/*
We integrate over each cell
(i, j+1)----(i+1, j+1)
| \ |
| \ |
| \ |
| \ |
| \ |
| \ |
| \ |
(i, j)----(i+1, j)
*/
PetscErrorCode ComputeRHS(KSP ksp, Vec b, void *ctx)
{
UserContext *user = (UserContext*)ctx;
PetscScalar phi = user->phi;
PetscScalar *array;
PetscInt ne,nc,i;
const PetscInt *e;
PetscErrorCode ierr;
Vec blocal;
DM da;
PetscFunctionBeginUser;
ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
/* access a local vector with room for the ghost points */
ierr = DMGetLocalVector(da,&blocal);CHKERRQ(ierr);
ierr = VecGetArray(blocal, (PetscScalar**) &array);CHKERRQ(ierr);
/* access the list of elements on this processor and loop over them */
ierr = DMDAGetElements(da,&ne,&nc,&e);CHKERRQ(ierr);
for (i=0; i<ne; i++) {
/* this is nonsense, but set each nodal value to phi (will actually do integration over element */
array[e[3*i]] = phi;
array[e[3*i+1]] = phi;
array[e[3*i+2]] = phi;
}
ierr = VecRestoreArray(blocal, (PetscScalar**) &array);CHKERRQ(ierr);
ierr = DMDARestoreElements(da,&ne,&nc,&e);CHKERRQ(ierr);
/* add our partial sums over all processors into b */
ierr = DMLocalToGlobalBegin(da,blocal,ADD_VALUES,b);CHKERRQ(ierr);
ierr = DMLocalToGlobalEnd(da,blocal, ADD_VALUES,b);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&blocal);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* Average the velocity (u,v) at time t^n over each element for time n+\phi */
PetscErrorCode CalculateElementVelocity(DM da, UserContext *user)
{
PetscScalar *u_n, *v_n;
PetscScalar *u_phi, *v_phi;
const PetscInt *necon;
PetscInt j, e, ne, nc;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = DMDAGetElements(da, &ne, &nc, &necon);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
ierr = PetscMalloc(ne*sizeof(PetscScalar),&u_phi);CHKERRQ(ierr);
ierr = PetscMalloc(ne*sizeof(PetscScalar),&v_phi);CHKERRQ(ierr);
for (e = 0; e < ne; e++) {
u_phi[e] = 0.0;
v_phi[e] = 0.0;
for (j = 0; j < 3; j++) {
u_phi[e] += u_n[necon[3*e+j]];
v_phi[e] += v_n[necon[3*e+j]];
}
u_phi[e] /= 3.0;
v_phi[e] /= 3.0;
}
ierr = PetscFree(u_phi);CHKERRQ(ierr);
ierr = PetscFree(v_phi);CHKERRQ(ierr);
ierr = DMDARestoreElements(da, &ne,&nc, &necon);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode CreateStructures(DM da, UserContext *user)
{
const PetscInt *necon;
PetscInt ne,nc;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = DMDAGetElements(da,&ne,&nc,&necon);CHKERRQ(ierr);
ierr = DMDARestoreElements(da,&ne,&nc,&necon);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_n.rho);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_n.rho_u);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_n.rho_v);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_n.rho_e);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_n.p);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_n.u);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_n.v);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_n.t);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD, &user->sol_phi.rho);CHKERRQ(ierr);
ierr = VecSetSizes(user->sol_phi.rho, ne, PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetType(user->sol_phi.rho,VECMPI);CHKERRQ(ierr);
ierr = VecDuplicate(user->sol_phi.rho, &user->sol_phi.rho_u);CHKERRQ(ierr);
ierr = VecDuplicate(user->sol_phi.rho, &user->sol_phi.rho_v);CHKERRQ(ierr);
ierr = VecDuplicate(user->sol_phi.rho, &user->sol_phi.u);CHKERRQ(ierr);
ierr = VecDuplicate(user->sol_phi.rho, &user->sol_phi.v);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_np1.rho);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_np1.rho_u);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_np1.rho_v);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_np1.rho_e);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_np1.p);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_np1.u);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->sol_np1.v);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->mu);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &user->kappa);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
We integrate over each cell
(i, j+1)----(i+1, j+1)
| \ |
| \ |
| \ |
| \ |
| \ |
| \ |
| \ |
(i, j)----(i+1, j)
However, the element stiffness matrix for the identity in linear elements is
1 /2 1 1\
- |1 2 1|
12 \1 1 2/
no matter what the shape of the triangle. The Laplacian stiffness matrix is
1 / (x_2 - x_1)^2 + (y_2 - y_1)^2 -(x_2 - x_0)(x_2 - x_1) - (y_2 - y_1)(y_2 - y_0) (x_1 - x_0)(x_2 - x_1) + (y_1 - y_0)(y_2 - y_1)\
- |-(x_2 - x_0)(x_2 - x_1) - (y_2 - y_1)(y_2 - y_0) (x_2 - x_0)^2 + (y_2 - y_0)^2 -(x_1 - x_0)(x_2 - x_0) - (y_1 - y_0)(y_2 - y_0)|
A \ (x_1 - x_0)(x_2 - x_1) + (y_1 - y_0)(y_2 - y_1) -(x_1 - x_0)(x_2 - x_0) - (y_1 - y_0)(y_2 - y_0) (x_1 - x_0)^2 + (y_1 - y_0)^2 /
where A is the area of the triangle, and (x_i, y_i) is its i'th vertex.
*/
PetscErrorCode ComputeMatrix(KSP ksp, Mat J, Mat jac, MatStructure *flag,void *ctx)
{
UserContext *user = (UserContext*)ctx;
/* not being used!
