Christophe Denis

Numerical 'health check' for scientific codes: the CADNA approach

Scientific computation has unavoidable approximations built into its very fabric. One important source of error that is difficult to detect and control is round-off error propagation which originates from the use of finite precision arithmetic. We propose that there is a need to perform regular numerical ‘health checks’ on scientific codes in order to detect the cancerous effect of round-off error propagation. This is particularly important in scientific codes that are built on legacy software. We advocate the use of the CADNA library as a suitable numerical screening tool. We present a case study to illustrate the practical use of CADNA in scientific codes that are of interest to the Computer Physics Communications readership. In doing so we hope to stimulate a greater awareness of round-off error propagation and present a practical means by which it can be analyzed and managed.

2DRMP: A suite of two-dimensional R-matrix propagation codes

The R-matrix method has proved to be a remarkably stable, robust and efficient technique for solving the close-coupling equations that arise in electron and photon collisions with atoms, ions and molecules. During the last thirty-four years a series of related R-matrix program packages have been published periodically in CPC. These packages are primarily concerned with low-energy scattering where the incident energy is insufficient to ionise the target. In this paper we describe 2DRMP, a suite of two-dimensional R-matrix propagation programs aimed at creating virtual experiments on high performance and grid architectures to enable the study of electron scattering from H-like atoms and ions at intermediate energies.

A load balancing method for a parallel application based on a domain decomposition

The parallel multiple front method, is used in mechanical engineering to solve large sparse linear systems issued, from finite element modeling. It is a parallel direct method, based, on a nonoverlapping domain decomposition method. The decomposition is usually built with a graph partitioning approach. However this approach is not well suited, to all parallel applications. It provides computing times over the subdomains, which can vary from simple to double for our parallel multiple method. We show that its computing time can be decreased by load balancing the computational volume over the subdomains. We present in this communication a sequential and a parallel version of our load balancing method, which corrects in computational volume an initial decomposition issued, from graph partitioning tools.

E-collisions using e-science

We describe a computational science research program primarily aimed at engineering numerically robust software that can exploit high performance on distributed computers in the study of electron collisions with atoms and ions. In particular, we describe the development of 2DRMP-G, a Grid aware 2-dimensional R-matrix propagator and its numerical validation using CADNA, a software tool based on discrete stochastic arithmetic.

Load Balancing Issues for a Multiple Front Method

We investigate a load balancing strategy that uses a model of the computational behavior of a parallel solver to correct an initial partition of data.

Solving large sparse linear systems in a grid environment: the GREMLINS code versus the PETSc library

Solving large sparse linear systems is essential in numerous scientific domains. Several algorithms, based on direct or iterative methods, have been developed for parallel architectures. On distributed grids consisting of processors located in distant geographical sites, their performance may be unsatisfactory because they suffer from too many synchronizations and communications. The GREMLINS code has been developed for solving large sparse linear systems on distributed grids. It implements the multisplitting method that consists in splitting the original linear system into several subsystems that can be solved independently. In this paper, the performance of the GREMLINS code obtained with several libraries for solving the linear subsystems is analyzed. Its performance is also compared with that of the widely used PETSc library that enables one to develop portable parallel applications. Numerical experiments have been carried out both on local clusters and on distributed grids.