ExecStatus
IntBase<VY>::prune_lower(Space& home, int* dis, int n_dis) {
assert(n_dis > 0);
// At least one more value will be needed
GECODE_ME_CHECK(y.gq(home,vs.size() + 1));
Region r(home);
// Only one additional value is allowed
if (y.max() == vs.size() + 1) {
// Compute possible values
ViewRanges<IntView>* r_dis = r.alloc<ViewRanges<IntView> >(n_dis);
for (int i=n_dis; i--; )
r_dis[i] = ViewRanges<IntView>(x[dis[i]]);
Iter::Ranges::NaryInter iv(r, r_dis, n_dis);
// Is there a common value at all?
if (!iv())
return ES_FAILED;
ValSet::Ranges vsr(vs);
Iter::Ranges::NaryUnion pv(r,iv,vsr);
// Enforce common values
for (int i=x.size(); i--; ) {
pv.reset();
GECODE_ME_CHECK(x[i].inter_r(home, pv, false));
}
return ES_OK;
}
// Compute independent set for lower bound
// ovl is a bit-matrix defining whether two views overlap
SymBitMatrix ovl(r,x.size());
// deg[i] is the degree of x[i]
int* deg = r.alloc<int>(x.size());
// ovl_i[i] is an array of indices j such that x[j] overlaps with x[i]
int** ovl_i = r.alloc<int*>(x.size());
// n_ovl_i[i] defines how many integers are stored for ovl_i[i]
int* n_ovl_i = r.alloc<int>(x.size());
{
#ifndef NDEBUG
// Initialize all to null pointers so that things crash ;-)
for (int i=x.size(); i--; )
ovl_i[i] = NULL;
#endif
// For each i there can be at most n_dis-1 entries in ovl_i[i]
int* m = r.alloc<int>(n_dis*(n_dis-1));
for (int i=n_dis; i--; ) {
deg[dis[i]] = 0;
ovl_i[dis[i]] = m; m += n_dis-1;
}
}
// Initialize overlap matrix by analyzing the view ranges
{
// Compute how many events are needed
// One event for the end marker
int n_re = 1;
// Two events for each range
for (int i=n_dis; i--; )
for (ViewRanges<IntView> rx(x[dis[i]]); rx(); ++rx)
n_re += 2;
// Allocate and initialize events
RangeEvent* re = r.alloc<RangeEvent>(n_re);
int j=0;
for (int i=n_dis; i--; )
for (ViewRanges<IntView> rx(x[dis[i]]); rx(); ++rx) {
// Event when a range starts
re[j].ret=RET_FST; re[j].val=rx.min(); re[j].view=dis[i]; j++;
// Event when a range ends
re[j].ret=RET_LST; re[j].val=rx.max(); re[j].view=dis[i]; j++;
}
// Make this the last event
re[j].ret=RET_END; re[j].val=Int::Limits::infinity;
assert(j+1 == n_re);
// Sort and process events
Support::quicksort(re,n_re);
// Current views with a range being active
Support::BitSet<Region> cur(r,static_cast<unsigned int>(x.size()));
// Process all events
for (int i=0; true; i++)
switch (re[i].ret) {
case RET_FST:
// Process all overlapping views
for (Iter::Values::BitSet<Support::BitSet<Region> > j(cur);
j(); ++j) {
int di = re[i].view, dj = j.val();
if (!ovl.get(di,dj)) {
ovl.set(di,dj);
ovl_i[di][deg[di]++] = dj;
ovl_i[dj][deg[dj]++] = di;
}
}
cur.set(static_cast<unsigned int>(re[i].view));
break;
case RET_LST:
cur.clear(static_cast<unsigned int>(re[i].view));
break;
case RET_END:
goto done;
default:
GECODE_NEVER;
}
done:
r.free<RangeEvent>(re,n_re);
}
// While deg changes, n_ovl_i remains unchanged and is needed, so copy it
for (int i=n_dis; i--; ) {
assert(deg[dis[i]] < n_dis);
n_ovl_i[dis[i]] = deg[dis[i]];
}
// Views in the independent set
int* ind = r.alloc<int>(n_dis);
int n_ind = 0;
while (n_dis > 0) {
int i_min = n_dis-1;
int d_min = deg[dis[i_min]];
unsigned int s_min = x[dis[i_min]].size();
// Find view with smallest (degree,size)
for (int i=n_dis-1; i--; )
if ((d_min > deg[dis[i]]) ||
((d_min == deg[dis[i]]) && (s_min > x[dis[i]].size()))) {
i_min = i;
d_min = deg[dis[i]];
s_min = x[dis[i]].size();
}
// i_min refers to view with smallest (degree,size)
ind[n_ind++] = dis[i_min]; dis[i_min] = dis[--n_dis];
// Filter out non disjoint views
for (int i=n_dis; i--; )
if (ovl.get(dis[i],ind[n_ind-1])) {
// Update degree information
for (int j=n_ovl_i[dis[i]]; j--; )
deg[ovl_i[dis[i]][j]]--;
// Eliminate view
dis[i] = dis[--n_dis];
}
}
// Enforce lower bound
GECODE_ME_CHECK(y.gq(home,vs.size() + n_ind));
// Prune, if possible
if (vs.size() + n_ind == y.max()) {
// Only values from the indepent set a can be taken
ViewRanges<IntView>* r_ind = r.alloc<ViewRanges<IntView> >(n_ind);
for (int i=n_ind; i--; )
r_ind[i] = ViewRanges<IntView>(x[ind[i]]);
Iter::Ranges::NaryUnion v_ind(r, r_ind, n_ind);
ValSet::Ranges vsr(vs);
v_ind |= vsr;
for (int i=x.size(); i--; ) {
v_ind.reset();
GECODE_ME_CHECK(x[i].inter_r(home,v_ind,false));
}
}
return ES_OK;
}
void FluidSim::solve_viscosity(float dt) {
int ni = liquid_phi.ni;
int nj = liquid_phi.nj;
//static obstacles for simplicity - for moving objects,
//use a spatially varying 2d array, and modify the linear system appropriately
float u_obj = 0;
float v_obj = 0;
Array2c u_state(ni+1,nj,(const char&)0);
Array2c v_state(ni,nj+1,(const char&)0);
const int SOLID = 1;
const int FLUID = 0;
printf("Determining states\n");
//just determine if the face position is inside the wall! That's it.