PetscScalar identity[9] = {0.16666666667, 0.08333333333, 0.08333333333,
0.08333333333, 0.16666666667, 0.08333333333,
0.08333333333, 0.08333333333, 0.16666666667};
*/
PetscScalar values[3][3];
PetscInt idx[3];
PetscScalar hx, hy, hx2, hy2, area,phi_dt2;
PetscInt i,mx,my,xm,ym,xs,ys;
PetscInt ne,nc;
const PetscInt *e;
PetscErrorCode ierr;
DM da;
PetscFunctionBeginUser;
ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
hx = 1.0 / (mx-1);
hy = 1.0 / (my-1);
area = 0.5*hx*hy;
phi_dt2 = user->phi*user->dt*user->dt;
hx2 = hx*hx/area*phi_dt2;
hy2 = hy*hy/area*phi_dt2;
/* initially all elements have identical geometry so all element stiffness are identical */
values[0][0] = hx2 + hy2; values[0][1] = -hy2; values[0][2] = -hx2;
values[1][0] = -hy2; values[1][1] = hy2; values[1][2] = 0.0;
values[2][0] = -hx2; values[2][1] = 0.0; values[2][2] = hx2;
ierr = DMDAGetElements(da,&ne,&nc,&e);CHKERRQ(ierr);
for (i=0; i<ne; i++) {
idx[0] = e[3*i];
idx[1] = e[3*i+1];
idx[2] = e[3*i+2];
ierr = MatSetValuesLocal(jac,3,idx,3,idx,(PetscScalar*)values,ADD_VALUES);CHKERRQ(ierr);
}
ierr = DMDARestoreElements(da,&ne,&nc,&e);CHKERRQ(ierr);
ierr = MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode ComputeCorrector(DM da, Vec uOld, Vec u)
{
Vec uOldLocal, uLocal;
PetscScalar *cOld;
PetscScalar *c;
PetscInt i,ne,nc;
const PetscInt *e;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = VecSet(u,0.0);CHKERRQ(ierr);
ierr = DMGetLocalVector(da, &uOldLocal);CHKERRQ(ierr);
ierr = DMGetLocalVector(da, &uLocal);CHKERRQ(ierr);
ierr = VecSet(uLocal,0.0);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da, uOld, INSERT_VALUES, uOldLocal);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da, uOld, INSERT_VALUES, uOldLocal);CHKERRQ(ierr);
ierr = VecGetArray(uOldLocal, &cOld);CHKERRQ(ierr);
ierr = VecGetArray(uLocal, &c);CHKERRQ(ierr);
/* access the list of elements on this processor and loop over them */
ierr = DMDAGetElements(da,&ne,&nc,&e);CHKERRQ(ierr);
for (i=0; i<ne; i++) {
/* this is nonsense, but copy each nodal value*/
c[e[3*i]] = cOld[e[3*i]];
c[e[3*i+1]] = cOld[e[3*i+1]];
c[e[3*i+2]] = cOld[e[3*i+2]];
}
ierr = DMDARestoreElements(da,&ne,&nc,&e);CHKERRQ(ierr);
ierr = VecRestoreArray(uOldLocal, &cOld);CHKERRQ(ierr);
ierr = VecRestoreArray(uLocal, &c);CHKERRQ(ierr);
ierr = DMLocalToGlobalBegin(da, uLocal, ADD_VALUES,u);CHKERRQ(ierr);
ierr = DMLocalToGlobalEnd(da, uLocal, ADD_VALUES,u);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da, &uOldLocal);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da, &uLocal);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode SetUpMatrices(AppCtx* user)
{
PetscErrorCode ierr;
PetscInt nele,nen,i;
const PetscInt *ele;
PetscScalar dt=user->dt;
Vec coords;
const PetscScalar *_coords;
PetscScalar x[3],y[3],xx[3],yy[3],w;
PetscInt idx[3];
PetscScalar phi[3],phider[3][2];
PetscScalar eM_0[3][3],eM_2[3][3];
Mat M=user->M;
PetscScalar gamma=user->gamma,theta_c=user->theta_c;
PetscInt m;
PetscInt j,k;
PetscInt row,cols[6],r;
PetscScalar vals[6];
PetscInt n,rstart;
IS isrow,iscol;
PetscFunctionBegin;
/* Get ghosted coordinates */
ierr = DMDAGetGhostedCoordinates(user->da,&coords);CHKERRQ(ierr);
ierr = VecGetArrayRead(coords,&_coords);CHKERRQ(ierr);
/* Get local element info */
ierr = DMDAGetElements(user->da,&nele,&nen,&ele);CHKERRQ(ierr);
for(i=0;i < nele;i++) {
idx[0] = ele[3*i]; idx[1] = ele[3*i+1]; idx[2] = ele[3*i+2];
x[0] = _coords[2*idx[0]]; y[0] = _coords[2*idx[0]+1];
x[1] = _coords[2*idx[1]]; y[1] = _coords[2*idx[1]+1];
x[2] = _coords[2*idx[2]]; y[2] = _coords[2*idx[2]+1];
ierr = PetscMemzero(xx,3*sizeof(PetscScalar));CHKERRQ(ierr);
ierr = PetscMemzero(yy,3*sizeof(PetscScalar));CHKERRQ(ierr);
Gausspoints(xx,yy,&w,x,y);
eM_0[0][0]=eM_0[0][1]=eM_0[0][2]=0.0;
eM_0[1][0]=eM_0[1][1]=eM_0[1][2]=0.0;
eM_0[2][0]=eM_0[2][1]=eM_0[2][2]=0.0;
eM_2[0][0]=eM_2[0][1]=eM_2[0][2]=0.0;
eM_2[1][0]=eM_2[1][1]=eM_2[1][2]=0.0;
eM_2[2][0]=eM_2[2][1]=eM_2[2][2]=0.0;
for(m=0;m<3;m++) {
ierr = PetscMemzero(phi,3*sizeof(PetscScalar));CHKERRQ(ierr);
phider[0][0]=phider[0][1]=0.0;
phider[1][0]=phider[1][1]=0.0;
phider[2][0]=phider[2][1]=0.0;
ShapefunctionsT3(phi,phider,xx[m],yy[m],x,y);
for(j=0;j<3;j++) {
for(k=0;k<3;k++) {
eM_0[k][j] += phi[j]*phi[k]*w;
eM_2[k][j] += phider[j][0]*phider[k][0]*w + phider[j][1]*phider[k][1]*w;
}
}
}
for(r=0;r<3;r++) {
row = 2*idx[r];
cols[0] = 2*idx[0]; vals[0] = dt*eM_2[r][0];
cols[1] = 2*idx[0]+1; vals[1] = eM_0[r][0];
cols[2] = 2*idx[1]; vals[2] = dt*eM_2[r][1];
cols[3] = 2*idx[1]+1; vals[3] = eM_0[r][1];
cols[4] = 2*idx[2]; vals[4] = dt*eM_2[r][2];
cols[5] = 2*idx[2]+1; vals[5] = eM_0[r][2];
/* Insert values in matrix M for 1st dof */
ierr = MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);CHKERRQ(ierr);
row = 2*idx[r]+1;
cols[0] = 2*idx[0]; vals[0] = -eM_0[r][0];
cols[1] = 2*idx[0]+1; vals[1] = gamma*eM_2[r][0]-theta_c*eM_0[r][0];
cols[2] = 2*idx[1]; vals[2] = -eM_0[r][1];
cols[3] = 2*idx[1]+1; vals[3] = gamma*eM_2[r][1]-theta_c*eM_0[r][1];
cols[4] = 2*idx[2]; vals[4] = -eM_0[r][2];
cols[5] = 2*idx[2]+1; vals[5] = gamma*eM_2[r][2]-theta_c*eM_2[r][2];
/* Insert values in matrix M for 2nd dof */
ierr = MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = DMDARestoreElements(user->da,&nele,&nen,&ele);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(coords,&_coords);CHKERRQ(ierr);
ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Create ISs to extract matrix M_0 from M */
ierr = MatGetLocalSize(M,&n,PETSC_NULL);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(M,&rstart,PETSC_NULL);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_WORLD,n/2,rstart,2,&isrow);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_WORLD,n/2,rstart+1,2,&iscol);CHKERRQ(ierr);
/* Extract M_0 from M */
ierr = MatGetSubMatrix(M,isrow,iscol,MAT_INITIAL_MATRIX,&user->M_0);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&user->u);CHKERRQ(ierr);
ierr = VecSetSizes(user->u,n/2,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(user->u);CHKERRQ(ierr);
ierr = VecDuplicate(user->u,&user->work1);CHKERRQ(ierr);
ierr = ISDestroy(&isrow);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* Notice that this requires the previous momentum solution.
