static void regular_constraints(
Constraint *constraints,
MatrixPairList *gen_list,
ObjectiveFunction objective_function,
Boolean *may_be_saddle_point)
{
/*
* The documentation at the top of this file shows that the image
* height h corresponding to a matrix m is
*
* h = m00 + (m01 - m10)dx + (m02 - m20)dy + (m03 - m30)dz.
*
* Each regular constraint will say that the image height h for the
* given matrix must remain greater than the image height h' of the
* matrix used for the objective function. In symbols, h >= h'.
* Since a Constraint says that some quantity must remain negative,
* we express the constraint as h' - h <= 0.
*
* The Boolean *may_be_saddle_point will be set to TRUE if some
* constraint suggests a saddle point. Otherwise it gets set to FALSE.
*/
int i;
MatrixPair *matrix_pair;
Constraint *constraint;
double h[4],
c;
/*
* Assume we're not at a saddle point unless we encounter
* evidence to the contrary.
*/
*may_be_saddle_point = FALSE;
/*
* Skip the identity and the MatrixPair used to define the objective
* function, and begin with the next MatrixPair on the list.
* Write a constraint for it and each successive MatrixPair.
*
* Skip the first three Constraints in the constraints array.
* They contain the step size constraints.
*/
for ( matrix_pair = gen_list->begin.next->next->next,
constraint = constraints + 3;
matrix_pair != &gen_list->end;
matrix_pair = matrix_pair->next,
constraint++)
{
/*
* Compute h. (As explained in set_objective_function(),
* it doesn't matter which of the two matrices we use.)
*/
for (i = 0; i < 3; i++)
h[i] = matrix_pair->m[0][0][i+1] - matrix_pair->m[0][i+1][0];
h[3] = matrix_pair->m[0][0][0];
/*
* Set the constraint to h' - h.
* (The objective function is h' in the above notation.)
*/
for (i = 0; i < 4; i++)
(*constraint)[i] = objective_function[i] - h[i];
/*
* Does the constraint plane pass through the origin?
*/
if ((*constraint)[3] > - CONSTRAINT_EPSILON)
{
/*
* Does the constraint have nonzero derivative?
* If not, then h and h' must have equal but nonzero derivatives.
* We know h' has nonzero derivative because we checked it
* when we computed the objective function.
* Its OK for h and h' to have equal but nonzero derivatives --
* it simply means that as we move avoid from the closest
* translate of the basepoint, we're moving away from some
* other translate as well -- be we don't want to divide by
* length3(*constraint).
*/
if (length3(*constraint) > ZERO_DERIV_EPSILON)
{
/*
* Check whether the constraint plane is parallel
* to the level sets of the objective function.
*
* Use the formula <u,v> = |u| |v| cos(angle).
*/
c = inner3(objective_function, *constraint) /
(length3(objective_function) * length3(*constraint));
/*
* If it is parallel, set *may_be_saddle_point to TRUE.
*/
if (fabs(c) > 1.0 - SADDLE_EPSILON)
*may_be_saddle_point = TRUE;
/*
* If necessary we could be more sophisticated at this point,
* and check whether the gradients of h and h' are parallel
* or antiparallel. Typically one expects them to be
* antiparallel (the MatrixPairs are, after all, the face
* pairings of a Dirichlet domain, so we don't have to worry
* about squares of a matrix), but if they were parallel one
* might want to ask which is longer (depending on which is
* longer, you will or will not be able to move the basepoint
* in that direction).
