), grad(\phi)) * return 3 values. * */ void phgQuadGradDof3GradBas(ELEMENT *e, DOF *gradu, DOF *u, int m, int order, FLOAT *values) { int i; const FLOAT *g2, *gu, *w, *lambda; FLOAT d1, d2, d3, dd1, dd2, dd3, vol; QUAD *quad; assert(gradu->dim == 9 && u->dim == 3); if (order < 0) order = 2 * BasisOrder(u, e, m) - 1; if (order < 0) order = 0; quad = phgQuadGetQuad3D(order); gu = phgQuadGetDofValues(e, gradu, quad); g2 = phgQuadGetBasisGradient(e, u, m, quad); dd1 = dd2 = dd3 = 0.; lambda = quad->points; w = quad->weights; for (i = 0; i < quad->npoints; i++) { d1 = d2 = d3 = 0.; d1 += (*(gu++)) * (*(g2)); d1 += (*(gu++)) * (*(g2 + 1)); d1 += (*(gu++)) * (*(g2 + 2)); d2 += (*(gu++)) * (*(g2)); d2 += (*(gu++)) * (*(g2 + 1)); d2 += (*(gu++)) * (*(g2 + 2)); d3 += (*(gu++)) * (*(g2)); d3 += (*(gu++)) * (*(g2 + 1)); d3 += (*(gu++)) * (*(g2 + 2)); dd1 += d1 * (*w); dd2 += d2 * (*w); dd3 += d3 * (*w); g2 += 3; w++; lambda += Dim + 1; } vol = phgGeomGetVolume(u->g, e); values[0] = dd1 * vol; values[1] = dd2 * vol; values[2] = dd3 * vol; return; }
/* **************************************** * ( d[uvw]/d[xyz]*phi_j, phi_i ) * return static float[9] managed by user. * */ void phgQuadGradDofBasDotBas(ELEMENT *e, DOF *gradu, DOF *u, int m, int n, int order, FLOAT *value) { int i; const FLOAT *g1, *g2, *gu, *w, *lambda; FLOAT d[9], *pd, vol; QUAD *quad; assert(gradu->dim == 9 && u->dim == 3); if (order < 0) order = DofTypeOrder(gradu, e) + BasisOrder(u, e, m) + BasisOrder(u, e, n) ; if (order < 0) order = 0; quad = phgQuadGetQuad3D(order); gu = phgQuadGetDofValues(e, gradu, quad); g1 = phgQuadGetBasisValues(e, u, m, quad); g2 = phgQuadGetBasisValues(e, u, n, quad); lambda = quad->points; w = quad->weights; for (i = 0; i < 9; i++) d[i] = 0; for (i = 0; i < quad->npoints; i++) { pd = d; (*pd++) += (*(gu++)) * (*g1) * (*g2) * (*w); /* du/dx phi_m phi_n */ (*pd++) += (*(gu++)) * (*g1) * (*g2) * (*w); /* du/dy phi_m phi_n */ (*pd++) += (*(gu++)) * (*g1) * (*g2) * (*w); /* du/dz phi_m phi_n */ (*pd++) += (*(gu++)) * (*g1) * (*g2) * (*w); /* dv/dx phi_m phi_n */ (*pd++) += (*(gu++)) * (*g1) * (*g2) * (*w); /* dv/dy phi_m phi_n */ (*pd++) += (*(gu++)) * (*g1) * (*g2) * (*w); /* dv/dz phi_m phi_n */ (*pd++) += (*(gu++)) * (*g1) * (*g2) * (*w); /* dw/dx phi_m phi_n */ (*pd++) += (*(gu++)) * (*g1) * (*g2) * (*w); /* dw/dy phi_m phi_n */ (*pd++) += (*(gu++)) * (*g1) * (*g2) * (*w); /* dw/dz phi_m phi_n */ g1++; g2++; w++; lambda += Dim + 1; } vol = phgGeomGetVolume(u->g, e); for (i = 0; i < 9; i++) value[i] = d[i] * vol; return; }
/* ********************** * \grad phi_j \times \phi_i * return 3 values * */ void phgQuadGradBasDotBas3(ELEMENT *e, DOF *s, int m, DOF *v, int n, FLOAT *values, int order) { int i, j, nvalues = DofTypeDim(v); const FLOAT *g1, *g2, *w, *lambda; FLOAT d1, d2, d3, dd1, dd2, dd3; QUAD *quad; assert(!SpecialDofType(s->type) && !SpecialDofType(v->type)); if (nvalues != DofTypeDim(s)) phgError(1, "%s:%d, dimensions mismatch: grad(%s) <==> (%s)\n", __FILE__, __LINE__, s->name, v->name); if (order < 0) order = BasisOrder(s, e, m) - 1 + BasisOrder(v, e, n); if (order < 0) order = 0; quad = phgQuadGetQuad3D(order); g1 = phgQuadGetBasisGradient(e, s, m, quad); g2 = phgQuadGetBasisValues(e, v, n, quad); dd1 = 0.; dd2 = 0.; dd3 = 0.; lambda = quad->points; w = quad->weights; for (i = 0; i < quad->npoints; i++) { d1 = d2 = d3 = 0.; for (j = 0; j < nvalues; j++) { d1 += *(g1++) * *g2; d2 += *(g1++) * *g2; d3 += *(g1++) * *g2; g2++; } dd1 += d1 * *w; dd2 += d2 * *w; dd3 += d3 * *w; w++; lambda += Dim + 1; } values[0] = dd1 * phgGeomGetVolume(s->g, e); values[1] = dd2 * phgGeomGetVolume(s->g, e); values[2] = dd3 * phgGeomGetVolume(s->g, e); return; }
