Schur complement system

Lisandro Dalcin dalcinl at
Mon Mar 10 12:00:58 CDT 2008

On 3/10/08, Matthew Knepley <knepley at> wrote:
> By 4 matrices, I assume you mean A, B, C where
>   S = B^T A^{-1} B + C
>  right?

Yes, but actually four matrices, [[A_II, A_IB], [A_BI, A_BB]], were

S = (A_BB - A_BI * A_II^{-1} * A_IB)

'B' are interface nodes and 'I' are interior nodes. The operator does
not need to be symmetric.

However, I have the strong feeling (from therory as well as practice)
that my implementation is not actually better than ASM, except for the
fact that I'm iterating over interface nodes only. I need to work a
bit on ASM to enable partitioning subdomains (or use the support for
setting local subdomain indices) to experiment and be completely sure
about this.

Lisandro Dalcín
Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC)
Instituto de Desarrollo Tecnológico para la Industria Química (INTEC)
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
PTLC - Güemes 3450, (3000) Santa Fe, Argentina
Tel/Fax: +54-(0)342-451.1594

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