## Fast integral equation solver for Maxwell’s equations in layered media with FMM for Bessel functions.(English)Zbl 1306.78010

Summary: The paper presents a new fast integral equation solver for Maxwell’s equations in 3-D layered media. First, the spectral domain dyadic Green’s function is derived, and the 0-th and the 1-st order Hankel transforms or Sommerfeld-type integrals are used to recover all components of the dyadic Green’s function in real space. The Hankel transforms are performed with the adaptive generalized Gaussian quadrature points and window functions to minimize the computational cost. Subsequently, a fast integral equation solver with $$O(N_z^2N_xN_y\log(N_xN_y))$$ in layered media is developed by rewriting the layered media integral operator in terms of Hankel transforms and using the new fast multipole method for the $$n$$-th order Bessel function in 2-D. Computational cost and parallel efficiency of the new algorithm are presented.

### MSC:

 78M16 Multipole methods applied to problems in optics and electromagnetic theory 65F10 Iterative numerical methods for linear systems 65R20 Numerical methods for integral equations 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 65T50 Numerical methods for discrete and fast Fourier transforms 65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs 78A48 Composite media; random media in optics and electromagnetic theory 65D30 Numerical integration

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