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I would like to ask for help with the use

of the Intel MKL interface to PARDISO.

Assume that you have a sparse matrix

A partitioned into 2x2 blocks

A= [ A_II A_IG ]

[ A_GI A_GG ],

and that you want to solve linear systems

with A and A_II using only one sparse LU

decomposition of the global system A:

A = [L_II 0] [U_II U_IG]

[L_GI L_GG] [0 U_GG]

Neglecting pivoting for numerical

stability, the solution of linear systems

of the form A_II x_I = b_I can be performed

as follows:

1) Solve [L_II 0] [y_I] = [b_I]

[L_GI L_GG] [y_G] = [ * ]

2) Y_G <- 0

3) Solve [U_II U_IG] [ x_I ] = [y_I]

[0 U_GG] [ x_G=0 ] = [ 0 ]

This algorithm can be implemented with

the Intel MKL interface of PARDISO because

it allows to separate among forward and

backward substitution, so that you can

zero-out Y_G between steps 1 and 3. The problem

that I have is that this workaround

is no longer valid when numerical pivoting enters the scene

(for example, with symmetric indefinite matrices)

Do you know whether there is a simple strategy

to tell PARDISO to restrict numerical pivoting

to a particular block (i.e., A_II) or otherwise

to tell PARDISO to solve a subblock given a

global LU factorization of the global system ?.

I want to avoid to compute both a factorization

of A_II and A.

Thanks a lot for your help.

Best regards,

Alberto.

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Pardiso is direct solver based on LU decomposition with global reordering of initial matrix. In your case you want to set specific reordering to PARDISO so it could be implemented by 2 variants:

1. Use own perm vector by set iparm[4]=1

2. Use partial solve by set iparm[30] = 1

Nevertheless using this parameters could decrease performance and increase internal memory size of PARDISO so I strongly recommend you just factorize by pardiso 2 different matrix: A_II and full initial matrix.

With best regards,

Alexander Kalinkin

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