void FeProblem::create(SparseMatrix* mat)
{
assert(mat != NULL);
if (is_up_to_date())
{
verbose("Reusing matrix sparse structure.");
mat->zero();
return;
}
// spaces have changed: create the matrix from scratch
mat->free();
int ndof = get_num_dofs();
mat->prealloc(ndof);
AUTOLA_CL(AsmList, al, wf->neq);
AUTOLA_OR(Mesh*, meshes, wf->neq);
bool **blocks = wf->get_blocks();
// init multi-mesh traversal
for (int i = 0; i < wf->neq; i++)
meshes[i] = spaces[i]->get_mesh();
Traverse trav;
trav.begin(wf->neq, meshes);
// loop through all elements
Element **e;
while ((e = trav.get_next_state(NULL, NULL)) != NULL)
{
// obtain assembly lists for the element at all spaces
for (int i = 0; i < wf->neq; i++)
// TODO: do not get the assembly list again if the element was not changed
if (e[i] != NULL)
spaces[i]->get_element_assembly_list(e[i], al + i);
// go through all equation-blocks of the local stiffness matrix
for (int m = 0; m < wf->neq; m++)
for (int n = 0; n < wf->neq; n++)
if (blocks[m][n] && e[m] != NULL && e[n] != NULL)
{
AsmList *am = al + m;
AsmList *an = al + n;
// pretend assembling of the element stiffness matrix
// register nonzero elements
for (int i = 0; i < am->cnt; i++)
if (am->dof[i] >= 0)
for (int j = 0; j < an->cnt; j++)
if (an->dof[j] >= 0)
mat->pre_add_ij(am->dof[i], an->dof[j]);
}
}
trav.finish();
delete [] blocks;
mat->alloc();
// save space seq numbers and weakform seq number, so we can detect their changes
for (int i = 0; i < wf->neq; i++)
sp_seq[i] = spaces[i]->get_seq();
wf_seq = wf->get_seq();
struct_changed = true;
have_matrix = true;
}
void FeProblem::assemble(_Vector *rhs, _Matrix *jac, Tuple<Solution*> u_ext)
{
// Sanity checks.
if (!have_spaces) error("You have to call set_spaces() before calling assemble().");
for (int i=0; i<this->wf->neq; i++) {
if (this->spaces[i] == NULL) error("A space is NULL in assemble().");
}
int k, m, n, marker;
AUTOLA_CL(AsmList, al, wf->neq);
AsmList *am, *an;
bool bnd[4];
AUTOLA_OR(bool, nat, wf->neq);
AUTOLA_OR(bool, isempty, wf->neq);
EdgePos ep[4];
reset_warn_order();
// create slave pss's for test functions, init quadrature points
AUTOLA_OR(PrecalcShapeset*, spss, wf->neq);
PrecalcShapeset *fu, *fv;
AUTOLA_CL(RefMap, refmap, wf->neq);
for (int i = 0; i < wf->neq; i++)
{
spss[i] = new PrecalcShapeset(pss[i]);
pss [i]->set_quad_2d(&g_quad_2d_std);
spss[i]->set_quad_2d(&g_quad_2d_std);
refmap[i].set_quad_2d(&g_quad_2d_std);
}
// initialize buffer
buffer = NULL;
mat_size = 0;
get_matrix_buffer(9);
// obtain a list of assembling stages
std::vector<WeakForm::Stage> stages;
wf->get_stages(spaces, NULL, stages, jac == NULL);
// Loop through all assembling stages -- the purpose of this is increased performance
// in multi-mesh calculations, where, e.g., only the right hand side uses two meshes.
// In such a case, the matrix forms are assembled over one mesh, and only the rhs
// traverses through the union mesh. On the other hand, if you don't use multi-mesh
// at all, there will always be only one stage in which all forms are assembled as usual.