for(int j = 0; j < nj; ++j) {
for(int i = 0; i < ni+1; ++i) {
if(i - 1 < 0 || i >= ni || (nodal_solid_phi(i,j+1) + nodal_solid_phi(i,j))/2 <= 0)
u_state(i,j) = SOLID;
else
u_state(i,j) = FLUID;
}
}
for(int j = 0; j < nj+1; ++j) {
for(int i = 0; i < ni; ++i) {
if(j - 1 < 0 || j >= nj || (nodal_solid_phi(i+1,j) + nodal_solid_phi(i,j))/2 <= 0)
v_state(i,j) = SOLID;
else
v_state(i,j) = FLUID;
}
}
printf("Building matrix\n");
int elts = (ni+1)*nj + ni*(nj+1);
if(vrhs.size() != elts) {
vrhs.resize(elts);
velocities.resize(elts);
vmatrix.resize(elts);
}
vmatrix.zero();
float factor = dt/sqr(dx);
for(int j = 1; j < nj-1; ++j) for(int i = 1; i < ni-1; ++i) {
if(u_state(i,j) == FLUID ) {
int index = u_ind(i,j);
vrhs[index] = u_vol(i,j) * u(i,j);
vmatrix.set_element(index,index,u_vol(i,j));
//uxx terms
float visc_right = viscosity(i,j);
float visc_left = viscosity(i-1,j);
float vol_right = c_vol(i,j);
float vol_left = c_vol(i-1,j);
//u_x_right
vmatrix.add_to_element(index,index, 2*factor*visc_right*vol_right);
if(u_state(i+1,j) == FLUID)
vmatrix.add_to_element(index,u_ind(i+1,j), -2*factor*visc_right*vol_right);
else if(u_state(i+1,j) == SOLID)
vrhs[index] -= -2*factor*visc_right*vol_right*u_obj;
//u_x_left
vmatrix.add_to_element(index,index, 2*factor*visc_left*vol_left);
if(u_state(i-1,j) == FLUID)
vmatrix.add_to_element(index,u_ind(i-1,j), -2*factor*visc_left*vol_left);
else if(u_state(i-1,j) == SOLID)
vrhs[index] -= -2*factor*visc_left*vol_left*u_obj;
//uyy terms
float visc_top = 0.25f*(viscosity(i-1,j+1) + viscosity(i-1,j) + viscosity(i,j+1) + viscosity(i,j));
float visc_bottom = 0.25f*(viscosity(i-1,j) + viscosity(i-1,j-1) + viscosity(i,j) + viscosity(i,j-1));
float vol_top = n_vol(i,j+1);
float vol_bottom = n_vol(i,j);
//u_y_top
vmatrix.add_to_element(index,index, +factor*visc_top*vol_top);
if(u_state(i,j+1) == FLUID)
vmatrix.add_to_element(index,u_ind(i,j+1), -factor*visc_top*vol_top);
else if(u_state(i,j+1) == SOLID)
vrhs[index] -= -u_obj*factor*visc_top*vol_top;
//u_y_bottom
vmatrix.add_to_element(index,index, +factor*visc_bottom*vol_bottom);
if(u_state(i,j-1) == FLUID)
vmatrix.add_to_element(index,u_ind(i,j-1), -factor*visc_bottom*vol_bottom);
else if(u_state(i,j-1) == SOLID)
vrhs[index] -= -u_obj*factor*visc_bottom*vol_bottom;
//vxy terms
//v_x_top
if(v_state(i,j+1) == FLUID)
vmatrix.add_to_element(index,v_ind(i,j+1), -factor*visc_top*vol_top);
else if(v_state(i,j+1) == SOLID)
vrhs[index] -= -v_obj*factor*visc_top*vol_top;
if(v_state(i-1,j+1) == FLUID)
vmatrix.add_to_element(index,v_ind(i-1,j+1), factor*visc_top*vol_top);
else if(v_state(i-1,j+1) == SOLID)
vrhs[index] -= v_obj*factor*visc_top*vol_top;
//v_x_bottom
if(v_state(i,j) == FLUID)
vmatrix.add_to_element(index,v_ind(i,j), +factor*visc_bottom*vol_bottom);
else if(v_state(i,j) == SOLID)
vrhs[index] -= v_obj*factor*visc_bottom*vol_bottom;
if(v_state(i-1,j) == FLUID)
vmatrix.add_to_element(index,v_ind(i-1,j), -factor*visc_bottom*vol_bottom);
