Multi-stage waveform Relaxation and Multisplitting Methods for Differential Algebraic Systems

2016/01/04 by Jürgen Geiser, Geiser, Juergen
Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1601.00495

openalex publication_date 2016/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are motivated to solve differential algebraic equations with new multi-stage and multisplitting methods. The multi-stage strategy of the waveform relaxation (WR) methods are given with outer and inner iterations. While the outer iterations decouple the initial value problem of differential algebraic equations (DAEs) in the form of A (d y(t))/(dt) + B y(t) = f(t) to M_A \fracd y^k+1(t)dt + M₁ y^k+1(t) = N₁ y^k(t) + N_A \fracd y^k(t) + f(t), where A = M_A - N_A, B = M₁ - N₁. The inner iterations decouple further M₁ = M₂ - N₂ and M₂ = M₃ - N₃ with additional iterative processes, such that we result to invert simpler matrices and accelerate the solver process. The multisplitting method use additional a decomposition of the outer iterative process with parallel algorithms, based on the partition of unity, such that we could improve the solver method. We discuss the different algorithms and present a first experiment based on a DAE system.

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