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template<typename TreeType > |
TreeType::Ptr | solve (const TreeType &, math::pcg::State &, bool staggered=false) |
| Solve ∇2x = b for x, where b is a vector comprising the values of all of the active voxels in the input tree. More...
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template<typename TreeType , typename Interrupter > |
TreeType::Ptr | solve (const TreeType &, math::pcg::State &, Interrupter &, bool staggered=false) |
| Solve ∇2x = b for x, where b is a vector comprising the values of all of the active voxels in the input tree. More...
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template<typename TreeType , typename BoundaryOp , typename Interrupter > |
TreeType::Ptr | solveWithBoundaryConditions (const TreeType &, const BoundaryOp &, math::pcg::State &, Interrupter &, bool staggered=false) |
| Solve ∇2x = b for x with user-specified boundary conditions, where b is a vector comprising the values of all of the active voxels in the input tree or domain mask if provided. More...
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template<typename PreconditionerType , typename TreeType , typename BoundaryOp , typename Interrupter > |
TreeType::Ptr | solveWithBoundaryConditionsAndPreconditioner (const TreeType &, const BoundaryOp &, math::pcg::State &, Interrupter &, bool staggered=false) |
| Solve ∇2x = b for x with user-specified boundary conditions, where b is a vector comprising the values of all of the active voxels in the input tree or domain mask if provided. More...
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template<typename PreconditionerType , typename TreeType , typename DomainTreeType , typename BoundaryOp , typename Interrupter > |
TreeType::Ptr | solveWithBoundaryConditionsAndPreconditioner (const TreeType &, const DomainTreeType &, const BoundaryOp &, math::pcg::State &, Interrupter &, bool staggered=false) |
| Solve ∇2x = b for x with user-specified boundary conditions, where b is a vector comprising the values of all of the active voxels in the input tree or domain mask if provided. More...
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template<typename VIndexTreeType > |
void | populateIndexTree (VIndexTreeType &) |
| Overwrite each active voxel in the given scalar tree with a sequential index, starting from zero. More...
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template<typename TreeType > |
TreeType::template ValueConverter< VIndex >::Type::Ptr | createIndexTree (const TreeType &) |
| Iterate over the active voxels of the input tree and for each one assign its index in the iteration sequence to the corresponding voxel of an integer-valued output tree. More...
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template<typename VectorValueType , typename SourceTreeType > |
math::pcg::Vector< VectorValueType >::Ptr | createVectorFromTree (const SourceTreeType &source, const typename SourceTreeType::template ValueConverter< VIndex >::Type &index) |
| Return a vector of the active voxel values of the scalar-valued source tree. More...
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template<typename TreeValueType , typename VIndexTreeType , typename VectorValueType > |
VIndexTreeType::template ValueConverter< TreeValueType >::Type::Ptr | createTreeFromVector (const math::pcg::Vector< VectorValueType > &values, const VIndexTreeType &index, const TreeValueType &background) |
| Return a tree with the same active voxel topology as the index tree but whose voxel values are taken from the the given vector. More...
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template<typename BoolTreeType > |
LaplacianMatrix::Ptr | createISLaplacian (const typename BoolTreeType::template ValueConverter< VIndex >::Type &vectorIndexTree, const BoolTreeType &interiorMask, bool staggered=false) |
| Generate a sparse matrix of the index-space (Δx = 1) Laplacian operator using second-order finite differences. More...
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template<typename BoolTreeType , typename BoundaryOp > |
LaplacianMatrix::Ptr | createISLaplacianWithBoundaryConditions (const typename BoolTreeType::template ValueConverter< VIndex >::Type &vectorIndexTree, const BoolTreeType &interiorMask, const BoundaryOp &boundaryOp, typename math::pcg::Vector< LaplacianMatrix::ValueType > &source, bool staggered=false) |
| Generate a sparse matrix of the index-space (Δx = 1) Laplacian operator with user-specified boundary conditions using second-order finite differences. More...
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Solve Poisson's equation ∇2x = b for x, where b is a vector comprising the values of all of the active voxels in a grid.
- Authors
- D.J. Hill, Peter Cucka
- Example:
- Solve for the pressure in a cubic tank of liquid, assuming uniform boundary conditions:
source.fill(CoordBBox(Coord(0, -10, 0), Coord(10, 0, 10)), 0.0f);
- Example:
- Solve for the pressure, P, in a cubic tank of liquid that is open at the top. Boundary conditions are P = 0 at the top, ∂P/∂y = −1 at the bottom and ∂P/∂x = 0 at the sides:
P = 0
+--------+ (N,0,N)
/| /|
(0,0,0) +--------+ |
| | | | dP/dx = 0
dP/dx = 0 | +------|-+
|/ |/
(0,-N,0) +--------+ (N,-N,0)
dP/dy = -1
const int N = 10;
source.fill(CoordBBox(Coord(0, -N, 0), Coord(N, 0, N)), 0.0);
double& source, double& diagonal)
{
if (neighbor.x() == ijk.
x() && neighbor.z() == ijk.
z()) {
if (neighbor.y() < ijk.
y()) source -= 1.0;
else diagonal -= 1.0;
}
};
util::NullInterrupter interrupter;
source, boundary, state, interrupter);