*/
}
}
}
}
void peano::applications::faxen::lbf::mappings::RegularGrid2SwitchFromLB2NSE::handleCell(
peano::applications::faxen::lbf::RegularGridBlockVertex* const vertices,
peano::applications::faxen::lbf::RegularGridBlockCell& cell,
const peano::kernel::gridinterface::VertexEnumerator& enumerator
) {
logTraceInWith2Arguments( "handleCell()", enumerator.toString(), cell );
// only for 2D implementation
/*
* positions of LB cells that are used for velocities interpolation
* for NSE grid
*/
tarch::la::Vector<DIMENSIONS,double> positionU0;
tarch::la::Vector<DIMENSIONS,double> positionU1;
tarch::la::Vector<DIMENSIONS,double> positionU2;
tarch::la::Vector<DIMENSIONS,double> positionU3;
tarch::la::Vector<DIMENSIONS,double> positionV0;
tarch::la::Vector<DIMENSIONS,double> positionV1;
tarch::la::Vector<DIMENSIONS,double> positionV2;
tarch::la::Vector<DIMENSIONS,double> positionV3;
// cellSize
tarch::la::Vector<DIMENSIONS,double> cellSize = enumerator.getCellSize();
// cellCenter
tarch::la::Vector<DIMENSIONS,double> cellCenter = enumerator.getCellCenter();
// particles index
int index;
if(LB_BLOCKSIZE%2 == 0) {
positionU0[0] = cellCenter[0] + cellSize[0]/2 - _dx/2;
positionU0[1] = cellCenter[1] - _dx/2;
positionU1[0] = cellCenter[0] + cellSize[0]/2 + _dx/2;
positionU1[1] = cellCenter[1] - _dx/2;
positionU2[0] = cellCenter[0] + cellSize[0]/2 - _dx/2;
positionU2[1] = cellCenter[1] + _dx/2;
positionU3[0] = cellCenter[0] + cellSize[0]/2 + _dx/2;
positionU3[1] = cellCenter[1] + _dx/2;
positionV0[0] = cellCenter[0] - _dx/2;
positionV0[1] = cellCenter[1] + cellSize[1]/2 - _dx/2;
positionV1[0] = cellCenter[0] + _dx/2;
positionV1[1] = cellCenter[1] + cellSize[1]/2 - _dx/2;
positionV2[0] = cellCenter[0] - _dx/2;
positionV2[1] = cellCenter[1] + cellSize[1]/2 + _dx/2;
positionV3[0] = cellCenter[0] +_dx/2;
positionV3[1] = cellCenter[1] + cellSize[1]/2 + _dx/2;
} else {
positionU0[0] = cellCenter[0] + cellSize[0]/2;
positionU0[1] = cellCenter[1] - _dx/2;
positionU1[0] = cellCenter[0] + cellSize[0]/2;
positionU1[1] = cellCenter[1] + _dx/2;
positionV0[0] = cellCenter[0] - _dx/2;
positionV0[1] = cellCenter[1] + cellSize[1]/2;
positionV1[0] = cellCenter[0] + _dx/2;
positionV1[1] = cellCenter[1] + cellSize[1]/2;
}
// load bottom left vertex
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().
loadVertex(vertices[enumerator(0)].getVertexNumber());
std::bitset<LB_BLOCK_NUMBER_OF_CELLS>& inner0(
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().getInner());
tarch::la::Vector<LB_BLOCK_NUMBER_OF_CELLS,double>& density0(
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().getDensity());
_p[0] = inner0[LB_BLOCK_NUMBER_OF_CELLS-1] ? density0[LB_BLOCK_NUMBER_OF_CELLS-1] : 0.0;
// load bottom right vertex
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().