/* *********************** * p \times \grad \phi_m * return 3 values. * */ void phgQuadDofAGradBas3(ELEMENT *e, DOF *p, DOF *v, int m, int order, FLOAT *values) { int i, j; const FLOAT *g1, *g2, *w; FLOAT d1, d2, d3, vol; QUAD *quad; assert(!SpecialDofType(v->type)); assert(p->dim == 1); if (order < 0) { order = ((j = DofTypeOrder(p, e)) >= 0 ? j : BasisOrder(v, e, m)); order += BasisOrder(v, e, m) - 1; } quad = phgQuadGetQuad3D(order); g1 = phgQuadGetDofValues(e, p, quad); g2 = phgQuadGetBasisGradient(e, v, m, quad); w = quad->weights; d1 = d2 = d3 = 0.; for (i = 0; i < quad->npoints; i++) { d1 += *(g1) * (*g2++) * (*w); d2 += *(g1) * (*g2++) * (*w); d3 += *(g1) * (*g2++) * (*w); g1++; w++; } vol = phgGeomGetVolume(p->g, e); values[0] = d1 * vol; values[1] = d2 * vol; values[2] = d3 * vol; return; }
static void build_matrices(MAT *ma, MAT *mb, VEC *rhs_vec, DOF *u_h, DOF *f) /* build stiffness (ma) and mass (mb) matrices */ { int N = u_h->type->nbas; /* number of element basis functions */ int i, j, k, l; GRID *g = u_h->g; ELEMENT *e; FLOAT A[N][3][N][3], buffer[N], rhs[N][3], d; static FLOAT *B0 = NULL; FLOAT B[N][N]; INT I[N][3], J[3][N]; QUAD *quad = phgQuadGetQuad3D((u_h->type->order - 1) * 2); assert(u_h->type->dim == 1 && u_h->dim == 3); assert(mb == NULL || u_h->type->invariant); if (mb != NULL && B0 == NULL && g->nroot > 0) { /* (\int \phi_j\cdot\phi_i)/vol is independent of element */ FreeAtExit(B0); B0 = phgAlloc(N * N * sizeof(*B0)); e = g->roots; d = 1. / phgGeomGetVolume(g, e); for (i = 0; i < N; i++) for (j = 0; j <= i; j++) B0[i * N + j] = B0[i + j * N] = d * phgQuadBasDotBas(e, u_h, j, u_h, i, QUAD_DEFAULT); } ForAllElements(g, e) { d = phgGeomGetVolume(g, e) * rho; for (i = 0; i < N; i++) { for (k = 0; k < 3; k++) J[k][i] = I[i][k] = phgMapE2L(ma->rmap, 0, e, i * 3 + k); for (j = 0; j <= i; j++) { /* the stiffness matrix */ stiffness_matrix(e, u_h, i, j, E, nu, 3 * N, &A[i][0][j][0], quad); if (j != i) { for (k = 0; k < 3; k++) for (l = 0; l < 3; l++) A[j][k][i][l] = A[i][l][j][k]; } /* the mass matrix: \int \phi_i\cdot\phi_j */ if (mb != NULL) B[j][i] = B[i][j] = B0[i * N + j] * d; } } #if 0 /* print element stiffness matrix */ FLOAT *p = (void *)A; printf("vol = %0.16lg;\n", phgGeomGetVolume(g, e)); printf("a = [\n"); for (i = 0; i < 3 * N; i++) { for (j = 0; j < 3 * N; j++) printf("%0.16lg ", p[i * 3 * N + j]); printf("\n"); } printf("];\n"); printf("b = [\n"); for (i = 0; i < N; i++) for (k = 0; k < 3; k++) { for (j = 0; j < N; j++) for (l = 0; l < 3; l++) printf("%0.16lg ", l == k ? B[i][j] : 0.0); printf("\n"); } printf("];\n"); exit(0); #endif /* loop on basis functions */ for (i = 0; i < N; i++) { if (phgDofDirichletBC(u_h, e, i, func_g, buffer, rhs[i], DOF_PROJ_NONE)) { /* Dirichlet boundary */ for (k = 0; k < 3; k++) { phgMatAddEntries(ma, 1, I[i] + k, N, J[k], buffer); if (mb != NULL) phgMatAddEntries(mb, 1, I[i] + k, N, J[k], buffer); } } else { /* interior node */ phgMatAddEntries(ma, 3, I[i], 3 * N, I[0], &A[i][0][0][0]); if (mb == NULL) { phgQuadDofTimesBas(e, f, u_h, i, QUAD_DEFAULT, rhs[i]); for (k = 0; k < 3; k++) rhs[i][k] = -rhs[i][k]; } else { for (k = 0; k < 3; k++) phgMatAddEntries(mb, 1, I[i] + k, N, J[k], B[i]); } } } if (rhs_vec != NULL) phgVecAddEntries(rhs_vec, 0, N * 3, I[0], rhs[0]); }
