Preprint Article Version 1 This version is not peer-reviewed

Serial and Parallel Iterative Splitting Methods: Algorithms and Applications

Version 1 : Received: 12 December 2019 / Approved: 13 December 2019 / Online: 13 December 2019 (10:45:22 CET)

How to cite: Geiser, J.; Martínez, E.; Hueso, J.L. Serial and Parallel Iterative Splitting Methods: Algorithms and Applications. Preprints 2019, 2019120181 (doi: 10.20944/preprints201912.0181.v1). Geiser, J.; Martínez, E.; Hueso, J.L. Serial and Parallel Iterative Splitting Methods: Algorithms and Applications. Preprints 2019, 2019120181 (doi: 10.20944/preprints201912.0181.v1).

Abstract

The properties of iterative splitting methods with serial versions have been analyzed since recent years, see [1] and [3]. We extend the iterative splitting methods to a class of parallel versions, which allow to reduce the computational time and keep the bene t of the higher accuracy with each iterative step. Parallel splitting methods are nowadays important to solve large problems, which can be splitted in subproblems and computed independently with the di erent processors. We present a novel parallel iterative splitting method, which is based on the multi-splitting methods, see [2], [10] and [15]. Such a exibilisation with multisplitting methods allow to decompose large iterative splitting methods and recover the bene t of their underlying waveform-relaxation (WR) methods. We discuss the convergence results of the parallel iterative splitting methods, while we could reformulate such an error to a summation of the individual WR methods. We discuss the numerical convergence of the serial and parallel iterative splitting methods and present di erent numerical applications to validate the bene t of the parallel versions.

Subject Areas

Multisplitting method; iterative splitting method; numerical analysis; operator-splitting method; initial value problem; iterative solver method; Waveform relaxation method.

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