PCLDUFactorisation Class Reference

#include <PCLDUFactorisation.hpp>

Collaboration diagram for PCLDUFactorisation:

List of all members.

Public Member Functions

PCLDUFactorisation (KSP &rKspObject)

Public Attributes

PCLDUFactorisationContext mPCContext

PC mPetscPCObject

Private Member Functions

void PCLDUFactorisationCreate (KSP &rKspObject)

void PCLDUFactorisationSetUp ()

Classes

struct PCLDUFactorisationContext

Detailed Description

This class defines a PETSc-compliant purpose-built preconditioner.

Let A be a matrix arising in the FEM discretisation of the bidomain equations with the following block structure:

A = (A11 B') (B A22)

Let A=LDU be the following matrix factorisation

LDU = (I 0)(A11 0)(I inv(A11)B') (B*A11' I)(0 S)(0 I)

with I the identity matrix and S=A22-B*inv(A11)*B'

Let inv(A) be a preconditioner

inv(A) = inv(U)inv(D)inv(L) = (I -inv(A11)B')(inv(A11) 0)(I 0) (0 I)(0 inv(S))(-B*inv(A11) I)

This class implements an approximation of inv(A) where S=A22

inv(P) ~ inv(A)

inv(P) = (I -inv(A11)B')(inv(A11) 0)(I 0) (0 I)(0 inv(S=A22))(-B*inv(A11) I)

inv(P) = (inv(A11) -inv(A11)B'inv(S=A22))(I 0) (0 inv(S=A22))(-B*inv(A11) I)

In order to compute [y1 y2]' = inv(P)[x1 x2]' we do

z = inv(A11)*x1 y2 = inv(A22)*(x2 - B*z) y1 = z - inv(A11)(B*y2)

The inverses are approximate with one cycle of AMG.

Note: This class requires PETSc to be build including HYPRE library. If it's not available, it will throw the following error:

[0]PETSC ERROR: --------------------- Error Message ------------------------------------ [0]PETSC ERROR: Unknown type. Check for miss-spelling or missing external package needed for type! [0]PETSC ERROR: Unable to find requested PC type hypre!

and will approximate the inverse of the subblocks with PETSc's default preconditioner (bjacobi at the time of writing this).

Definition at line 102 of file PCLDUFactorisation.hpp.

Constructor & Destructor Documentation

PCLDUFactorisation::PCLDUFactorisation ( KSP & rKspObject )

Constructor

Parameters:

rKspObject

KSP object where we want to install the block diagonal preconditioner.

Definition at line 35 of file PCLDUFactorisation.cpp.

References mPCContext, PCLDUFactorisationCreate(), and PCLDUFactorisationSetUp().

Member Function Documentation

void PCLDUFactorisation::PCLDUFactorisationCreate ( KSP & rKspObject ) [private]

Creates all the state data required by the preconditioner

Parameters:

rKspObject

KSP object where we want to install the block diagonal preconditioner.

Definition at line 80 of file PCLDUFactorisation.cpp.

Referenced by PCLDUFactorisation().

void PCLDUFactorisation::PCLDUFactorisationSetUp ( ) [private]

Setups preconditioner

Definition at line 231 of file PCLDUFactorisation.cpp.

References PCLDUFactorisation::PCLDUFactorisationContext::A11_matrix_subblock, PCLDUFactorisation::PCLDUFactorisationContext::A22_matrix_subblock, mPCContext, PCLDUFactorisation::PCLDUFactorisationContext::PC_amg_A11, and PCLDUFactorisation::PCLDUFactorisationContext::PC_amg_A22.

Referenced by PCLDUFactorisation().

Member Data Documentation

PCLDUFactorisationContext PCLDUFactorisation::mPCContext

PC context, this will be passed to PCBlockDiagonalApply when PETSc returns control to our preconditioner subroutine. See PCShellSetContext().

Definition at line 132 of file PCLDUFactorisation.hpp.

Referenced by PCLDUFactorisation(), PCLDUFactorisationCreate(), and PCLDUFactorisationSetUp().

PC PCLDUFactorisation::mPetscPCObject

Generic PETSc preconditioner object

Definition at line 133 of file PCLDUFactorisation.hpp.

Referenced by PCLDUFactorisationCreate().

The documentation for this class was generated from the following files:

linalg/src/PCLDUFactorisation.hpp
linalg/src/PCLDUFactorisation.cpp


Public Member Functions
	PCLDUFactorisation (KSP &rKspObject)
Public Attributes
PCLDUFactorisationContext	mPCContext
PC	mPetscPCObject
Private Member Functions
void	PCLDUFactorisationCreate (KSP &rKspObject)
void	PCLDUFactorisationSetUp ()
Classes
struct	PCLDUFactorisationContext