Skip to main content

Hybrid Solvers

For the moment, I am developing an Non-Overlapping Domain Decomposition Hybrid Solver for scalar PDE in 2D/3D domains.

It decomposes the underlying mesh into regions, solves the Schur Complement System onto frontier nodes between regions and then solves the problem into each inner region nodes.

This type of solver is said to be HYBRID because the Schur complement system is solved by a preconditioned iterative method whereas the inner problems are solved by a direct method. So it mixes the approach. However it requires less memory (and possibly time) than any direct solvers and in the same time suffer less of bad conditioning than iterative ones (the Schur complement system is well conditioned in that case).

This technique allows to split computation easily since each regions are more or less independent during all the process. It has been used with success on computer clusters, and I wish to use it with shared memory paradigm in mind to solve huge systems on (relatively modest) desktop computers.

In some time I will report my advance here, and the capabilities of the code I am developing, with performance profiles.
Labels:

Comments

Post a Comment

Popular posts from this blog

Shear waves, medecine and brain

Yesterday evening, too bored by what TV was proposing to me, I decided to watch a conference of Mathias Fink , a french researcher working on multidisciplinary application of waves. Specially shear waves.  Here is a brief summary of his talk. In solids, waves have two principal components:  compression waves (P-waves for primary) moving in the direction of propagation, and shear waves (S-waves, for secondary) that make ripples in the plane orthogonal to that direction. Since compression waves propagate in the direction of propagation, they move faster than shear waves. Usually ultrasound equipment in medicine only use compressional waves. But since human tissues have a high bulk modulus, the P-wave speed is relatively constant (around 1580 m/s). Human tissues are very stiff if you apply isotropic constraints on them (like pressure of water). However M. Fink and his colleagues proposed a new way to investigate human tissues by first sending a strong compressional wave in ...
Post a Comment
Read more

Hypnothic patterns of integrer decomposition

http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/
Post a Comment
Read more

Beauty is in the eyes(n,n)

Any people interested by sparse matrix algorithms should know the University of Florida sparse matrix collection and, by the way, Tim Davis . If you don't, please spend some time using the above links, it really worth it ! It collects many different kind of matrices, real, hermitian, symmetric, unsymmetric, rectangular, etc, etc. Moreover you have a nice colored view of each matrices obtained by spectral mapping and colouring. Could you guess for which kind of problem each of the matrices below arised ?
Post a Comment
Read more