A Simple Test Case for Convergence Order in Time and Energy Conservation of Black-Box Coupling Schemes

Abstract

The most commonly used coupling schemes in partitioned multiphysics simulations suffer from a decrease in the order of convergence, specifically in the time domain; a phenomenon we call order degradation. This paper discusses when this issue arises and how it can be studied with a simple example. We present a simple mass-spring system of ordinary differential equations (ODEs) to analyze accuracy and energy conservation of different coupling schemes. The ability to restore higher order of convergence by using Strang splitting or waveform iterations is verified in the context of the presented example. This paper provides details on some aspects of the talk titled 'Design and evaluation of a waveform iteration­based approach for coupling heterogeneous time stepping methods via preCICE' given at WCCM-APCOM 2022.

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