Traverse trav;
for (unsigned ss = 0; ss < stages.size(); ss++)
{
WeakForm::Stage* s = &stages[ss];
for (unsigned i = 0; i < s->idx.size(); i++)
s->fns[i] = pss[s->idx[i]];
for (unsigned i = 0; i < s->ext.size(); i++)
s->ext[i]->set_quad_2d(&g_quad_2d_std);
trav.begin(s->meshes.size(), &(s->meshes.front()), &(s->fns.front()));
// assemble one stage
Element** e;
while ((e = trav.get_next_state(bnd, ep)) != NULL)
{
// find a non-NULL e[i]
Element* e0;
for (unsigned int i = 0; i < s->idx.size(); i++)
if ((e0 = e[i]) != NULL) break;
if (e0 == NULL) continue;
// set maximum integration order for use in integrals, see limit_order()
update_limit_table(e0->get_mode());
// obtain assembly lists for the element at all spaces, set appropriate mode for each pss
memset(isempty, 0, sizeof(bool) * wf->neq);
for (unsigned int i = 0; i < s->idx.size(); i++)
{
int j = s->idx[i];
if (e[i] == NULL) { isempty[j] = true; continue; }
spaces[j]->get_element_assembly_list(e[i], al+j);
spss[j]->set_active_element(e[i]);
spss[j]->set_master_transform();
refmap[j].set_active_element(e[i]);
refmap[j].force_transform(pss[j]->get_transform(), pss[j]->get_ctm());
u_ext[j]->set_active_element(e[i]);
u_ext[j]->force_transform(pss[j]->get_transform(), pss[j]->get_ctm());
}
marker = e0->marker;
init_cache();
//// assemble volume matrix forms //////////////////////////////////////
if (jac != NULL)
{
for (unsigned ww = 0; ww < s->mfvol.size(); ww++)
{
WeakForm::MatrixFormVol* mfv = s->mfvol[ww];
if (isempty[mfv->i] || isempty[mfv->j]) continue;
if (mfv->area != H2D_ANY && !wf->is_in_area(marker, mfv->area)) continue;
m = mfv->i; fv = spss[m]; am = &al[m];
n = mfv->j; fu = pss[n]; an = &al[n];
bool tra = (m != n) && (mfv->sym != 0);
bool sym = (m == n) && (mfv->sym == 1);
// assemble the local stiffness matrix for the form mfv
scalar bi, **mat = get_matrix_buffer(std::max(am->cnt, an->cnt));
for (int i = 0; i < am->cnt; i++)
{
if (!tra && (k = am->dof[i]) < 0) continue;
fv->set_active_shape(am->idx[i]);
if (!sym) // unsymmetric block
{
for (int j = 0; j < an->cnt; j++) {
fu->set_active_shape(an->idx[j]);
bi = eval_form(mfv, u_ext, fu, fv, refmap+n, refmap+m) * an->coef[j] * am->coef[i];
if (an->dof[j] >= 0) mat[i][j] = bi;
}
}
else // symmetric block
{
for (int j = 0; j < an->cnt; j++) {
if (j < i && an->dof[j] >= 0) continue;
fu->set_active_shape(an->idx[j]);
bi = eval_form(mfv, u_ext, fu, fv, refmap+n, refmap+m) * an->coef[j] * am->coef[i];
if (an->dof[j] >= 0) mat[i][j] = mat[j][i] = bi;
}
}
}
// insert the local stiffness matrix into the global one
jac->add(am->cnt, an->cnt, mat, am->dof, an->dof);
// insert also the off-diagonal (anti-)symmetric block, if required
if (tra)
{
if (mfv->sym < 0) chsgn(mat, am->cnt, an->cnt);
transpose(mat, am->cnt, an->cnt);
jac->add(am->cnt, an->cnt, mat, am->dof, an->dof);
}
}
}
//// assemble volume linear forms ////////////////////////////////////////
if (rhs != NULL)
{
for (unsigned int ww = 0; ww < s->vfvol.size(); ww++)
{
WeakForm::VectorFormVol* vfv = s->vfvol[ww];
if (isempty[vfv->i]) continue;
if (vfv->area != H2D_ANY && !wf->is_in_area(marker, vfv->area)) continue;
m = vfv->i; fv = spss[m]; am = &al[m];
for (int i = 0; i < am->cnt; i++)
{
