Tailored Finite Cell Method for Solving Helmholtz Equation in Layered Heterogeneous Medium (Journal of Computational Mathematics, 2018)
In this paper, we propose a tailored finite cell method for the computation of two-dimensional Helmholtz equation in layered heterogeneous medium. The idea underlying the method is to construct a numerical scheme based on a local approximation of the solution to Helmholtz equation. This provides a computational tool of achieving high accuracy with coarse mesh even for large wave number (high frequency). The stability analysis and error estimates of this method are also proved. We present several numerical results to show its efficiency and accuracy.
Keywords: Tailored finite cell method; Helmholtz equation; Heterogeneous media; Sommerfeld condition.