The element stiffness matrix for the identity in linear elements is
1 /2 1 1\
- |1 2 1|
12 \1 1 2/
no matter what the shape of the triangle. */
PetscErrorCode TaylorGalerkinStepIIMassEnergy(DM da, UserContext *user)
{
MPI_Comm comm;
Mat mat;
Vec rhs_m, rhs_e;
PetscScalar identity[9] = {0.16666666667, 0.08333333333, 0.08333333333,
0.08333333333, 0.16666666667, 0.08333333333,
0.08333333333, 0.08333333333, 0.16666666667};
PetscScalar *u_n, *v_n, *p_n, *t_n, *mu_n, *kappa_n;
PetscScalar *rho_n, *rho_u_n, *rho_v_n, *rho_e_n;
PetscScalar *u_phi, *v_phi;
PetscScalar *rho_u_np1, *rho_v_np1;
PetscInt idx[3];
PetscScalar psi_x[3], psi_y[3];
PetscScalar values_m[3];
PetscScalar values_e[3];
PetscScalar phi = user->phi;
PetscScalar mu, kappa, tau_xx, tau_xy, tau_yy, q_x, q_y;
PetscReal hx, hy, area;
KSP ksp;
const PetscInt *necon;
PetscInt j, k, e, ne, nc, mx, my;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = PetscObjectGetComm((PetscObject) da, &comm);CHKERRQ(ierr);
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da, &mat);CHKERRQ(ierr);
ierr = MatSetOption(mat,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &rhs_m);CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &rhs_e);CHKERRQ(ierr);
ierr = KSPCreate(comm, &ksp);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
hx = 1.0 / (PetscReal)(mx-1);
hy = 1.0 / (PetscReal)(my-1);
area = 0.5*hx*hy;
ierr = VecGetArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.p, &p_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.t, &t_n);CHKERRQ(ierr);
ierr = VecGetArray(user->mu, &mu_n);CHKERRQ(ierr);
ierr = VecGetArray(user->kappa, &kappa_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.rho, &rho_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.rho_u, &rho_u_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.rho_v, &rho_v_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.rho_e, &rho_e_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.u, &u_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.v, &v_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_np1.rho_u, &rho_u_np1);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_np1.rho_v, &rho_v_np1);CHKERRQ(ierr);
ierr = DMDAGetElements(da, &ne, &nc, &necon);CHKERRQ(ierr);
for (e = 0; e < ne; e++) {
for (j = 0; j < 3; j++) {
idx[j] = necon[3*e+j];
values_m[j] = 0.0;
values_e[j] = 0.0;
}
/* Get basis function deriatives (we need the orientation of the element here) */
if (idx[1] > idx[0]) {
psi_x[0] = -hy; psi_x[1] = hy; psi_x[2] = 0.0;
psi_y[0] = -hx; psi_y[1] = 0.0; psi_y[2] = hx;
} else {
psi_x[0] = hy; psi_x[1] = -hy; psi_x[2] = 0.0;
psi_y[0] = hx; psi_y[1] = 0.0; psi_y[2] = -hx;
}
/* <\nabla\psi, F^*>: Divergence of the predicted convective fluxes */
for (j = 0; j < 3; j++) {
values_m[j] += (psi_x[j]*(phi*rho_u_np1[idx[j]] + rho_u_n[idx[j]]) + psi_y[j]*(rho_v_np1[idx[j]] + rho_v_n[idx[j]]))/3.0;
values_e[j] += values_m[j]*((rho_e_n[idx[j]] + p_n[idx[j]]) / rho_n[idx[j]]);
}
/* -<\nabla\psi, F^n_v>: Divergence of the viscous fluxes */
for (j = 0; j < 3; j++) {
/* \tau_{xx} = 2/3 \mu(T) (2 {\partial u\over\partial x} - {\partial v\over\partial y}) */
/* \tau_{xy} = \mu(T) ( {\partial u\over\partial y} + {\partial v\over\partial x}) */
/* \tau_{yy} = 2/3 \mu(T) (2 {\partial v\over\partial y} - {\partial u\over\partial x}) */
/* q_x = -\kappa(T) {\partial T\over\partial x} */
/* q_y = -\kappa(T) {\partial T\over\partial y} */
/* above code commeted out - causing ininitialized variables. */
q_x =0; q_y =0;
mu = 0.0;
kappa = 0.0;
tau_xx = 0.0;
tau_xy = 0.0;
tau_yy = 0.0;
for (k = 0; k < 3; k++) {
mu += mu_n[idx[k]];
kappa += kappa_n[idx[k]];
tau_xx += 2.0*psi_x[k]*u_n[idx[k]] - psi_y[k]*v_n[idx[k]];
tau_xy += psi_y[k]*u_n[idx[k]] + psi_x[k]*v_n[idx[k]];
tau_yy += 2.0*psi_y[k]*v_n[idx[k]] - psi_x[k]*u_n[idx[k]];
q_x += psi_x[k]*t_n[idx[k]];
q_y += psi_y[k]*t_n[idx[k]];
}
mu /= 3.0;
kappa /= 3.0;
tau_xx *= (2.0/3.0)*mu;
tau_xy *= mu;
tau_yy *= (2.0/3.0)*mu;
values_e[j] -= area*(psi_x[j]*(u_phi[e]*tau_xx + v_phi[e]*tau_xy + q_x) + psi_y[j]*(u_phi[e]*tau_xy + v_phi[e]*tau_yy + q_y));
}
/* Accumulate to global structures */
ierr = VecSetValuesLocal(rhs_m, 3, idx, values_m, ADD_VALUES);CHKERRQ(ierr);
ierr = VecSetValuesLocal(rhs_e, 3, idx, values_e, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesLocal(mat, 3, idx, 3, idx, identity, ADD_VALUES);CHKERRQ(ierr);
}
