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research-article

The immersed interface method for Helmholtz equations with degenerate diffusion

Authors:

Francisco Medina Dorantes,

Reymundo Itzá Balam,

Miguel Uh ZapataAuthors Info & Claims

Volume 190, Issue C

Pages 280 - 302

https://doi.org/10.1016/j.matcom.2021.05.021

Published: 01 December 2021 Publication History

Abstract

In this paper, we consider a second-order immersed interface method for Helmholtz equations of the form ∇ ( β ∇ u ) − σ u = f with a degenerate diffusion term β. We assume that the diffusion term is discontinuous across an interface and β is zero to one side of it. The method is applied to one-dimensional domains with multiple interfaces, and two-dimensional domains with circular and straight interfaces. The numerical solution is obtained by applying away from the interface the standard centered finite differences scheme and a new scheme across of the interface. Numerical results on one- and two-dimensional domains are used to compare and demonstrate the proposed numerical method’s capabilities. In all numerical experiments, the solutions of the interface problem is second order of accuracy.

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Index Terms

The immersed interface method for Helmholtz equations with degenerate diffusion
1. Applied computing
  1. Physical sciences and engineering
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
      2. Partial differential equations
    2. Numerical analysis
      1. Computations in finite fields
      2. Numerical differentiation

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Mathematics and Computers in Simulation

Mathematics and Computers in Simulation Volume 190, Issue C

Dec 2021

1446 pages

ISSN:0378-4754

Issue’s Table of Contents

International Association for Mathematics and Computers in Simulation (IMACS).

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 December 2021

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