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Numerical solutions for Helmholtz equation with stochastic interface based on PML method. (English) Zbl 1479.78012

Summary: In this paper, the stochastic interface for diffraction grating is considered and the model is formulated as the Helmholtz interface problems (HIPs). In order to have more accuracy simulation, PML boundary is used to describe the stochastic interface. Then we develop shape-Taylor expansion for the solution of HIPs, through perturbation method, we obtain the approximate simulations of second and third order. Error estimation and efficient computation of solutions by low-rank approximation are given. Finally, we illustrate these results with numerical simulations.

MSC:

78A45 Diffraction, scattering
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78M31 Monte Carlo methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65C05 Monte Carlo methods
65N15 Error bounds for boundary value problems involving PDEs
35A15 Variational methods applied to PDEs
35B25 Singular perturbations in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35Q60 PDEs in connection with optics and electromagnetic theory
35R60 PDEs with randomness, stochastic partial differential equations
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References:

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