ierr = DMDARestoreElements(da, &ne, &nc, &necon);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.p, &p_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.t, &t_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->mu, &mu_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->kappa, &kappa_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.rho, &rho_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.rho_u, &rho_u_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.rho_v, &rho_v_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.rho_e, &rho_e_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.u, &u_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.v, &v_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_np1.rho_u, &rho_u_np1);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_np1.rho_v, &rho_v_np1);CHKERRQ(ierr);
ierr = VecAssemblyBegin(rhs_m);CHKERRQ(ierr);
ierr = VecAssemblyBegin(rhs_e);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecAssemblyEnd(rhs_m);CHKERRQ(ierr);
ierr = VecAssemblyEnd(rhs_e);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecScale(rhs_m, user->dt);CHKERRQ(ierr);
ierr = VecScale(rhs_e, user->dt);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp, mat, mat, DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPSolve(ksp, rhs_m, user->sol_np1.rho);CHKERRQ(ierr);
ierr = KSPSolve(ksp, rhs_e, user->sol_np1.rho_e);CHKERRQ(ierr);
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = MatDestroy(&mat);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da, &rhs_m);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da, &rhs_e);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
The element stiffness matrix for the identity in linear elements is
1 /2 1 1\
- |1 2 1|
12 \1 1 2/
no matter what the shape of the triangle. */
PetscErrorCode TaylorGalerkinStepIIMomentum(DM da, UserContext *user)
{
MPI_Comm comm;
KSP ksp;
Mat mat;
Vec rhs_u, rhs_v;
PetscScalar identity[9] = {0.16666666667, 0.08333333333, 0.08333333333,
0.08333333333, 0.16666666667, 0.08333333333,
0.08333333333, 0.08333333333, 0.16666666667};
PetscScalar *u_n, *v_n, *mu_n;
PetscScalar *u_phi, *v_phi;
PetscScalar *rho_u_phi, *rho_v_phi;
PetscInt idx[3];
PetscScalar values_u[3];
PetscScalar values_v[3];
PetscScalar psi_x[3], psi_y[3];
PetscScalar mu, tau_xx, tau_xy, tau_yy;
PetscReal hx, hy, area;
const PetscInt *necon;
PetscInt j, k, e, ne, nc, mx, my;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = PetscObjectGetComm((PetscObject) da, &comm);CHKERRQ(ierr);
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da, &mat);CHKERRQ(ierr);
ierr = MatSetOption(mat,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &rhs_u);CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &rhs_v);CHKERRQ(ierr);
ierr = KSPCreate(comm, &ksp);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
hx = 1.0 / (PetscReal)(mx-1);
hy = 1.0 / (PetscReal)(my-1);
area = 0.5*hx*hy;
ierr = VecGetArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
ierr = VecGetArray(user->mu, &mu_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.u, &u_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.v, &v_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.rho_u, &rho_u_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.rho_v, &rho_v_phi);CHKERRQ(ierr);
ierr = DMDAGetElements(da, &ne, &nc, &necon);CHKERRQ(ierr);
for (e = 0; e < ne; e++) {
for (j = 0; j < 3; j++) {
idx[j] = necon[3*e+j];
values_u[j] = 0.0;
values_v[j] = 0.0;
}
/* Get basis function deriatives (we need the orientation of the element here) */
if (idx[1] > idx[0]) {
psi_x[0] = -hy; psi_x[1] = hy; psi_x[2] = 0.0;
psi_y[0] = -hx; psi_y[1] = 0.0; psi_y[2] = hx;
} else {
psi_x[0] = hy; psi_x[1] = -hy; psi_x[2] = 0.0;
psi_y[0] = hx; psi_y[1] = 0.0; psi_y[2] = -hx;
}
/* <\nabla\psi, F^{n+\phi}_e>: Divergence of the element-averaged convective fluxes */
for (j = 0; j < 3; j++) {
values_u[j] += psi_x[j]*rho_u_phi[e]*u_phi[e] + psi_y[j]*rho_u_phi[e]*v_phi[e];
values_v[j] += psi_x[j]*rho_v_phi[e]*u_phi[e] + psi_y[j]*rho_v_phi[e]*v_phi[e];
}
/* -<\nabla\psi, F^n_v>: Divergence of the viscous fluxes */
for (j = 0; j < 3; j++) {
/* \tau_{xx} = 2/3 \mu(T) (2 {\partial u\over\partial x} - {\partial v\over\partial y}) */
/* \tau_{xy} = \mu(T) ( {\partial u\over\partial y} + {\partial v\over\partial x}) */
/* \tau_{yy} = 2/3 \mu(T) (2 {\partial v\over\partial y} - {\partial u\over\partial x}) */
mu = 0.0;
tau_xx = 0.0;
tau_xy = 0.0;
tau_yy = 0.0;
for (k = 0; k < 3; k++) {
mu += mu_n[idx[k]];
tau_xx += 2.0*psi_x[k]*u_n[idx[k]] - psi_y[k]*v_n[idx[k]];
tau_xy += psi_y[k]*u_n[idx[k]] + psi_x[k]*v_n[idx[k]];
tau_yy += 2.0*psi_y[k]*v_n[idx[k]] - psi_x[k]*u_n[idx[k]];
}
mu /= 3.0;
tau_xx *= (2.0/3.0)*mu;
tau_xy *= mu;
tau_yy *= (2.0/3.0)*mu;
values_u[j] -= area*(psi_x[j]*tau_xx + psi_y[j]*tau_xy);
values_v[j] -= area*(psi_x[j]*tau_xy + psi_y[j]*tau_yy);
}
/* Accumulate to global structures */
ierr = VecSetValuesLocal(rhs_u, 3, idx, values_u, ADD_VALUES);CHKERRQ(ierr);
ierr = VecSetValuesLocal(rhs_v, 3, idx, values_v, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesLocal(mat, 3, idx, 3, idx, identity, ADD_VALUES);CHKERRQ(ierr);
}
