The paper improves a preliminary experimental study on a cluster by adding both theoretical results and experimental tests on a grid platform. These algorithms solve univalued and multivalued pseudo-linear problems using parallel asynchronous multisplitting methods combined with Krylov’s methods. This paper also analyses these algorithms using contraction techniques. Two distinct applications, with discretized boundary value problems, are analyzed and simulated. First, a univalued convection-diffusion problem perturbed by an increasing diagonal operator is presented. Then, follows the description of a diffusion problem whose solution is constrained. This situation classically leads to the solution of a multivalued pseudo-linear problem in which the linear part is perturbed by an increasing diagonal multivalued operator. Parallel asynchronous and synchronous algorithms were implemented and tested on a grid platform composed of physically adjacent or geographically distant machines. In addition, the simulation results are detailed and show that the elapsed times obtained for the asynchronous algorithms are significantly less than those obtained for the synchronous algorithms.

通过在网格平台上添加理论结果和实验测试，本文改进了对集群的初步实验研究。这些算法使用并行异步多重分裂方法与Krylov方法相结合来解决单值和多值伪线性问题。本文还使用收缩技术分析了这些算法。分析和模拟了离散离散边值问题的两种不同应用。首先，提出了一个由对角算子增加引起的单值对流扩散问题。然后，描述其解受约束的扩散问题。从经典意义上讲，这种情况导致了多值伪线性问题的解决，其中线性部分受到对角多值算子的增加的干扰。在由物理上相邻或地理位置遥远的机器组成的网格平台上实现并测试了并行异步和同步算法。此外，详细的仿真结果表明，异步算法获得的经过时间明显少于同步算法获得的经过时间。