Multidomain pseudospectral computation of Maxwell's equations in 3-D general curvilinear coordinates

doi:10.1016/S0168-9274(99)00094-X

Applied Numerical Mathematics

Volume 33, Issues 1–4, May 2000, Pages 281-289

https://doi.org/10.1016/S0168-9274(99)00094-X Get rights and content

Abstract

We discuss the numerical solution of the 3-D Maxwell's equations in general curvilinear coordinates using a multidomain pseudospectral (Chebyshev collocation) scheme. The formulation of the equations and the method as well as the multidomain patching procedure is reviewed. We also discussed the modeling of various materials.

Very accurate numerical results are obtained when simulating scattering by perfect electrically conducting (PEC), dielectric, and lossy dielectric objects such as a cube, a sphere, and a cylinder. The use of spectral methods, especially multidomain spectral methods, appears to be very promising for accurately simulating electromagnetic wave problems.

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Citation Excerpt :
The proposed method is also somewhat similar in its objective to the direct solver for Poisson’s equation described by Greengard and Etheridge [7], but the solver of [7] requires the kernel of the solution operator to be known analytically, which is not the case in the present context. The discretization technique we use is similar to earlier work on multidomain pseudospectral methods, see, e.g., [19,37], and in particular Pfeiffer et al. [27]. A difference is that we immediately eliminate all degrees of freedom associated with nodes that are internal to each patch (i.e., nodes not shared with any other patch) and formulate a linear system that involves only the boundary nodes.
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^☆: This work was partially supported by DARPA/AFOSR Grant F49620-96-1-0426.

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Multidomain pseudospectral computation of Maxwell's equations in 3-D general curvilinear coordinates☆

Abstract