/**************************************************************** * Build RHS which is the residual of the nonlinear system. ***************************************************************/ void phgNSBuildSolverURHS(NSSolver *ns) { GRID *g = ns->g; SIMPLEX *e; SOLVER *solver_u = ns->solver_u; int i, k, l, q, s; FLOAT *dt = ns->dt; BOOLEAN tstep_minus = (ns->u[-1] != NULL); VEC *vec_rhs = phgMapCreateVec(solver_u->rhs->map, 1); FLOAT Theta = _nsp->Theta, nu = _nsp->nu, Thet1; int viscosity_type = ns->viscosity_type; SURF_BAS *surf_bas = ns->surf_bas; DOF *surf_dof = surf_bas->dof; BOOLEAN *rotated = surf_bas->rotated; const FLOAT *Trans = DofData(surf_dof); #if STEADY_STATE assert(fabs(Theta - 1) < 1e-12); Thet1 = 0; Unused(Thet1); Unused(dt); #else Thet1 = 1 - Theta; Unused(dt); #endif /* STEADY_STATE */ phgPrintf(" DB_mask: ["); for (k = 0; k < Dim; k++) phgPrintf("%d ", ns->u[1]->DB_masks[k]); phgPrintf("] "); nu_max = -1e10; nu_min = +1e10; phgVecDisassemble(vec_rhs); ForAllElements(g, e) { int M = ns->u[1]->type->nbas; /* num of bases of Velocity */ int N = ns->p[1]->type->nbas; /* num of bases of Pressure */ int order = DofTypeOrder(ns->u[1], e) * 3 - 1; /* Note: * quad order is really high here, * highest order term (u \nabla u, phi) */ FLOAT bufu[M], bufp[N], rhsu[M][Dim], rhsp[N]; INT Iu[M][Dim], Ip[N]; QUAD *quad; FLOAT vol, area, det; const FLOAT *w, *p, *normal, **vu, *vu_queue[3], *vf[2], *gu[2], *vp[2], *vw, *vT; FLOAT *vf_cache[2]; vu = vu_queue + 1; quad = phgQuadGetQuad3D(order); vu[0] = phgQuadGetDofValues(e, ns->u[0], quad); /* u^{n} */ vp[0] = phgQuadGetDofValues(e, ns->p[0], quad); /* p^{n} */ gu[0] = phgQuadGetDofValues(e, ns->gradu[0], quad); /* grad u^{n} */ vw = phgQuadGetDofValues(e, ns->wind, quad); /* wind */ vT = phgQuadGetDofValues(e, ns->T[1], quad); /* T^{n} */ if (tstep_minus) { vu[-1] = phgQuadGetDofValues(e, ns->u[-1], quad); /* u^{n-1} */ } else { vu[-1] = vu[0]; } #if STEADY_STATE || TIME_DEP_NON vu[1] = phgQuadGetDofValues(e, ns->u[1], quad); /* u^{n+1} */ gu[1] = phgQuadGetDofValues(e, ns->gradu[1], quad); /* grad u^{n} */ vp[1] = phgQuadGetDofValues(e, ns->p[1], quad); /* p^{n+1} */ #else TIME_DEP_LINEAR_ENTRY; /* Unavailable */ #endif /* STEADY_STATE || TIME_DEP_NON */ Unused(l); Unused(vf); Unused(vf_cache); if (!_nsp->no_extern_source) { /* cache f values */ for (l = 0; l < 2; l++) { const FLOAT *cache; size_t cache_size; setFuncTime(ns->time[l]); /* set static time in ins-test.c */ /* cache f */ cache_size = Dim * quad->npoints * sizeof(FLOAT); cache = phgQuadGetFuncValues(g, e, Dim, func_f, quad); vf[l] = vf_cache[l] = phgAlloc(cache_size); memcpy(vf_cache[l], cache, cache_size); phgQuadGetFuncValues(NULL, NULL, 0, NULL, NULL); /* clear cache */ } } /* Global Matrix */ Bzero(rhsu); Bzero(rhsp); p = quad->points; w = quad->weights; for (q = 0; q < quad->npoints; q++) { phgGeomGetCurvedJacobianAtLambda(g, e, p, &det); vol = fabs(det / 6.); /* rhs u */ for (i = 0; i < M; i++) { /* interior node or Neumann */ const FLOAT *gi_u = phgQuadGetBasisValues(e, ns->u[1], i, quad) + q; /* phi_i */ const FLOAT *ggi_u = phgQuadGetBasisCurvedGradient(e, ns->u[1], i, quad, q); /* grad phi_i */ for (k = 0; k < Dim; k++) { #if ICE_BENCH_TEST nu = get_effective_viscosity(gu[1], 0, 0, viscosity_type); FLOAT eu[DDim]; MAT3_SYM(gu[1], eu); rhsu[i][k] += vol*(*w) * EQU_SCALING * (- nu * INNER_PRODUCT(eu+k*Dim, ggi_u) + (*vp[1]) * *(ggi_u+k) * LEN_SCALING * PRES_SCALING ); /* left */ if (k == Z_DIR) { const FLOAT rho = RHO_ICE; const FLOAT grav = GRAVITY; const FLOAT a = SEC_PER_YEAR; const FLOAT f = rho*grav * EQU_SCALING * LEN_SCALING2; Unused(a); rhsu[i][k] += vol*(*w) * (-f * (*gi_u) ); /* right */ } #elif ESIMINT_TEST || \ HEINO_TEST || \ TEST_CASE == ICE_GREEN_LAND nu = get_effective_viscosity(gu[1], *vT, 0, viscosity_type); FLOAT eu[DDim]; MAT3_SYM(gu[1], eu); rhsu[i][k] += vol*(*w) * EQU_SCALING * (- nu * INNER_PRODUCT(eu+k*Dim, ggi_u) + (*vp[1]) * *(ggi_u+k) * LEN_SCALING * PRES_SCALING ); /* left */ if (k == Z_DIR) { const FLOAT rho = RHO_ICE; const FLOAT grav = GRAVITY; const FLOAT a = SEC_PER_YEAR; const FLOAT f = rho*grav * EQU_SCALING * LEN_SCALING2; Unused(a); rhsu[i][k] += vol*(*w) * (-f * (*gi_u) ); /* right */ } #elif STEADY_STATE rhsu[i][k] += vol*(*w) * (- nu * INNER_PRODUCT(gu[1]+k*Dim, ggi_u) + (*vp[1]) * *(ggi_u+k) ); /* left */ if (!_nsp->no_extern_source) rhsu[i][k] += vol*(*w) * (*(vf[1]+k) * (*gi_u) ); /* right */ #elif TIME_DEP_NON rhsu[i][k] -= vol*(*w) * ((vu[1][k] - vu[0][k]) * (*gi_u) / dt[0] + Theta * (nu * INNER_PRODUCT(gu[1]+k*Dim, ggi_u) ) - (*vp[1]) * *(ggi_u+k) + Thet1 * (nu * INNER_PRODUCT(gu[0]+k*Dim, ggi_u) ) ); /* left */ if (!_nsp->no_extern_source) rhsu[i][k] += vol*(*w) * (Theta * *(vf[1]+k) * (*gi_u) + Thet1 * *(vf[0]+k) * (*gi_u) ); /* right */ #else TIME_DEP_LINEAR_ENTRY; /* Unavailable */ #endif /* STEADY_STATE */ } } /* rhs p */ for (i = 0; i < N; i++) { const FLOAT *gi_p = phgQuadGetBasisValues(e, ns->p[1], i, quad) + q; /* psi_i */ FLOAT divu1 = gu[1][0] + gu[1][4] + gu[1][8]; //FLOAT divu0 = gu[0][0] + gu[0][4] + gu[0][8]; rhsp[i] += vol*(*w) * (divu1 * (*gi_p) ); } if (tstep_minus) vu[-1] += Dim; #if STEADY_STATE || TIME_DEP_NON vu[1] += Dim; gu[1] += Dim*Dim; vp[1]++; #else TIME_DEP_LINEAR; /* Unavailable */ #endif /* STEADY_STATE || TIME_DEP_NON */ vu[0] += Dim; gu[0] += Dim * Dim; vp[0]++; vw += Dim; if (!_nsp->no_extern_source) { vf[0] += Dim; vf[1] += Dim; } vT++; w++; p += Dim + 1; } if (!_nsp->no_extern_source) { phgFree(vf_cache[0]); phgFree(vf_cache[1]); } normal = NULL; Unused(normal); area = 0; Unused(area); if (!_nsp->enclosed_flow) { /* slip boundary */ for (s = 0; s < NFace; s++) { if (e->bound_type[s] & INFLOW) { int v0, v1, v2; int nbas_face = NbasFace(ns->u[1]); SHORT bases[nbas_face]; FLOAT lambda[Dim + 1], x,y,z, beta; order = DofTypeOrder(ns->u[1], e) * 3 - 1; phgDofGetBasesOnFace(ns->u[1], e, s, bases); v0 = GetFaceVertex(s, 0); v1 = GetFaceVertex(s, 1); v2 = GetFaceVertex(s, 2); lambda[s] = 0.; area = phgGeomGetFaceArea(g, e, s); normal = phgGeomGetFaceOutNormal(g, e, s); quad = phgQuadGetQuad2D(order); p = quad->points; w = quad->weights; for (q = 0; q < quad->npoints; q++) { FLOAT vu[Dim]; lambda[v0] = *(p++); lambda[v1] = *(p++); lambda[v2] = *(p++); phgGeomLambda2XYZ(g, e, lambda, &x, &y, &z); func_beta(x, y, z, &beta); phgDofEval(ns->u[1], e, lambda, vu); for (i = 0; i < nbas_face; i++) { int ii = bases[i]; FLOAT gi_u = *ns->u[1]->type->BasFuncs(ns->u[1], e, ii, ii + 1, lambda); for (k = 0; k < Dim; k++) { #if STEADY_STATE rhus[ii][k] += 0.; #elif TIME_DEP_NON # if