loadVertex(vertices[enumerator(1)].getVertexNumber());
std::bitset<LB_BLOCK_NUMBER_OF_CELLS>& inner1(
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().getInner());
tarch::la::Vector<LB_BLOCK_NUMBER_OF_CELLS,double>& density1(
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().getDensity());
_p[1] = inner1[LB_BLOCK_NUMBER_OF_CELLS-LB_BLOCKSIZE] ? density1[LB_BLOCK_NUMBER_OF_CELLS-LB_BLOCKSIZE] : 0.0;
tarch::la::Vector<LB_BLOCK_NUMBER_OF_CELLS*DIMENSIONS,double>& velocity1(peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().getVelocity());
if(LB_BLOCKSIZE%2 == 0) {
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionU0)) != -1 ){
_u[0] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[0]/_dxbydt;
} else {
_u[0] = inner1[(2*LB_BLOCK_NUMBER_OF_CELLS-LB_BLOCKSIZE-2)/2] ? velocity1[2*LB_BLOCK_NUMBER_OF_CELLS-LB_BLOCKSIZE-2] : 0.0;
}
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionU1)) != -1 ){
_u[1] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[0]/_dxbydt;
} else {
_u[1] = inner1[(2*LB_BLOCK_NUMBER_OF_CELLS-LB_BLOCKSIZE)/2] ? velocity1[2*LB_BLOCK_NUMBER_OF_CELLS-LB_BLOCKSIZE] : 0.0;
}
} else {
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionU0)) != -1 ){
_u[0] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[0]/_dxbydt;
} else {
_u[0] = inner1[(2*LB_BLOCK_NUMBER_OF_CELLS-LB_BLOCKSIZE)/2] ? velocity1[2*LB_BLOCK_NUMBER_OF_CELLS-LB_BLOCKSIZE] : 0.0;
}
}
// load top left vertex
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().
loadVertex(vertices[enumerator(2)].getVertexNumber());
std::bitset<LB_BLOCK_NUMBER_OF_CELLS>& inner2(
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().getInner());
tarch::la::Vector<LB_BLOCK_NUMBER_OF_CELLS,double>& density2(
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().getDensity());
_p[2] = inner2[LB_BLOCKSIZE-1] ? density2[LB_BLOCKSIZE-1] : 0.0;
tarch::la::Vector<LB_BLOCK_NUMBER_OF_CELLS*DIMENSIONS,double>& velocity2(
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().getVelocity());
if(LB_BLOCKSIZE%2 == 0) {
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionV0)) != -1 ){
_v[0] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[1]/_dxbydt;
} else {
_v[0] = inner2[(LB_BLOCK_NUMBER_OF_CELLS-1)/2] ? velocity2[LB_BLOCK_NUMBER_OF_CELLS-1] : 0.0;
}
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionV2)) != -1 ){
_v[2] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[1]/_dxbydt;
} else {
_v[2] = inner2[(LB_BLOCK_NUMBER_OF_CELLS+2*LB_BLOCKSIZE-1)/2] ? velocity2[LB_BLOCK_NUMBER_OF_CELLS+2*LB_BLOCKSIZE-1] : 0.0;
}
} else {
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionV0)) != -1 ){
_v[0] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[1]/_dxbydt;
} else {
_v[0] = inner2[(LB_BLOCK_NUMBER_OF_CELLS+LB_BLOCKSIZE-1)/2] ? velocity2[LB_BLOCK_NUMBER_OF_CELLS+LB_BLOCKSIZE-1] : 0.0;
}
}
// load top right vertex
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().