ierr = DMDARestoreElements(da, &ne, &nc, &necon);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->mu, &mu_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.u, &u_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.v, &v_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.rho_u, &rho_u_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.rho_v, &rho_v_phi);CHKERRQ(ierr);
ierr = VecAssemblyBegin(rhs_u);CHKERRQ(ierr);
ierr = VecAssemblyBegin(rhs_v);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecAssemblyEnd(rhs_u);CHKERRQ(ierr);
ierr = VecAssemblyEnd(rhs_v);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecScale(rhs_u,user->dt);CHKERRQ(ierr);
ierr = VecScale(rhs_v,user->dt);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp, mat, mat, DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPSolve(ksp, rhs_u, user->sol_np1.rho_u);CHKERRQ(ierr);
ierr = KSPSolve(ksp, rhs_v, user->sol_np1.rho_v);CHKERRQ(ierr);
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = MatDestroy(&mat);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da, &rhs_u);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da, &rhs_v);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* This is equation 32,
U^{n+\phi}_E = {1\over Vol_E} \left(\int_\Omega [N]{U^n} d\Omega - \phi\Delta t \int_\Omega [\nabla N]\cdot{F^n} d\Omega \right) + \phi\Delta t Q^n
which is really simple for linear elements
U^{n+\phi}_E = {1\over3} \sum^3_{i=1} U^n_i - \phi\Delta t [\nabla N]\cdot{F^n} + \phi\Delta t Q^n
where
U^{n+\phi}_E = {\rho \rho u \rho v}^{n+\phi}_E
and the x and y components of the convective fluxes F are
f^n = {\rho u \rho u^2 \rho uv}^n g^n = {\rho v \rho uv \rho v^2}^n
*/
PetscErrorCode TaylorGalerkinStepI(DM da, UserContext *user)
{
PetscScalar phi_dt = user->phi*user->dt;
PetscScalar *u_n, *v_n;
PetscScalar *rho_n, *rho_u_n, *rho_v_n;
PetscScalar *rho_phi, *rho_u_phi, *rho_v_phi;
PetscScalar Fx_x, Fy_y;
PetscScalar psi_x[3], psi_y[3];
PetscInt idx[3];
PetscReal hx, hy;
const PetscInt *necon;
PetscInt j, e, ne, nc, mx, my;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
hx = 1.0 / (PetscReal)(mx-1);
hy = 1.0 / (PetscReal)(my-1);
ierr = VecSet(user->sol_phi.rho,0.0);CHKERRQ(ierr);
ierr = VecSet(user->sol_phi.rho_u,0.0);CHKERRQ(ierr);
ierr = VecSet(user->sol_phi.rho_v,0.0);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.rho, &rho_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.rho_u, &rho_u_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.rho_v, &rho_v_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.rho, &rho_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.rho_u, &rho_u_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.rho_v, &rho_v_phi);CHKERRQ(ierr);
ierr = DMDAGetElements(da, &ne, &nc, &necon);CHKERRQ(ierr);
for (e = 0; e < ne; e++) {
/* Average the existing fields over the element */
for (j = 0; j < 3; j++) {
idx[j] = necon[3*e+j];
rho_phi[e] += rho_n[idx[j]];
rho_u_phi[e] += rho_u_n[idx[j]];
rho_v_phi[e] += rho_v_n[idx[j]];
}
rho_phi[e] /= 3.0;
rho_u_phi[e] /= 3.0;
rho_v_phi[e] /= 3.0;
/* Get basis function deriatives (we need the orientation of the element here) */
if (idx[1] > idx[0]) {
psi_x[0] = -hy; psi_x[1] = hy; psi_x[2] = 0.0;
psi_y[0] = -hx; psi_y[1] = 0.0; psi_y[2] = hx;
} else {
psi_x[0] = hy; psi_x[1] = -hy; psi_x[2] = 0.0;
psi_y[0] = hx; psi_y[1] = 0.0; psi_y[2] = -hx;
}
/* Determine the convective fluxes for \rho^{n+\phi} */
Fx_x = 0.0; Fy_y = 0.0;
for (j = 0; j < 3; j++) {
Fx_x += psi_x[j]*rho_u_n[idx[j]];
Fy_y += psi_y[j]*rho_v_n[idx[j]];
}
rho_phi[e] -= phi_dt*(Fx_x + Fy_y);
/* Determine the convective fluxes for (\rho u)^{n+\phi} */
Fx_x = 0.0; Fy_y = 0.0;
for (j = 0; j < 3; j++) {
Fx_x += psi_x[j]*rho_u_n[idx[j]]*u_n[idx[j]];
Fy_y += psi_y[j]*rho_v_n[idx[j]]*u_n[idx[j]];
}
rho_u_phi[e] -= phi_dt*(Fx_x + Fy_y);
/* Determine the convective fluxes for (\rho v)^{n+\phi} */
Fx_x = 0.0; Fy_y = 0.0;
for (j = 0; j < 3; j++) {
Fx_x += psi_x[j]*rho_u_n[idx[j]]*v_n[idx[j]];
Fy_y += psi_y[j]*rho_v_n[idx[j]]*v_n[idx[j]];
}
rho_v_phi[e] -= phi_dt*(Fx_x + Fy_y);
}
ierr = DMDARestoreElements(da, &ne, &nc, &necon);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.rho, &rho_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.rho_u, &rho_u_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.rho_v, &rho_v_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.rho, &rho_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.rho_u, &rho_u_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.rho_v, &rho_v_phi);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode SetUpMatrices(AppCtx *user)
{
PetscErrorCode ierr;
PetscInt nele,nen,i,n;
const PetscInt *ele;
PetscScalar dt=user->dt,h;
PetscInt idx[2];
PetscScalar eM_0[2][2],eM_2[2][2];
Mat M =user->M;
Mat M_0=user->M_0;
PetscInt Mda;
PetscFunctionBeginUser;
