MultiThreading and Direct Solvers

The next step towards an efficient Hybrid Solver is to optimize the computation of the Schur complement on each subdomain. Actually this part of the algorithm is the slowest, and it can be very slow.

First of all the reordering is special, since the degrees of freedom on the interior must be numbered first. I use the CAMD ordering by Tim Davis and al., that provide satisfaying enough orderings.

After that, I am concentrating on the code that computes the Schur complement. There is much work to do here. At the begining I was thinking about using MUMPS for this, since it has a subroutine for Schur complement computation and it is multithreaded. By googling around I found there is may be a (slightly) better solution, that would be to implement a sparse Cholesky solver based on the Direct Acyclic Graph (DAG) of the tasks. The computational tasks and their dependencies are expressed as an acyclic graph which is used to organize the thread hierachy to compute the Cholesky decomposition. It seems to be faster than MUMPS on multicore processors.

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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 ...

Hypnothic patterns of integrer decomposition

http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/

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 ?

New Horizons

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