if (am->dof[i] < 0) continue;
fv->set_active_shape(am->idx[i]);
rhs->add(am->dof[i], eval_form(vfv, u_ext, fv, refmap + m) * am->coef[i]);
}
}
}
// assemble surface integrals now: loop through boundary edges of the element
for (unsigned int edge = 0; edge < e0->nvert; edge++)
{
if (!bnd[edge]) continue;
marker = ep[edge].marker;
// obtain the list of shape functions which are nonzero on this edge
for (unsigned int i = 0; i < s->idx.size(); i++) {
if (e[i] == NULL) continue;
int j = s->idx[i];
if ((nat[j] = (spaces[j]->bc_type_callback(marker) == BC_NATURAL)))
spaces[j]->get_edge_assembly_list(e[i], edge, al + j);
}
// assemble surface matrix forms ///////////////////////////////////
if (jac != NULL)
{
for (unsigned int ww = 0; ww < s->mfsurf.size(); ww++)
{
WeakForm::MatrixFormSurf* mfs = s->mfsurf[ww];
if (isempty[mfs->i] || isempty[mfs->j]) continue;
if (mfs->area != H2D_ANY && !wf->is_in_area(marker, mfs->area)) continue;
m = mfs->i; fv = spss[m]; am = &al[m];
n = mfs->j; fu = pss[n]; an = &al[n];
if (!nat[m] || !nat[n]) continue;
ep[edge].base = trav.get_base();
ep[edge].space_v = spaces[m];
ep[edge].space_u = spaces[n];
scalar bi, **mat = get_matrix_buffer(std::max(am->cnt, an->cnt));
for (int i = 0; i < am->cnt; i++)
{
if ((k = am->dof[i]) < 0) continue;
fv->set_active_shape(am->idx[i]);
for (int j = 0; j < an->cnt; j++)
{
fu->set_active_shape(an->idx[j]);
bi = eval_form(mfs, u_ext, fu, fv, refmap+n, refmap+m, ep+edge) * an->coef[j] * am->coef[i];
if (an->dof[j] >= 0) mat[i][j] = bi;
}
}
jac->add(am->cnt, an->cnt, mat, am->dof, an->dof);
}
}
// assemble surface linear forms /////////////////////////////////////
if (rhs != NULL)
{
for (unsigned ww = 0; ww < s->vfsurf.size(); ww++)
{
WeakForm::VectorFormSurf* vfs = s->vfsurf[ww];
if (isempty[vfs->i]) continue;
if (vfs->area != H2D_ANY && !wf->is_in_area(marker, vfs->area)) continue;
m = vfs->i; fv = spss[m]; am = &al[m];
if (!nat[m]) continue;
ep[edge].base = trav.get_base();
ep[edge].space_v = spaces[m];
for (int i = 0; i < am->cnt; i++)
{
if (am->dof[i] < 0) continue;
fv->set_active_shape(am->idx[i]);
rhs->add(am->dof[i], eval_form(vfs, u_ext, fv, refmap+m, ep+edge) * am->coef[i]);
}
}
}
}
delete_cache();
}
trav.finish();
}
for (int i = 0; i < wf->neq; i++) delete spss[i];
delete [] buffer;
buffer = NULL;
mat_size = 0;
}
void L2OrthoHP::get_optimal_refinement(Element* e, int order, Solution* rsln, int& split, int p[4],
bool h_only, bool iso_only, double conv_exp, int max_order)
{
int i, j, k, n = 0;
const int maxcand = 300;
order = std::max(get_h_order(order), get_v_order(order));
bool tri = e->is_triangle();
// calculate maximal order of elements
// linear elements = 9
// curvilinear elements = depends on iro_cache (how curved they are)
if (max_order == -1)
max_order = (20 - e->iro_cache)/2 - 2; // default
else
max_order = std::min( max_order, (20 - e->iro_cache)/2 - 2); // user specified
AUTOLA_CL(Cand, cand, maxcand);
#define make_p_cand(q) { \
assert(n < maxcand); \
cand[n].split = -1; \
cand[n].p[1] = cand[n].p[2] = cand[n].p[3] = 0; \
cand[n++].p[0] = (q); }
#define make_hp_cand(q0, q1, q2, q3) { \
assert(n < maxcand); \
cand[n].split = 0; \
cand[n].p[0] = (q0); \
cand[n].p[1] = (q1); \
cand[n].p[2] = (q2); \