ierr = MatGetLocalSize(M,&n,NULL);CHKERRQ(ierr);
ierr = DMDAGetInfo(user->da1,NULL,&Mda,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
if (user->periodic) h = (user->xmax-user->xmin)/Mda;
else h = (user->xmax-user->xmin)/(Mda-1.0);
if (user->lumpedmass) {
eM_0[0][0] = h/2.0;
eM_0[1][1] = h/2.0;
eM_0[0][1] = eM_0[1][0] = 0.0;
} else {
eM_0[0][0]=eM_0[1][1]=h/3.0;
eM_0[0][1]=eM_0[1][0]=h/6.0;
}
eM_2[0][0]=eM_2[1][1]=1.0/h;
eM_2[0][1]=eM_2[1][0]=-1.0/h;
/* Get local element info */
ierr = DMDAGetElements(user->da1,&nele,&nen,&ele);CHKERRQ(ierr);
for (i=0; i < nele; i++) {
idx[0] = ele[2*i]; idx[1] = ele[2*i+1];
PetscInt row,cols[4],r,row_M_0,cols2[2];
PetscScalar vals[4],vals_M_0[2],vals2[2];
for (r=0; r<2; r++) {
row_M_0 = idx[r];
vals_M_0[0]=eM_0[r][0];
vals_M_0[1]=eM_0[r][1];
ierr = MatSetValuesLocal(M_0,1,&row_M_0,2,idx,vals_M_0,ADD_VALUES);CHKERRQ(ierr);
row = 3*idx[r];
cols[0] = 3*idx[0]; vals[0] = dt*eM_2[r][0]*user->Mv;
cols[1] = 3*idx[1]; vals[1] = dt*eM_2[r][1]*user->Mv;
cols[2] = 3*idx[0]+1; vals[2] = eM_0[r][0];
cols[3] = 3*idx[1]+1; vals[3] = eM_0[r][1];
/* Insert values in matrix M for 1st dof */
ierr = MatSetValuesLocal(M,1,&row,4,cols,vals,ADD_VALUES);CHKERRQ(ierr);
row = 3*idx[r]+1;
cols[0] = 3*idx[0]; vals[0] = -eM_0[r][0];
cols[1] = 3*idx[1]; vals[1] = -eM_0[r][1];
cols[2] = 3*idx[0]+1; vals[2] = 2.0*user->kav*eM_2[r][0];
cols[3] = 3*idx[1]+1; vals[3] = 2.0*user->kav*eM_2[r][1];
/* Insert values in matrix M for 2nd dof */
ierr = MatSetValuesLocal(M,1,&row,4,cols,vals,ADD_VALUES);CHKERRQ(ierr);
row = 3*idx[r]+2;
cols2[0] = 3*idx[0]+2; vals2[0] = eM_0[r][0] + user->dt*2.0*user->L*user->kaeta*eM_2[r][0];
cols2[1] = 3*idx[1]+2; vals2[1] = eM_0[r][1] + user->dt*2.0*user->L*user->kaeta*eM_2[r][1];
ierr = MatSetValuesLocal(M,1,&row,2,cols2,vals2,ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(M_0,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(M_0,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = DMDARestoreElements(user->da1,&nele,&nen,&ele);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode SetInitialGuess(Vec X,AppCtx *user)
{
PetscErrorCode ierr;
PetscInt n,i,Mda;
PetscScalar *xx,*cv_p,*wv_p,*eta_p;
PetscViewer view_out;
/* needed for the void growth case */
PetscScalar xmid,cv_v=1.0,cv_m=user->Sv*user->cv0,eta_v=1.0,eta_m=0.0,h,lambda;
PetscInt nele,nen,idx[2];
const PetscInt *ele;
PetscScalar x[2];
Vec coords;
const PetscScalar *_coords;
PetscScalar xwidth = user->xmax - user->xmin;
PetscFunctionBeginUser;
ierr = VecGetLocalSize(X,&n);CHKERRQ(ierr);
ierr = DMDAGetInfo(user->da2,NULL,&Mda,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(user->da2,&coords);CHKERRQ(ierr);
ierr = VecGetArrayRead(coords,&_coords);CHKERRQ(ierr);
if (user->periodic) h = (user->xmax-user->xmin)/Mda;
else h = (user->xmax-user->xmin)/(Mda-1.0);
xmid = (user->xmax + user->xmin)/2.0;
lambda = 4.0*h;
ierr = DMDAGetElements(user->da2,&nele,&nen,&ele);CHKERRQ(ierr);
for (i=0; i < nele; i++) {
idx[0] = ele[2*i]; idx[1] = ele[2*i+1];
x[0] = _coords[idx[0]];
x[1] = _coords[idx[1]];
PetscInt k;
PetscScalar vals_DDcv[2],vals_cv[2],vals_eta[2],s,hhr,r;
for (k=0; k < 2; k++) {
s = PetscAbs(x[k] - xmid);
if (s <= xwidth*(5.0/64.0)) {
vals_cv[k] = cv_v;
vals_eta[k] = eta_v;
vals_DDcv[k] = 0.0;
} else if (s> xwidth*(5.0/64.0) && s<= xwidth*(7.0/64.0)) {
/*r = (s - xwidth*(6.0/64.0))/(0.5*lambda);*/
r = (s - xwidth*(6.0/64.0))/(xwidth/64.0);
hhr = 0.25*(-r*r*r + 3*r + 2);
vals_cv[k] = cv_m + (1.0 - hhr)*(cv_v - cv_m);
vals_eta[k] = eta_m + (1.0 - hhr)*(eta_v - eta_m);
vals_DDcv[k] = (cv_v - cv_m)*r*6.0/(lambda*lambda);
} else {
vals_cv[k] = cv_m;
vals_eta[k] = eta_m;
vals_DDcv[k] = 0.0;
}
}
ierr = VecSetValuesLocal(user->cv,2,idx,vals_cv,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecSetValuesLocal(user->eta,2,idx,vals_eta,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecSetValuesLocal(user->work2,2,idx,vals_DDcv,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = DMDARestoreElements(user->da2,&nele,&nen,&ele);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(coords,&_coords);CHKERRQ(ierr);
ierr = VecAssemblyBegin(user->cv);CHKERRQ(ierr);
ierr = VecAssemblyEnd(user->cv);CHKERRQ(ierr);
ierr = VecAssemblyBegin(user->eta);CHKERRQ(ierr);
ierr = VecAssemblyEnd(user->eta);CHKERRQ(ierr);
ierr = VecAssemblyBegin(user->work2);CHKERRQ(ierr);
ierr = VecAssemblyEnd(user->work2);CHKERRQ(ierr);
ierr = DPsi(user);CHKERRQ(ierr);
ierr = VecCopy(user->DPsiv,user->wv);CHKERRQ(ierr);
ierr = VecAXPY(user->wv,-2.0*user->kav,user->work2);CHKERRQ(ierr);
ierr = VecGetArray(X,&xx);CHKERRQ(ierr);
ierr = VecGetArray(user->wv,&wv_p);CHKERRQ(ierr);
ierr = VecGetArray(user->cv,&cv_p);CHKERRQ(ierr);
ierr = VecGetArray(user->eta,&eta_p);CHKERRQ(ierr);
for (i=0; i<n/3; i++) {
xx[3*i] =wv_p[i];
xx[3*i+1]=cv_p[i];
