MARS : A METHOD FOR THE ADAPTIVE REMOVAL OF STIFFNESS IN PDES

Jens Eggers, L Duchemin

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

The EIN method was developed recently to remove numerical instability from PDE’s,
5 adding and subtracting an operator D of arbitrary structure, one of which is treated implicitly, the
6 other explicitly. Here we extend this idea by devising an adaptive procedure to find an optimal
7 approximation for D. We propose a measure of the numerical error which detects numerical noise
8 across all wavelengths, and adjust each Fourier component of D to the smallest value such that
9 numerical instability is suppressed. We show that for a highly nonlinear and non-local PDE, the
10 spectrum of D adapts automatically and dynamically to the theoretical result for stability. Our
11 method thus has the same stability properties as a fully implicit method, while only requiring an
12 explicit solver. The adaptive implicit part is diagonal in Fourier space, and thus leads to minimal
13 overhead compared to the explicit method.
Original languageEnglish
JournalSIAM Journal on Numerical Analysis
Publication statusSubmitted - 19 Jul 2018

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