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.

Comments

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 ...

We're not playing dices !

Software programming and design is an amazingly complex task. Specially when it concerns numerical applications, that generally require optimization to get results in a reasonable time. For that purpose the basic pattern is usually to write the code as simple as possible, debug it and when it works to begin the optimization process. This asks for some nerves, and patience, two things I usually don't have in real life , but for programming yes. This design pattern makes sense because we are doing things really sequentially. You first wrote some c++ class and then add some feature progressively, and when you come up with essentially different concept (I mean a concept that should be well separated from the first one), you write an other class and so on... Usually the class-writing process follows the solving process you have in mind. For instance you have to make some initialization on your model first, then you declare some variables for the computation, the computation then f...

5 Tips to work with legacy code

As engineers, we like to move things forward and, for those who have a little bit of experience (like me), having to work with legacy code can be a huge set back because we know it can be long, painful and slow-paced. But you don't have to make it harder that it needs to be for you and your team! Below are some common mistakes that occur when working with legacy code and possible ways to overcome them. 1. Should you really use it? That's probably the first and foremost question. Is it really necessary for your application to tap into this legacy code? Have you done extensive researches to see if there isn't a more modern library out there, with better licensing, design, architecture, library initialization, newest code features, documentation, unit tests, whatever than this old piece of code which is on your shelves? In case there is, ponder with caution the possible consequences of any choice, using as many criteria that you care for! Remember that this is an important cha...

New Horizons

Search This Blog