xx[3*i+2]=eta_p[i];
}
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_initial",FILE_MODE_WRITE,&view_out);CHKERRQ(ierr);
ierr = VecView(user->wv,view_out);CHKERRQ(ierr);
ierr = VecView(user->cv,view_out);CHKERRQ(ierr);
ierr = VecView(user->eta,view_out);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&view_out);CHKERRQ(ierr);
ierr = VecRestoreArray(X,&xx);CHKERRQ(ierr);
ierr = VecRestoreArray(user->wv,&wv_p);CHKERRQ(ierr);
ierr = VecRestoreArray(user->cv,&cv_p);CHKERRQ(ierr);
ierr = VecRestoreArray(user->eta,&eta_p);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode SetUpMatrices(AppCtx *user)
{
PetscErrorCode ierr;
PetscInt nele,nen,i,j;
const PetscInt *ele;
PetscScalar dt=user->dt;
PetscScalar y[3];
PetscInt idx[3];
PetscScalar eM_0[3][3],eM_2_odd[3][3],eM_2_even[3][3];
Mat M =user->M;
PetscScalar epsilon=user->epsilon;
PetscScalar hx;
PetscInt n,Mda,Nda;
DM da;
PetscFunctionBeginUser;
/* Create the mass matrix M_0 */
ierr = MatGetLocalSize(M,&n,NULL);CHKERRQ(ierr);
/* ierr = MatCreate(PETSC_COMM_WORLD,&user->M_0);CHKERRQ(ierr);*/
ierr = DMDAGetInfo(user->da,NULL,&Mda,&Nda,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
hx = 1.0/(Mda-1);
ierr = DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,Mda,Nda,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr);
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&user->M_0);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
eM_0[0][0]=eM_0[1][1]=eM_0[2][2]=hx*hx/12.0;
eM_0[0][1]=eM_0[0][2]=eM_0[1][0]=eM_0[1][2]=eM_0[2][0]=eM_0[2][1]=hx*hx/24.0;
eM_2_odd[0][0] = eM_2_odd[0][1] = eM_2_odd[0][2] = 0.0;
eM_2_odd[1][0] = eM_2_odd[1][1] = eM_2_odd[1][2] = 0.0;
eM_2_odd[2][0] = eM_2_odd[2][1] = eM_2_odd[2][2] = 0.0;
eM_2_odd[0][0]=1.0;
eM_2_odd[1][1]=eM_2_odd[2][2]=0.5;
eM_2_odd[0][1]=eM_2_odd[0][2]=eM_2_odd[1][0]=eM_2_odd[2][0]=-0.5;
eM_2_even[0][0] = eM_2_even[0][1] = eM_2_even[0][2] = 0.0;
eM_2_even[0][0] = eM_2_even[0][1] = eM_2_even[0][2] = 0.0;
eM_2_even[0][0] = eM_2_even[0][1] = eM_2_even[0][2] = 0.0;
eM_2_even[1][1]=1;
eM_2_even[0][0]=eM_2_even[2][2]=0.5;
eM_2_even[0][1]=eM_2_even[1][0]=eM_2_even[1][2]=eM_2_even[2][1]=-0.5;
/* Get local element info */
ierr = DMDAGetElements(user->da,&nele,&nen,&ele);CHKERRQ(ierr);
for (i=0; i < nele; i++) {
idx[0] = ele[3*i]; idx[1] = ele[3*i+1]; idx[2] = ele[3*i+2];
PetscInt row,cols[3],r,row_M_0;
PetscScalar vals[3],vals_M_0[3];
for (r=0; r<3; r++) {
row_M_0 = idx[r];
vals_M_0[0]=eM_0[r][0];
vals_M_0[1]=eM_0[r][1];
vals_M_0[2]=eM_0[r][2];
ierr = MatSetValues(user->M_0,1,&row_M_0,3,idx,vals_M_0,ADD_VALUES);CHKERRQ(ierr);
if (y[1]==y[0]) {
row = 4*idx[r];
cols[0] = 4*idx[0]; vals[0] = eM_0[r][0]+dt*epsilon*epsilon*eM_2_odd[r][0];
cols[1] = 4*idx[1]; vals[1] = eM_0[r][1]+dt*epsilon*epsilon*eM_2_odd[r][1];
cols[2] = 4*idx[2]; vals[2] = eM_0[r][2]+dt*epsilon*epsilon*eM_2_odd[r][2];
/* Insert values in matrix M for 1st dof */
ierr = MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);CHKERRQ(ierr);
row = 4*idx[r]+1;
cols[0] = 4*idx[0]+1; vals[0] = eM_0[r][0]+dt*epsilon*epsilon*eM_2_odd[r][0];
cols[1] = 4*idx[1]+1; vals[1] = eM_0[r][1]+dt*epsilon*epsilon*eM_2_odd[r][1];
cols[2] = 4*idx[2]+1; vals[2] = eM_0[r][2]+dt*epsilon*epsilon*eM_2_odd[r][2];
/* Insert values in matrix M for 2nd dof */
ierr = MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);CHKERRQ(ierr);
row = 4*idx[r]+2;
cols[0] = 4*idx[0]+2; vals[0] = eM_0[r][0]+dt*epsilon*epsilon*eM_2_odd[r][0];
cols[1] = 4*idx[1]+2; vals[1] = eM_0[r][1]+dt*epsilon*epsilon*eM_2_odd[r][1];
cols[2] = 4*idx[2]+2; vals[2] = eM_0[r][2]+dt*epsilon*epsilon*eM_2_odd[r][2];
/* Insert values in matrix M for 3nd dof */
ierr = MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);CHKERRQ(ierr);
} else {
row = 4*idx[r];
cols[0] = 4*idx[0]; vals[0] = eM_0[r][0]+dt*epsilon*epsilon*eM_2_even[r][0];
cols[1] = 4*idx[1]; vals[1] = eM_0[r][1]+dt*epsilon*epsilon*eM_2_even[r][1];
cols[2] = 4*idx[2]; vals[2] = eM_0[r][2]+dt*epsilon*epsilon*eM_2_even[r][2];
/* Insert values in matrix M for 1st dof */
ierr = MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);CHKERRQ(ierr);
row = 4*idx[r]+1;
cols[0] = 4*idx[0]+1; vals[0] = eM_0[r][0]+dt*epsilon*epsilon*eM_2_even[r][0];
cols[1] = 4*idx[1]+1; vals[1] = eM_0[r][1]+dt*epsilon*epsilon*eM_2_even[r][1];
cols[2] = 4*idx[2]+1; vals[2] = eM_0[r][2]+dt*epsilon*epsilon*eM_2_even[r][2];
/* Insert values in matrix M for 2nd dof */
ierr = MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);CHKERRQ(ierr);
row = 4*idx[r]+2;
cols[0] = 4*idx[0]+2; vals[0] = eM_0[r][0]+dt*epsilon*epsilon*eM_2_even[r][0];
cols[1] = 4*idx[1]+2; vals[1] = eM_0[r][1]+dt*epsilon*epsilon*eM_2_even[r][1];
cols[2] = 4*idx[2]+2; vals[2] = eM_0[r][2]+dt*epsilon*epsilon*eM_2_even[r][2];
/* Insert values in matrix M for 3nd dof */