loadVertex(vertices[enumerator(3)].getVertexNumber());
std::bitset<LB_BLOCK_NUMBER_OF_CELLS>& inner3(
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().getInner());
tarch::la::Vector<LB_BLOCK_NUMBER_OF_CELLS,double>& density3(
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().getDensity());
_p[3] = inner3[0] ? density3[0] : 0.0;
tarch::la::Vector<LB_BLOCK_NUMBER_OF_CELLS*DIMENSIONS,double>& velocity3(
peano::applications::latticeboltzmann::blocklatticeboltzmann::services::GridManagementService::getInstance().getVelocity());
if(LB_BLOCKSIZE%2 == 0) {
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionU2)) != -1 ){
_u[2] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[0]/_dxbydt;
} else {
_u[2] = inner3[(LB_BLOCKSIZE-2)/2] ? velocity3[LB_BLOCKSIZE-2] : 0.0;
}
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionU3)) != -1 ){
_u[3] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[0]/_dxbydt;
} else {
_u[3] = inner3[LB_BLOCKSIZE/2] ? velocity3[LB_BLOCKSIZE] : 0.0;
}
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionV1)) != -1 ){
_v[1] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[1]/_dxbydt;
} else {
_v[1] = inner3[(LB_BLOCK_NUMBER_OF_CELLS-2*LB_BLOCKSIZE+1)/2] ? velocity3[LB_BLOCK_NUMBER_OF_CELLS-2*LB_BLOCKSIZE+1] : 0.0;
}
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionV3)) != -1 ){
_v[3] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[1]/_dxbydt;
} else {
_v[3] = inner3[(LB_BLOCK_NUMBER_OF_CELLS+1)/2] ? velocity3[LB_BLOCK_NUMBER_OF_CELLS+1] : 0.0;
}
} else {
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionU1)) != -1 ){
_u[1] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[0]/_dxbydt;
} else {
_u[1] = inner3[(LB_BLOCKSIZE-1)/2] ? velocity3[LB_BLOCKSIZE-1] : 0.0;
}
if( (index=peano::applications::faxen::lbf::services::ParticlesService::getInstance().belongs2Particle(positionV1)) != -1 ){
_v[1] = peano::applications::faxen::lbf::services::ParticlesService::getInstance().getParticlesVelocity(index)[1]/_dxbydt;
} else {
_v[1] = inner3[(LB_BLOCK_NUMBER_OF_CELLS-LB_BLOCKSIZE+1)/2] ? velocity3[LB_BLOCK_NUMBER_OF_CELLS-LB_BLOCKSIZE+1] : 0.0;
}
}
double P_new = ((_p[0]+_p[1]+_p[2]+_p[3])/4)*_dxbydt*_dxbydt*_rho/3;
double P_old = cell.getP();
// updating cell's pressure and its averages with neighbors.
vertices[enumerator(1)].updateP0(P_old,P_new);
vertices[enumerator(2)].updateP1(P_old,P_new);
vertices[enumerator(3)].updateP0(P_old,P_new);
vertices[enumerator(3)].updateP1(P_old,P_new);
cell.setP(P_new);
double U_new, V_new;
double U_old = cell.getU();
double V_old = cell.getV();
if(LB_BLOCKSIZE%2 == 0) {
U_new = _dxbydt*(_u[0]+_u[1]+_u[2]+_u[3])/4;
V_new = _dxbydt*(_v[0]+_v[1]+_v[2]+_v[3])/4;
} else {
U_new = _dxbydt*(_u[0]+_u[1])/2;
V_new = _dxbydt*(_v[0]+_v[1])/2;
}
// updating cell's horizontal velocity and its averages with neighbors.
vertices[enumerator(0)].updateU0(U_old,U_new);
vertices[enumerator(1)].updateU1(U_old,U_new);
vertices[enumerator(1)].updateU0(U_old,U_new);
vertices[enumerator(2)].updateU2(U_old,U_new);
vertices[enumerator(3)].updateU2(U_old,U_new);
vertices[enumerator(2)].updateU0(U_old,U_new);
vertices[enumerator(3)].updateU1(U_old,U_new);
vertices[enumerator(3)].updateU0(U_old,U_new);
cell.setU(U_new);
// updating cell's vertical velocity and its averages with neighbors.
vertices[enumerator(0)].updateV0(V_old,V_new);
vertices[enumerator(1)].updateV1(V_old,V_new);
vertices[enumerator(1)].updateV0(V_old,V_new);
vertices[enumerator(2)].updateV2(V_old,V_new);
vertices[enumerator(3)].updateV2(V_old,V_new);
vertices[enumerator(2)].updateV0(V_old,V_new);
vertices[enumerator(3)].updateV1(V_old,V_new);
vertices[enumerator(3)].updateV0(V_old,V_new);
cell.setV(V_new);
logTraceOut( "handleCell()" );
}