Intel® oneAPI Math Kernel Library
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## Help with the Intel MKL interface to PARDISO

Beginner
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`Dear Intel MKL experts, I would like to ask for help with the useof the Intel MKL interface to PARDISO.Assume that you have a sparse matrixA partitioned into 2x2 blocksA=    [ A_II A_IG ]        [ A_GI A_GG ],and that you want to solve linear systemswith A and A_II using only one sparse LUdecomposition of the global system A:A = [L_II        0] [U_II U_IG]      [L_GI L_GG] [0    U_GG]Neglecting pivoting for numericalstability, the solution of linear systemsof the form A_II x_I = b_I can be performedas follows:1) Solve [L_II        0] [y_I]  = [b_I]             [L_GI L_GG] [y_G] = [ * ]2) Y_G <- 03) Solve [U_II U_IG] [  x_I  ] = [y_I]             [0    U_GG] [ x_G=0 ] = [ 0 ]This algorithm can be implemented withthe Intel MKL interface of PARDISO becauseit allows to separate among forward andbackward substitution, so that you canzero-out Y_G between steps 1 and 3. The problemthat I have is that this workaroundis no longer valid when numerical pivoting enters the scene(for example, with symmetric indefinite matrices)Do you know whether there is a simple strategyto tell PARDISO to restrict numerical pivotingto a particular block (i.e., A_II) or otherwiseto tell PARDISO to solve a subblock given aglobal LU factorization of the global system ?.I want to avoid to compute both a factorizationof A_II and A.Thanks a lot for your help.Best regards,  Alberto.`
Employee
312 Views
Hi Alberto,
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,