topic PARDISO and boundary condition in Intel® oneAPI Math Kernel Library

PARDISO and boundary condition

array123 — Tue, 03 Aug 2010 05:38:01 GMT

hi,

I am having a coefficient matrix.While solving it with PARDISO if i apply neumann boundary condition on all 4 sides than it solves but if i change one boundary to dirichlet it does not solve linear equation rather it gives all values as zero.

PARDISO and boundary condition

Alexander_K_Intel2 — Tue, 03 Aug 2010 06:27:02 GMT

Hi,

PARDISO solve system of equation like Ax=b, where x is unknown vector. So could you provide way how you construct matrix A and rhs b with dirichle boundary condition?

With best regards,

Alexander Kalinkin

PARDISO and boundary condition

array123 — Tue, 03 Aug 2010 09:04:53 GMT

hi,

my domain looks like

11	21	31	41	51
12	22	32	42	52
13	23	33	43	53

now at each cell i have unknown x and at boundaries north, south and west Neumann condition is applied and for east boundary it is dirichlet.

each cell has coefficient AP(its own), AE(east), AW(west), AN(north) and AS(south)

on making coefficient matrix 'A' looks like

AP11	AE11	0	0	0	AN11	0	0	0	0	0	0	0	0	0

AW21	AP21	AE21	0	0	0	AN21	0	0	0	0	0	0	0	0

0	AW31	AP31	AE31	0	0	0	AN31	0	0	0	0	0	0	0

0	0	AW41	AP41	AE41	0	0	0	AN41	0	0	0	0	0	0

0	0	0	AW51	AP51	AE51	0	0	0	AN51	0	0	0	0	0

AS12	0	0	0	AW12	AP12	AE12	0	0	0	AN12	0	0	0	0

0	AS22	0	0	0	AW22	AP22	AE22	0	0	0	AN22	0	0	0

0	0	AS32	0	0	0	AW32	AP32	AE32	0	0	0	AN32	0	0

0	0	0	AS42	0	0	0	AW42	AP42	AE42	0	0	0	AN42	0

0	0	0	0	AS52	0	0	0	AW52	AP52	AE52	0	0	0	AN52

0	0	0	0	0	AS13	0	0	0	AW13	AP13	AE13	0	0	0

0	0	0	0	0	0	AS23	0	0	0	AW23	AP23	AE23	0	0

0	0	0	0	0	0	0	AS33	0	0	0	AW33	AP33	AE33	0

0	0	0	0	0	0	0	0	AS43	0	0	0	AW43	AP43	AE43

0	0	0	0	0	0	0	0	0	AS53	0	0	0	AW53	AP53

For doing this if neumann is to be applied at west then AP=AP +AW is done and AW=0 is set.

For doing dirichlet at say east AE=0 is set.

thus Ax =b forms here b is known and supplied.

while doing this if i am applying neumann bc's(on all sides) then PARDISO is running but if i apply dirichlet at one boundary then PARDISO does not solves equation.

PARDISO and boundary condition

Alexander_K_Intel2 — Tue, 03 Aug 2010 14:36:08 GMT

Hi,

PARDISO solves system of equation Ax=b, where A and b are user defined matrix and rhs. Could you check ||Ax-b|| where A and b are your matrix and rhs, x is solution probided by PARDISO, ||u|| - some norm of vector u. If this norm is not near zero could you attach here your matrix and rhs with real number (not symbolic) and way you use PARDISO to give us opportunity to investigate problem.

With best regards,

Alexander Kalinkin