A hierarchical basis preconditioner. More...
#include <hb.hh>
Detailed Description
class Kaskade::HierarchicalBasisPreconditioner< Grid, Domain, Range >
A hierarchical basis preconditioner.
This preconditioner realizes an approximative inverse of a Laplace operator with constant diffusion coefficient discretized by linear finite elements in nodal basis over the leaf view of the provided grid.
This implementation is geometry- and coefficient-agnostic, i.e. it assumes that the diagonal of the stiffness matrix is just the identity. The advantage of this approach are its extreme simplicity, both in terms of interface and implementation, a minimal memory footprint, and very cheap set-up phase and application. The drawback is, of course, a worse resulting condition number in case non-uniform coarse grids, anisotropic coarse grids, or spatially varying or anisotropic diffusion coefficients are to be treated.
Extending the implementation to take more structure (stiffness matrices, non-uniform grids) into account is probably not worth the while, as the iteration count grows anyway in proportion to the number of refinement levels in 2D or even faster in 3D. If the simplicity of the PrecondType::HB preconditioner does'nt pay off, have a look at MultigridSolver or BPXYPreconditioner.
We refer to Deuflhard/Weiser Chapter 7.3.
- Template Parameters
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Grid the grid on which the Laplace operator is discretized. This implementation assumes that the grid is purely simplicial and that on refinement new nodes are created only at edge midpoints. Domain the type of domain space vectors Range the type of range space vectors
Public Types | |
| typedef X::field_type | field_type |
Public Member Functions | |
| HierarchicalBasisPreconditioner (Grid const &grid) | |
| Constructor. More... | |
| virtual void | pre (Domain &x, Range &b) |
| Has to be called before the first call to apply. More... | |
| virtual void | apply (Domain &v, const Range &d) |
| applies the preconditioner to the residual More... | |
| virtual SymmetricPreconditioner< Domain, Range >::field_type | applyDp (Domain &v, const Range &d) override |
| Computes \( x \leftarrow By \) and returns \( \langle By, y \rangle \). More... | |
| virtual void | post (Domain &x) |
| Has to be called after the last call to apply. More... | |
| virtual bool | requiresInitializedInput () const |
| Returns true if the target vector x has to be initialized to zero before calling apply or applyDp. More... | |
| virtual Dune::SolverCategory::Category | category () const override |
| returns the category of the operator More... | |
Member Typedef Documentation
◆ field_type
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inherited |
Definition at line 211 of file symmetricOperators.hh.
Constructor & Destructor Documentation
◆ HierarchicalBasisPreconditioner()
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inlineexplicit |
Member Function Documentation
◆ apply()
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inlinevirtual |
applies the preconditioner to the residual
- d, which results in the correction
- v
Definition at line 188 of file hb.hh.
Referenced by Kaskade::HierarchicalBasisPreconditioner< Grid, Domain, Range >::applyDp().
◆ applyDp()
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inlineoverridevirtual |
Computes \( x \leftarrow By \) and returns \( \langle By, y \rangle \).
Implements Kaskade::SymmetricPreconditioner< Domain, Range >.
◆ category()
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inlineoverridevirtualinherited |
returns the category of the operator
From the Dune doxygen documentation it is unclear what this is supposed to mean. We return a dummy here.
Definition at line 242 of file symmetricOperators.hh.
◆ post()
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inlinevirtual |
Has to be called after the last call to apply.
Reimplemented from Kaskade::SymmetricPreconditioner< Domain, Range >.
◆ pre()
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inlinevirtual |
Has to be called before the first call to apply.
Reimplemented from Kaskade::SymmetricPreconditioner< Domain, Range >.
◆ requiresInitializedInput()
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inlinevirtual |
Returns true if the target vector x has to be initialized to zero before calling apply or applyDp.
Implements Kaskade::SymmetricPreconditioner< Domain, Range >.
The documentation for this class was generated from the following file:
