A time-domain finite element method for Helmholtz equations
Journal of Computational Physics
Dirichlet-to-Neumann boundary conditions for multiple scattering problems
Journal of Computational Physics
A Fast Algorithm for the Electromagnetic Scattering from a Large Cavity
SIAM Journal on Scientific Computing
Analysis of electromagnetic scattering from an overfilled cavity in the ground plane
Journal of Computational Physics
Applied Numerical Mathematics
Asymptotic Imaging of Perfectly Conducting Cracks
SIAM Journal on Scientific Computing
Journal of Computational Physics
A composite preconditioner for the electromagnetic scattering from a large cavity
Journal of Computational Physics
Stability and Resolution Analysis for a Topological Derivative Based Imaging Functional
SIAM Journal on Control and Optimization
An efficient algorithm for the generalized Foldy-Lax formulation
Journal of Computational Physics
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Here considered is the mathematical analysis and numerical computation of the electromagnetic wave scattering by multiple cavities embedded in an infinite ground plane. Above the ground plane the space is filled with a homogeneous medium, while the interiors of the cavities are filled with inhomogeneous media characterized by variable permittivities. By introducing a new transparent boundary condition on the cavity apertures, the multiple cavity scattering problem is reduced to a boundary value problem of the two-dimensional Helmholtz equation imposed in the separated interior domains of the cavities. The existence and uniqueness of the weak solution for the model problem is achieved via a variational approach. A block Gauss-Seidel iterative method is introduced to solve the coupled system of the multiple cavity scattering problem, where only a single cavity scattering problem is required to be solved at each iteration. Numerical examples demonstrate the efficiency and accuracy of the proposed method.