Optimal balance between mass and smoothed stiffness in simulation of acoustic problems

Eric Li, Z. C. He

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The Finite Element Method (FEM) is known to behave overly-stiff, which leads to an imbalance between the mass and stiffness matrices within discretized systems. In this work, for the first time, a model is developed that provides optimal balance between discretized mass and smoothed stiffness—the mass-redistributed alpha finite element method (MR-αFEM). This new method improves on the computational efficiency of the FEM and Smoothed Finite Element Methods (S-FEM). The rigorous research conducted ensures that stiffness with the parameter, α, optimally matches the mass with a flexible integration point, q. The optimal balance system significantly reduces the dispersion error of acoustic problems, including those of single and multi-fluids in both time and frequency domains. The excellent properties of the proposed MR-αFEM are validated using theoretical analyses and numerical examples.
Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalApplied Mathematical Modelling
Early online date19 May 2019
Publication statusPublished - 30 Nov 2019


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