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The immersed interface method for Helmholtz equations with degenerate diffusion

Author

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  • Medina Dorantes, Francisco
  • Itzá Balam, Reymundo
  • Uh Zapata, Miguel

Abstract

In this paper, we consider a second-order immersed interface method for Helmholtz equations of the form ∇(β∇u)−σu=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.

Suggested Citation

  • Medina Dorantes, Francisco & Itzá Balam, Reymundo & Uh Zapata, Miguel, 2021. "The immersed interface method for Helmholtz equations with degenerate diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 280-302.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:280-302
    DOI: 10.1016/j.matcom.2021.05.021
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