PCLDUFactorisation Class Reference

#include <PCLDUFactorisation.hpp>

Collaboration diagram for PCLDUFactorisation:

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

Detailed Description

This class defines a PETSc-compliant purpouse-build 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 98 of file PCLDUFactorisation.hpp.