USE_SLIDING_BC abort(); rhsu[ii][k] += SIGN_FRICTION * area*(*w) * beta * vu[k] * (gi_u) * EQU_SCALING * LEN_SCALING; # else Unused(gi_u); # endif #else TIME_DEP_LINEAR_ENTRY; /* Unavailable */ #endif /* STEADY_STATE */ } } /* end of bas_i */ w++; } /* end of quad point */ } /* end of face outflow */ } /* end of all outflow face in element */ } /* end out flow boundary */ #if USE_SLIDING_BC /* Rotate bases */ for (i = 0; i < M; i++) { INT id = phgDofMapE2D(surf_dof, e, i * (Dim*Dim)) / (Dim*Dim); if (!rotated[id]) continue; const FLOAT *trans = Trans + id*(Dim*Dim); trans_left(&rhsu[i][0], 1, 1, trans); } #else Unused(Trans); Unused(rotated); #endif /* Map: Element -> system */ for (i = 0; i < M; i++) for (k = 0; k < Dim; k++) Iu[i][k] = phgMapE2L(solver_u->rhs->map, 0, e, i * Dim + k); for (i = 0; i < N; i++) Ip[i] = phgMapE2L(solver_u->rhs->map, 1, e, i); /* set velocity dirichlet bdry */ FLOAT tmp[Dim]; for (i = 0; i < M; i++) for (k = 0; k < Dim; k++) if (phgDofDirichletBC_(ns->u[1], e, i*Dim+k, NULL, bufu, tmp, DOF_PROJ_NONE)) { rhsu[i][k] = 0.; } #if STEADY_STATE || TIME_DEP_NON /* set pressure dirichlet bdry for pinned point */ for (i = 0; i < N; i++) if (phgDofDirichletBC(ns->p[1], e, i, NULL, bufp, &rhsp[i], DOF_PROJ_NONE)) { if (!_nsp->enclosed_flow) phgError(1, "No dirichlet bc for Unenclosed flow!\n"); if (_nsp->pin_node) { # if PIN_AT_ROOT if (g->rank != 0) phgError(1, "Pinned node only on rank 0!\n"); if (g, e->verts[i] != ns->pinned_node_id) phgError(1, "Build rhs: pinned node e:%d, bas:%d, [%d] and [%d] " "doesn't coincide when build RHS!\n", e->index, i, e->verts[i], ns->pinned_node_id); # else if (GlobalVertex(g, e->verts[i]) != ns->pinned_node_id) phgError(1, "Build rhs: pinned node e:%d, bas:%d, [%d] and [%d] " "doesn't coincide when build RHS!\n", e->index, i, e->verts[i], ns->pinned_node_id); # endif /* PIN_AT_ROOT */ } } #else TIME_DEP_LINEAR; /* Unavailable */ #endif /* STEADY_STATE || TIME_DEP_NON */ /* Global res */ phgVecAddEntries(vec_rhs, 0, M * Dim, Iu[0], &rhsu[0][0]); phgVecAddEntries(vec_rhs, 0, N, Ip, rhsp); } /* end element */
static void getMoveDirection(MovingMesh *mmesh) { GRID *g = _m->g; SIMPLEX *e; DOF *logical_move = _m->logical_move; DOF *logical_node = _m->logical_node; DOF *move = _m->move; DOF *logical_node_new, *grad_logical_node; INT i, j, k, l0, l1; SOLVER *solver; DOF *mass_lumping; FLOAT *v_move, *v_mass; FLOAT max_vol = -1e10, min_vol = 1e10; /* Get new monitor */ _m->get_monitor(mmesh); DOF_SCALE(_m->monitor); logical_node_new = phgDofCopy(logical_node, NULL, NULL, "new logical node coordinates"); grad_logical_node = phgDofGradient(logical_node, NULL, NULL, "grad logical node coordinates"); /* if (logical_node_new->DB_mask == UNDEFINED) */ /* phgError(1, "g->types_vert and DB_mask is VAILD in moving mesh method!!!"); */ /* Create move solver */ phgOptionsPush(); #if 0 phgOptionsSetOptions("-default_solver mm_ml " "-mm_ml_solver gmres " "-mm_ml_pc mm_ml " "-mm_ml_sweep0 6 " "-solver_maxit 100 " "-solver_rtol 1e-12 "); #else phgOptionsSetOptions("-default_solver hypre " "-hypre_solver gmres " "-hypre_pc boomeramg " "-solver_maxit 100 " "-solver_rtol 1e-12 "); #endif phgOptionsSetOptions(_mp->move_opts); setMoveConstrain(mmesh, logical_node_new); solver = phgSolverCreate(SOLVER_DEFAULT, logical_node_new, NULL); solver->mat->mv_data = phgAlloc(sizeof(*solver->mat->mv_data)); solver->mat->mv_data[0] = (void *) mmesh; phgOptionsPop(); /* build mat */ ForAllElements(g, e) { int order = 1, q; int N = DofGetNBas(logical_node, e); /* number of bases in the element */ FLOAT A[N][Dim][N][Dim], rhs[N][Dim]; INT I[N][Dim]; QUAD *quad; const FLOAT *w, *lambda; FLOAT vol, mon; vol = phgGeomGetVolume(g, e); max_vol = MAX(max_vol, vol); min_vol = MIN(min_vol, vol); for (i = 0; i < N; i++) for (k = 0; k < Dim; k++) I[i][k] = phgMapE2L(solver->rhs->map, 0, e, i * Dim + k); bzero(A, sizeof(A)); bzero(rhs, sizeof(rhs)); quad = phgQuadGetQuad3D(order); mon = *DofElementData(_m->monitor, e->index); //printf("mon:%e\n", mon); lambda = quad->points; w = quad->weights; assert(quad->npoints == 1); for (q = 0; q < quad->npoints; q++) { for (i = 0; i < N; i++) { for (j = 0; j < N; j++) { const FLOAT *ggi = phgQuadGetBasisGradient(e, _m->move, i, quad) + q*Dim; /* grad phi_i */ const FLOAT *ggj = phgQuadGetBasisGradient(e, _m->move, j, quad) + q*Dim; /* grad phi_j */ FLOAT a = vol*(*w) * mon * INNER_PRODUCT(ggj, ggi); for (k = 0; k < Dim; k++) { A[i][k][j][k] += a; } } } w++; lambda += Dim + 1; } /* end quad point */ for (i = 0; i < N; i++) { INT vert0 = e->verts[i]; if (_mp->fix_bdry || MM_FIXED(g->types_vert[vert0])) { /* no move */ bzero(A[i], sizeof(A[i])); for (k = 0; k < Dim; k++) { A[i][k][i][k] = 1.; rhs[i][k] = logical_node->data[vert0 * Dim + k]; } } else if (g->types_vert[vert0] & MM_CONSTR) { VERT_CONSTRAIN *vert_constr = _m->vert_constr + _m->vert_constr_index[vert0]; FLOAT *trans = vert_constr->Trans; FLOAT *bb = vert_constr->bb; assert(_m->vert_constr_index[vert0] >= 0); assert(vert0 == vert_constr->index); trans_left_ (&A[i][0][0][0], Dim*N, Dim*N, trans); trans_right_(&A[0][0][i][0], Dim*N, Dim*N, trans); if (vert_constr->n_constrain == 2) { bzero(A[i][0], sizeof(A[i][0])); bzero(A[i][1], sizeof(A[i][1])); A[i][0][i][0] = 1.; A[i][1][i][1] = 1.; rhs[i][0] = bb[0]; rhs[i][1] = bb[1]; } else if (vert_constr->n_constrain == 1) { bzero(A[i][0], sizeof(A[i][0])); A[i][0][i][0] = 1.; rhs[i][0] = bb[0]; } else { abort(); } } } for (i = 0; i < N; i++) phgSolverAddMatrixEntries(solver, Dim, &I[i][0], N * Dim, I[0], &A[i][0][0][0]); phgSolverAddRHSEntries(solver, N * Dim, &I[0][0], &rhs[0][0]); }
void phgNSBuildPc(NSSolver *ns) { GRID *g = ns->g; SIMPLEX *e; FLOAT *dt = ns->dt; int i, j, q, s, k, l; FLOAT Theta = _nsp->Theta, nu = _nsp->nu, Thet1, nu0 = 0; DOF *tmp_u1 = phgDofNew(g, _nsp->utype, Dim, "tmp u1", func_u); int viscosity_type = ns->viscosity_type; LTYPE ltype = ns->ltype; #if STEADY_STATE assert(fabs(Theta - 1) < 1e-12); Thet1 = 0; Unused(Thet1); Unused(dt); #else Thet1 = 1 - Theta; #endif /* STEADY_STATE */ ForAllElements(g, e) { int M = ns->u[1]->type->nbas; /* num of bases of Velocity */ int N = ns->p[1]->type->nbas; /* num of bases of Pressure */ int order = 2 * DofTypeOrder(ns->p[1], e) + DofTypeOrder(ns->u[1], e) - 1; /* highest order term (u \nabla p, psi) */ FLOAT Ap[N][N], Fp[N][N], Qp[N][N], bufp[N], rhs1 = 1; FLOAT F[M*Dim][M*Dim], B[N][M*Dim], Bt[M*Dim][N]; INT Ip[N]; QUAD *quad; FLOAT vol, det; const FLOAT *w, *p, *vw, *gu, *vTe; quad = phgQuadGetQuad3D(order); vw = phgQuadGetDofValues(e, ns->wind, quad); /* value wind */ gu = phgQuadGetDofValues(e, ns->gradu[1], quad); /* grad u^{n+1} */ if (ns_params->noniter_temp) vTe = phgQuadGetDofValues(e, ns->T[1], quad); /* value temp */ else vTe = phgQuadGetDofValues(e, ns->T[0], quad); /* value temp */ vol = 0; Bzero(Ap); Bzero(Fp); Bzero(Qp); Bzero(F); Bzero(Bt); Bzero(B); Bzero(bufp); p = quad->points; w = quad->weights; for (q = 0; q < quad->npoints; q++) { phgGeomGetCurvedJacobianAtLambda(g, e, p, &det); vol = fabs(det / 6.); for (i = 0; i < N; i++) { const FLOAT *gi = phgQuadGetBasisValues(e, ns->p[1], i, quad) + q; /* phi_i */ const FLOAT *ggi = phgQuadGetBasisCurvedGradient(e, ns->p[1], i, quad, q); /* grad phi_i */ for (j = 0; j < N; j++) { const FLOAT *gj = phgQuadGetBasisValues(e, ns->p[1], j, quad) + q; /* phi_j */ const FLOAT *ggj = phgQuadGetBasisCurvedGradient(e, ns->p[1], j, quad, q); /* grad phi_i */ nu = get_effective_viscosity(gu, *vTe, 0, viscosity_type); if (i == 0 && j == 0) nu0 += nu; #if ICE_BENCH_TEST || \ ESIMINT_TEST || \ HEINO_TEST || \ TEST_CASE == ICE_EXACT || \ TEST_CASE == ICE_GREEN_LAND Unused(dt); /* Note: B Q^-1 Bt ~ Ap(nu=1), * Fp(nu varies) is very different to Ap */ Ap[i][j] += vol*(*w) * INNER_PRODUCT(ggj, ggi); # if USE_QP_ONLY //Qp[i][j] += vol*(*w) * LEN_SCALING * PRES_SCALING /(nu) * (*gj) * (*gi); Qp[i][j] += vol*(*w) * 1. /(EQU_SCALING * nu) * (*gj) * (*gi); /* if (i < NVert && j < NVert) { */ /* Qp[i][j] += vol*(*w) * LEN_SCALING * PRES_SCALING / (nu) * (*gj) * (*gi); */ /* } else if (i == NVert && j == NVert) { */ /* Qp[i][j] += vol*(*w) * LEN_SCALING * PRES_SCALING / (nu) * (*gj) * (*gi); */ /* } */ # else Qp[i][j] += vol*(*w) * (*gj) * (*gi); # endif Fp[i][j] += vol*(*w) * (EQU_SCALING * nu * INNER_PRODUCT(ggj, ggi) ); #elif STEADY_STATE Ap[i][j] += vol*(*w) * INNER_PRODUCT(ggj, ggi); Qp[i][j] += vol*(*w) * (*gj) * (*gi); Fp[i][j] += vol*(*w) * (nu * INNER_PRODUCT(ggj, ggi) * EQU_SCALING ); #elif TIME_DEP_NON Ap[i][j] += vol*(*w) * INNER_PRODUCT(ggj, ggi); Qp[i][j] += vol*(*w) * (*gj) * (*gi); Fp[i][j] += vol*(*w) * ((*gj) * (*gi) / dt[0] + Theta * (nu * INNER_PRODUCT(ggj, ggi) ) ); #else TIME_DEP_LINEAR_ENTRY; /* Unavailable */ #endif /* STEADY_STATE */ } } vw += Dim; gu += DDim; vTe++; w++; p += Dim+1; } /* Map: Element -> system */ for (i = 0; i < N; i++) Ip[i] = phgMapE2L(_pcd->matFp->cmap, 0, e, i); /* * PCD boundary setup I: * Automaticly decide inflow boundary condition using wind direction. * * NOT active. * */ if (FALSE && !_nsp->pin_node) { for (i = 0; i < N; i++) { BOOLEAN flag_inflow = FALSE; for (s = 0; s < NFace; s++) { SHORT bases[NbasFace(ns->p[1])]; FLOAT *coord, vw_[3]; const FLOAT *lam, *normal; if (!(e->bound_type[s] & BDRY_MASK)) //if (!(e->bound_type[s] & INFLOW)) continue; /* boundary face */ phgDofGetBasesOnFace(ns->p[1], e, s, bases); for (j = 0; j < NbasFace(ns->p[1]); j++) if (i == bases[j]) { normal = phgGeomGetFaceOutNormal(g, e, s); coord = phgDofGetElementCoordinates(ns->p[1], e, i); lam = phgGeomXYZ2Lambda(g, e, coord[0], coord[1], coord[2]); phgDofEval(tmp_u1, e, lam, vw_); if (INNER_PRODUCT(vw_, normal) > 1e-8) flag_inflow = TRUE; } } if (flag_inflow) { Bzero(bufp); bufp[i] = 1.0; phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, bufp); //phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, bufp); phgVecAddEntries(_pcd->rhsScale, 0, 1, Ip + i, &rhs1); } else { /* interior node Or Neumann */ phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, Ap[i]); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, Fp[i]); //phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, Qp[i]); } phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, Qp[i]); } } /* * PCD boundary setup II: * Enclose flow: use pinnode boundary. * * Qp is pinned, this is different to open flow. * * */ else if (_nsp->pin_node) { for (i = 0; i < N; i++) { if (phgDofDirichletBC(_pcd->pbc, e, i, NULL, bufp, NULL, DOF_PROJ_NONE)) { #if PIN_AT_ROOT if (g->rank != 0) phgError(1, "Pinned node only on rank 0!