The immersed interface method for Helmholtz equations with degenerate diffusion

Francisco Medina Dorantes, Reymundo Itzá Balam and Miguel Uh Zapata

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 280-302

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.

Keywords: Helmholtz equation; Degenerated diffusion; Immersed interface method; Second-order of accuracy; Two-dimensional; Straight interfaces (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:280-302

DOI: 10.1016/j.matcom.2021.05.021

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