ierr = MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);CHKERRQ(ierr);
}
}
}
ierr = MatAssemblyBegin(user->M_0,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(user->M_0,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscScalar vals[9];
vals[0] = -1.0; vals[1] = 0.0; vals[2] = 0.0;
vals[3] = 0.0; vals[4] = -1.0; vals[5] = 0.0;
vals[6] = 0.0; vals[7] = 0.0; vals[8] = -1.0;
for (j=0; j < nele; j++) {
idx[0] = ele[3*j]; idx[1] = ele[3*j+1]; idx[2] = ele[3*j+2];
PetscInt r,rows[3],cols[3];
for (r=0; r<3; r++) {
rows[0] = 4*idx[0]+r; cols[0] = 4*idx[0]+3;
rows[1] = 4*idx[1]+r; cols[1] = 4*idx[1]+3;
rows[2] = 4*idx[2]+r; cols[2] = 4*idx[2]+3;
ierr = MatSetValuesLocal(M,3,rows,3,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesLocal(M,3,cols,3,rows,vals,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = DMDARestoreElements(user->da,&nele,&nen,&ele);CHKERRQ(ierr);
ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&user->u1);CHKERRQ(ierr);
ierr = VecSetSizes(user->u1,n/4,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(user->u1);CHKERRQ(ierr);
ierr = VecDuplicate(user->u1,&user->u2);CHKERRQ(ierr);
ierr = VecDuplicate(user->u1,&user->u3);CHKERRQ(ierr);
ierr = VecDuplicate(user->u1,&user->work1);CHKERRQ(ierr);
ierr = VecDuplicate(user->u1,&user->work2);CHKERRQ(ierr);
ierr = VecDuplicate(user->u1,&user->work3);CHKERRQ(ierr);
ierr = VecDuplicate(user->u1,&user->work4);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode SetInitialGuess(Vec X,AppCtx *user)
{
PetscErrorCode ierr;
PetscInt nele,nen,n,i;
const PetscInt *ele;
Vec coords, rand1, rand2;
const PetscScalar *_coords;
PetscScalar x[3],y[3];
PetscInt idx[3];
PetscScalar *xx,*w1,*w2,*u1,*u2,*u3;
PetscViewer view_out;
PetscFunctionBeginUser;
/* Get ghosted coordinates */
ierr = DMGetCoordinatesLocal(user->da,&coords);CHKERRQ(ierr);
ierr = VecDuplicate(user->u1,&rand1);
ierr = VecDuplicate(user->u1,&rand2);
ierr = VecSetRandom(rand1,NULL);
ierr = VecSetRandom(rand2,NULL);
ierr = VecGetLocalSize(X,&n);CHKERRQ(ierr);
ierr = VecGetArrayRead(coords,&_coords);CHKERRQ(ierr);
ierr = VecGetArray(X,&xx);CHKERRQ(ierr);
ierr = VecGetArray(user->work1,&w1);
ierr = VecGetArray(user->work2,&w2);
ierr = VecGetArray(user->u1,&u1);
ierr = VecGetArray(user->u2,&u2);
ierr = VecGetArray(user->u3,&u3);
/* Get local element info */
ierr = DMDAGetElements(user->da,&nele,&nen,&ele);CHKERRQ(ierr);
for (i=0; i < nele; i++) {
idx[0] = ele[3*i]; idx[1] = ele[3*i+1]; idx[2] = ele[3*i+2];
x[0] = _coords[2*idx[0]]; y[0] = _coords[2*idx[0]+1];
x[1] = _coords[2*idx[1]]; y[1] = _coords[2*idx[1]+1];
x[2] = _coords[2*idx[2]]; y[2] = _coords[2*idx[2]+1];
PetscScalar vals1[3],vals2[3],valsrand[3];
PetscInt r;
for (r=0; r<3; r++) {
valsrand[r]=5*x[r]*(1-x[r])*y[r]*(1-y[r]);
if (x[r]>=0.5 && y[r]>=0.5) {
vals1[r]=0.75;
vals2[r]=0.0;
}
if (x[r]>=0.5 && y[r]<0.5) {
vals1[r]=0.0;
vals2[r]=0.0;
}
if (x[r]<0.5 && y[r]>=0.5) {
vals1[r]=0.0;
vals2[r]=0.75;
}
if (x[r]<0.5 && y[r]<0.5) {
vals1[r]=0.75;
vals2[r]=0.0;
}
}
ierr = VecSetValues(user->work1,3,idx,vals1,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecSetValues(user->work2,3,idx,vals2,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecSetValues(user->work3,3,idx,valsrand,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(user->work1);CHKERRQ(ierr);
ierr = VecAssemblyEnd(user->work1);CHKERRQ(ierr);
ierr = VecAssemblyBegin(user->work2);CHKERRQ(ierr);
ierr = VecAssemblyEnd(user->work2);CHKERRQ(ierr);
ierr = VecAssemblyBegin(user->work3);CHKERRQ(ierr);
ierr = VecAssemblyEnd(user->work3);CHKERRQ(ierr);
ierr = VecAXPY(user->work1,1.0,user->work3);CHKERRQ(ierr);
ierr = VecAXPY(user->work2,1.0,user->work3);CHKERRQ(ierr);
for (i=0; i<n/4; i++) {
xx[4*i] = w1[i];
if (xx[4*i]>1) xx[4*i]=1;
xx[4*i+1] = w2[i];
if (xx[4*i+1]>1) xx[4*i+1]=1;
if (xx[4*i]+xx[4*i+1]>1) xx[4*i+1] = 1.0 - xx[4*i];
xx[4*i+2] = 1.0 - xx[4*i] - xx[4*i+1];
xx[4*i+3] = 0.0;
u1[i] = xx[4*i];
u2[i] = xx[4*i+1];
u3[i] = xx[4*i+2];
}
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_initial",FILE_MODE_WRITE,&view_out);CHKERRQ(ierr);
ierr = VecView(user->u1,view_out);CHKERRQ(ierr);
ierr = VecView(user->u2,view_out);CHKERRQ(ierr);
ierr = VecView(user->u3,view_out);CHKERRQ(ierr);
PetscViewerDestroy(&view_out);
ierr = DMDARestoreElements(user->da,&nele,&nen,&ele);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(coords,&_coords);CHKERRQ(ierr);
ierr = VecRestoreArray(X,&xx);CHKERRQ(ierr);
ierr = VecRestoreArray(user->work2,&w1);CHKERRQ(ierr);
ierr = VecRestoreArray(user->work4,&w2);CHKERRQ(ierr);
ierr = VecRestoreArray(user->u1,&u1);CHKERRQ(ierr);
ierr = VecRestoreArray(user->u2,&u2);CHKERRQ(ierr);
ierr = VecRestoreArray(user->u3,&u3);CHKERRQ(ierr);
ierr = VecDestroy(&rand1);CHKERRQ(ierr);
ierr = VecDestroy(&rand2);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
