DUNE-FEM (unstable)
Sequential DILU preconditioner. More...
#include <dune/istl/preconditioners.hh>
Public Types | |
using | matrix_type = M |
The matrix type the preconditioner is for. | |
using | block_type = typename matrix_type::block_type |
block type of matrix | |
using | domain_type = X |
The domain type of the preconditioner. | |
using | range_type = Y |
The range type of the preconditioner. | |
using | field_type = typename X::field_type |
The field type of the preconditioner. | |
using | scalar_field_type = Simd::Scalar< field_type > |
scalar type underlying the field_type | |
using | real_field_type = typename FieldTraits< scalar_field_type >::real_type |
real scalar type underlying the field_type | |
Public Member Functions | |
SeqDILU (const M &A, real_field_type w) | |
Constructor. More... | |
SeqDILU (const std::shared_ptr< const AssembledLinearOperator< M, X, Y > > &A, const ParameterTree &configuration) | |
Constructor. More... | |
SeqDILU (const M &A, const ParameterTree &config) | |
Constructor. More... | |
void | pre (X &x, Y &b) override |
Prepare the preconditioner. More... | |
void | apply (X &v, const Y &d) override |
Apply the preconditioner. More... | |
void | post (X &x) override |
Clean up. More... | |
SolverCategory::Category | category () const override |
Category of the preconditioner (see SolverCategory::Category) | |
Protected Attributes | |
const M & | _A_ |
The matrix we operate on. | |
const real_field_type | _w |
The relaxation factor to use. | |
const bool | wNotIdentity_ |
true if w != 1.0 | |
Detailed Description
class Dune::SeqDILU< M, X, Y, l >
Sequential DILU preconditioner.
Wraps the naked ISTL generic DILU preconditioner into the solver framework.
The Diagonal Incomplete LU factorization (DILU) is a simplified variant of the ILU(0) factorization, where only the diagonal elements are factorised. This preconditioner can be written as
M = (D + L_A) D^{-1} (D + U_A),
where L_A and U_A are the strictly lower and upper parts of A and D is the diagonal matrix containing the generated pivot values. The matrix M has the property
diag(A) = diag(M) = diag((D + L_A) D^{-1} (D + U_A)) = diag(D + L_A D^{-1} U_A)
such that the diagonal matrix D can be constructed:
D_11 = A_11 D_22 = A22 - L_A_{21} D_{11}^{-1} U_A_{12} and etc.
Note that when applying the preconditioner, M is never explicitly created but instead a lower and upper triangualr solve is performed using the values of A and D^-1. When applying the preconditioner, we are working with the residual d = b - Ax and update v = x_{n+1} - x_n, such that:
v = M^{-1} d = (D + U_A)^{-1} D (D + L_A)^{-1} d
define y = (D + L_A)^{-1} d
lower triangular solve: (D + L_A) y = d upper triangular solve: (D + U_A) v = D y
This means that the preconditioner only requires an additional storage of the diagonal matrix D^{-1}
For more details, see: R. Barrett et al., "Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods", 1994. Available from: https://www.netlib.org/templates/templates.pdf
- Template Parameters
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M The matrix type to operate on X Type of the update Y Type of the defect l Ignored. Just there to have the same number of template arguments as other preconditioners.
Constructor & Destructor Documentation
◆ SeqDILU() [1/3]
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inline |
Constructor.
Constructor invoking DILU gets all parameters to operate the prec.
- Parameters
-
A The matrix to operate on. w The relaxation factor.
◆ SeqDILU() [2/3]
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inline |
Constructor.
- Parameters
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A The assembled linear operator to use. configuration ParameterTree containing preconditioner parameters.
ParameterTree Key | Meaning |
---|---|
relaxation | The relaxation factor. default=1.0 |
See ISTL_Factory for the ParameterTree layout and examples.
◆ SeqDILU() [3/3]
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inline |
Constructor.
- Parameters
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A The matrix to operate on. config ParameterTree containing preconditioner parameters.
ParameterTree Key | Meaning |
---|---|
relaxation | The relaxation factor. default=1.0 |
See ISTL_Factory for the ParameterTree layout and examples.
Member Function Documentation
◆ apply()
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inlineoverridevirtual |
Apply the preconditioner.
Apply one step of the preconditioner to the system A(v)=d.
On entry v=0 and d=b-A(x) (although this might not be computed in that way. On exit v contains the update, i.e one step computes \( v = M^{-1} d \) where \( M \) is the approximate inverse of the operator \( A \) characterizing the preconditioner.
- Parameters
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[out] v The update to be computed d The current defect.
Implements Dune::Preconditioner< X, Y >.
◆ post()
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inlineoverridevirtual |
Clean up.
Clean up.
This method is called after the last apply call for the linear system to be solved. Memory may be deallocated safely here. x is the solution of the linear equation.
- Parameters
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x The right hand side of the equation.
Implements Dune::Preconditioner< X, Y >.
◆ pre()
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inlineoverridevirtual |
Prepare the preconditioner.
Prepare the preconditioner.
A solver solves a linear operator equation A(x)=b by applying one or several steps of the preconditioner. The method pre() is called before the first apply operation. b and x are right hand side and solution vector of the linear system respectively. It may. e.g., scale the system, allocate memory or compute a (I)LU decomposition. Note: The ILU decomposition could also be computed in the constructor or with a separate method of the derived method if several linear systems with the same matrix are to be solved.
- Note
- if a preconditioner is copied (e.g. for a second thread) again the pre() method has to be called to ensure proper memory management.
- Parameters
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x The left hand side of the equation. b The right hand side of the equation.
Implements Dune::Preconditioner< X, Y >.
The documentation for this class was generated from the following file:
- dune/istl/preconditioners.hh