else if(v_state(i-1,j) == SOLID)
vrhs[index] -= -v_obj*factor*visc_bottom*vol_bottom;
}
}
for(int j = 1; j < nj; ++j) for(int i = 1; i < ni-1; ++i) {
if(v_state(i,j) == FLUID) {
int index = v_ind(i,j);
vrhs[index] = v_vol(i,j)*v(i,j);
vmatrix.set_element(index, index, v_vol(i,j));
//vyy
float visc_top = viscosity(i,j);
float visc_bottom = viscosity(i,j-1);
float vol_top = c_vol(i,j);
float vol_bottom = c_vol(i,j-1);
//vy_top
vmatrix.add_to_element(index,index, +2*factor*visc_top*vol_top);
if(v_state(i,j+1) == FLUID)
vmatrix.add_to_element(index,v_ind(i,j+1), -2*factor*visc_top*vol_top);
else if (v_state(i,j+1) == SOLID)
vrhs[index] -= -2*factor*visc_top*vol_top*v_obj;
//vy_bottom
vmatrix.add_to_element(index,index, +2*factor*visc_bottom*vol_bottom);
if(v_state(i,j-1) == FLUID)
vmatrix.add_to_element(index,v_ind(i,j-1), -2*factor*visc_bottom*vol_bottom);
else if(v_state(i,j-1) == SOLID)
vrhs[index] -= -2*factor*visc_bottom*vol_bottom*v_obj;
//vxx terms
float visc_right = 0.25f*(viscosity(i,j-1) + viscosity(i+1,j-1) + viscosity(i,j) + viscosity(i+1,j));
float visc_left = 0.25f*(viscosity(i,j-1) + viscosity(i-1,j-1) + viscosity(i,j) + viscosity(i-1,j));
float vol_right = n_vol(i+1,j);
float vol_left = n_vol(i,j);
//v_x_right
vmatrix.add_to_element(index,index, +factor*visc_right*vol_right);
if(v_state(i+1,j) == FLUID)
vmatrix.add_to_element(index,v_ind(i+1,j), -factor*visc_right*vol_right);
else if(v_state(i+1,j) == SOLID)
vrhs[index] -= -v_obj*factor*visc_right*vol_right;
//v_x_left
vmatrix.add_to_element(index,index, +factor*visc_left*vol_left);
if(v_state(i-1,j) == FLUID)
vmatrix.add_to_element(index,v_ind(i-1,j), -factor*visc_left*vol_left);
else if(v_state(i-1,j) == SOLID)
vrhs[index] -= -v_obj*factor*visc_left*vol_left;
//uyx
//u_y_right
if(u_state(i+1,j) == FLUID)
vmatrix.add_to_element(index,u_ind(i+1,j), -factor*visc_right*vol_right);
else if(u_state(i+1,j) == SOLID)
vrhs[index] -= -u_obj*factor*visc_right*vol_right;
if(u_state(i+1,j-1) == FLUID)
vmatrix.add_to_element(index,u_ind(i+1,j-1), factor*visc_right*vol_right);
else if(u_state(i+1,j-1) == SOLID)
vrhs[index] -= u_obj*factor*visc_right*vol_right;
//u_y_left
if(u_state(i,j) == FLUID)
vmatrix.add_to_element(index,u_ind(i,j), factor*visc_left*vol_left);
else if(u_state(i,j) == SOLID)
vrhs[index] -= u_obj*factor*visc_left*vol_left;
if(u_state(i,j-1) == FLUID)
vmatrix.add_to_element(index,u_ind(i,j-1), -factor*visc_left*vol_left);
else if(u_state(i,j-1) == SOLID)
vrhs[index] -= -u_obj*factor*visc_left*vol_left;
}
}
double res_out;
int iter_out;
solver.solve(vmatrix, vrhs, velocities, res_out, iter_out);
for(int j = 0; j < nj; ++j)
for(int i = 0; i < ni+1; ++i)
if(u_state(i,j) == FLUID)
u(i,j) = (float)velocities[u_ind(i,j)];
else if(u_state(i,j) == SOLID)
u(i,j) = u_obj;
for(int j = 0; j < nj+1; ++j)
for(int i = 0; i < ni; ++i)
if(v_state(i,j) == FLUID)
v(i,j) = (float)velocities[v_ind(i,j)];
else if(v_state(i,j) == SOLID)
v(i,j) = v_obj;
}