\n"); if (e->verts[i] != ns->pinned_node_id) phgError(1, "pinned node [%d] & [%d] doesn't coincide when build pc!\n", e->verts[i], ns->pinned_node_id); #else if (GlobalVertex(g, e->verts[i]) != ns->pinned_node_id) phgError(1, "pinned node [%d] & [%d] doesn't coincide when build pc!\n", e->verts[i], ns->pinned_node_id); #endif /* PIN_AT_ROOT */ phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, bufp); phgVecAddEntries(_pcd->rhsScale, 0, 1, Ip + i, &rhs1); } else { /* interior node Or Neumann */ phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, Ap[i]); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, Fp[i]); phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, Qp[i]); } } } /* * PCD boundary setup III: * Open flow: there could be varies kinds of combination on seting up * boundary conditon, but Inflow:Robin & Outflow:scaled Dirich is * prefered. See Ref[2]. * * */ else { for (i = 0; i < N; i++) { /*****************/ /* Inflow */ /*****************/ #warning PCD B.C.: Step 2.1. build mat, all neumann, add dirich entries if (FALSE && phgDofDirichletBC(_pcd->dof_inflow, e, i, NULL, bufp, NULL, DOF_PROJ_NONE)) { phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, bufp); phgVecAddEntries(_pcd->rhsScale, 0, 1, Ip + i, &rhs1); } else if (FALSE && phgDofDirichletBC(_pcd->dof_outflow, e, i, NULL, bufp, NULL, DOF_PROJ_NONE) && !(phgDofGetElementBoundaryType(ns->p[1], e, i) & INFLOW) ) { ERROR_MSG("Fp, Qp"); nu = get_effective_viscosity(NULL, 0, 0, viscosity_type); phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, bufp); bufp[i] *= EQU_SCALING * nu; phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, bufp); phgVecAddEntries(_pcd->rhsScale, 0, 1, Ip + i, &rhs1); //phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, bufp); } else if (FALSE && phgDofDirichletBC(_pcd->pbc, e, i, NULL, bufp, NULL, DOF_PROJ_NONE)) { phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, bufp); phgVecAddEntries(_pcd->rhsScale, 0, 1, Ip + i, &rhs1); } else if (FALSE) { /* interior node Or Neumann */ ERROR_MSG("Fp, Qp"); phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, Ap[i]); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, Fp[i]); //phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, Qp[i]); } /******************/ /* No bdry */ /******************/ //phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, Fp[i]); phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, Qp[i]); } } if (0) { /* Special term <[[p_i]], [[p_j]]> */ int face; nu0 /= quad->npoints; for (face = 0; face < NFace; face++) { FLOAT area = phgGeomGetFaceArea(g, e, face); //FLOAT value = {area, -area}; FLOAT values[2] = {vol * 1. /(EQU_SCALING * nu0), -vol * 1. /(EQU_SCALING * nu0)}; SIMPLEX *e_neigh; phgMatAddEntries(_pcd->matQp, 1, Ip+NVert, 1, Ip+NVert, values); if ((e_neigh = GetNeighbour(e, face)) != NULL) { INT Ip_neigh = phgMapE2L(_pcd->matFp->cmap, 0, e_neigh, NVert); phgMatAddEntries(_pcd->matQp, 1, Ip+NVert, 1, &Ip_neigh, values + 1); } } } } /* end element */