We present and study a parallel iterative solver for reaction-diffusion systems in three dimensions arising in computational electrocardiology, such as the Bidomain and Monodomain models. The models include intramural fiber rotation and anisotropic conductivity coefficients that can be fully orthotropic or axially symmetric around the fiber direction. These cardiac models are coupled with a mem...

We consider the primal problem of finding the zeros of the sum of a maximal monotone operator and the composition of another maximal monotone operator with a linear continuous operator. By formulating its Attouch-Théra-type dual inclusion problem, a primal-dual splitting algorithm which simultaneously solves the two problems in finitedimensional spaces is presented. The proposed scheme uses at ...

n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudo-contractive of browder-petryshyn type mapping. our resultsimprove and extend the results announced by many others.

A new HSS-like iterative method is first proposed based on HSS-like splitting of nonHermitian (1,1) block for solving saddle point problems. The convergence analysis for the new method is given. Meanwhile, we consider the solution of saddle point systems by preconditioned Krylov subspace method and discuss some spectral properties of the preconditioned saddle point matrices. Numerical experimen...

Abstract The motivation for our studies is coming from simulation of earthquakes, that are modelled by elastic wave equations. In our paper we focus on stiff phanomenons for the wave equations. In the course of this article we discuss iterative operator splitting methods for wave equations motivated by realistic problems dealing with seismic sources and waves. The operator splitting methods are...

Iterative numerical methods are an important ingredient for the solution of continuous time Markov dependability models of faulttolerant systems. In this paper we make a numerical comparison of several splitting-based iterative methods. We consider the computation of steady-state reward rate on rewarded models. This measure requires the solution of a singular linear system. We consider two clas...

We present an explicit formulation of the splitting associated with the Mutiplicative Schwartz iteration. We give an implementation of the new formulation on a parallel computer and show its advantages when used as a preconditionner for a Krylov method. In the paper the implementation is described in PETCs standard. Keywords— Domain decomposition, Multiplicative Schwarz preconditionner, iterati...