cand[n++].p[3] = (q3); }
#define make_ani_cand(q0, q1, iso) { \
assert(n < maxcand); \
cand[n].split = iso; \
cand[n].p[2] = cand[n].p[3] = 0; \
cand[n].p[0] = (q0); \
cand[n++].p[1] = (q1); }\
if (h_only)
{
make_p_cand(order);
make_hp_cand(order, order, order, order);
make_ani_cand(order, order, 1);
make_ani_cand(order, order, 2);
}
else
{
// prepare p-candidates
int p0, p1 = std::min(max_order, order+1);
for (p0 = order; p0 <= p1; p0++)
make_p_cand(p0);
// prepare hp-candidates
p0 = (order+1) / 2;
p1 = std::min(p0 + 3, order);
int q0, q1, q2, q3;
for (q0 = p0; q0 <= p1; q0++)
for (q1 = p0; q1 <= p1; q1++)
for (q2 = p0; q2 <= p1; q2++)
for (q3 = p0; q3 <= p1; q3++)
make_hp_cand(q0, q1, q2, q3);
// prepare anisotropic candidates
// only for quadrilaterals
// too distorted (curved) elements cannot have aniso refinement (produces even worse elements)
if ((!tri) && (e->iro_cache < 8) && !iso_only) {
p0 = 2 * (order+1) / 3;
int p_max = std::min(max_order, order+1);
p1 = std::min(p0 + 3, p_max);
for (q0 = p0; q0 <= p1; q0++)
for (q1 = p0; q1 <= p1; q1++) {
if ((q0 < order+1) || (q1 < order+1)) {
make_ani_cand(q0, q1, 1);
make_ani_cand(q0, q1, 2);
}
}
}
}
// calculate (partial) projection errors
double herr[8][11], perr[11];
calc_projection_errors(e, order, rsln, herr, perr);
// evaluate candidates (sum partial projection errors, calculate dofs)
double avg = 0.0;
double dev = 0.0;
for (i = k = 0; i < n; i++)
{
Cand* c = cand + i;
if (c->split == 0)
{
c->error = 0.0;
c->dofs = tri ? 6 : 9;
for (j = 0; j < 4; j++)
{
int o = c->p[j];
c->error += herr[j][o] * 0.25; // spravny vypocet chyby
if (tri) {
c->dofs += (o-2)*(o-1)/2;
if (j < 3) c->dofs += std::min(o, c->p[3])-1 + 2*(o-1);
}
else {
c->dofs += sqr(o)-1;
c->dofs += 2 * std::min(o, c->p[j>0 ? j-1 : 3]) - 1;
}
}
}
else if (c->split == 1 || c->split == 2) // aniso splits
{
c->dofs = 6 /* vertex */ + 3*(c->p[0] - 1 + c->p[1] - 1); // edge fns
c->dofs += std::min(c->p[0], c->p[1]) - 1; // common edge
c->dofs += sqr(c->p[0] - 1) + sqr(c->p[1] - 1); // bubbles
for (c->error = 0.0, j = 0; j < 2; j++)
c->error += herr[(c->split == 1) ? j+4 : j+6][c->p[j]] * 0.5; // spravny vypocet chyby
}
else
{
int o = c->p[0];
c->error = perr[o];
c->dofs = tri ? (o+1)*(o+2)/2 : sqr(o+1);
}
c->error = sqrt(c->error);
//verbose("Cand #%d: Orders %d %d %d %d, Error %g, Dofs %d", i, c->p[0],c->p[1],c->p[2],c->p[3],c->error, c->dofs);
if (!i || c->error <= cand[0].error)
{
avg += log(c->error);
dev += sqr(log(c->error));
k++;
}
}
avg /= k; // mean
dev /= k; // second moment
dev = sqrt(dev - sqr(avg)); // deviation is square root of variance
// select an above-average candidate with the steepest error decrease
int imax = 0;
double score, maxscore = 0.0;
for (i = 1; i < n; i++)
{
if ((log(cand[i].error) < avg + dev) && (cand[i].dofs > cand[0].dofs))
{
score = (log(cand[0].error) - log(cand[i].error)) /
//(pow(cand[i].dofs, conv_exp) - pow(cand[0].dofs, conv_exp));
pow(cand[i].dofs - cand[0].dofs, conv_exp);
if (score > maxscore) { maxscore = score; imax = i; }
}
}
// return result
split = cand[imax].split;
memcpy(p, cand[imax].p, 4*sizeof(int));
//verbose("Selected Candidate #%d: Orders %d %d %d %d\n", imax, p[0],p[1],p[2],p[3]);
}
