Adaptation and Evaluation of the Multisplitting-Newton and Waveform Relaxation Methods Over Distributed Volatile Environments

This paper presents new adaptations of two methods that solve large differential equations systems, to the grid context. The first method is based on the Multisplitting concept and the second on the Waveform Relaxation concept. Their adaptations are implemented according to the asynchronous iteration model which is well suited to volatile architectures that suffer from high latency networks. Many experiments were conducted to evaluate and compare the accuracy and performance of both methods while solving the advection-diffusion problem over heterogeneous, distributed and volatile architectures. The JACEP2P-V2 middleware provided the fault tolerant asynchronous environment, required for these experiments.