Improved Parallel Computation of Electromagnetic Scattering

An improved method of parallel computation of the electromagnetic-scattering characteristics of complexly shaped objects has been devised. This method belongs to a class of methods that involve the finite-element solution of Maxwell's equations on unstructured grids. ("Unstructured grids" in this context does not signify grids that lack structure; instead, it is a specialized term for grids with arbitrarily specified, complex, and/or irregular structures.) As explained below, the present method effects a simplification (relative to the older methods in the same class) in the use of parallel computers, and involves an algorithm that is scalable in the sense that it is readily useable on large, massively parallel computers. A finite-element mathematical model is needed to represent a typical electromagnetic-scattering structure that includes components made of various electromagnetically penetrable (e.g., dielectric) and/or impenetrable (electrically conductive) materials. An unstructured grid is needed to represent the complexity of the geometry of such a structure and its components. In the present method as in the other methods of the same class, the computational grid or mesh for a given problem must be truncated at a surface that surrounds the scattering structure at a suitable distance. The surface must be chosen consistently with the need to both maintain accuracy of the computed electromagnetic field and limit the meshed volume of free space. Maxwell's equations for the electromagnetic field are put in three-dimensional Helmholtz wave-equation form and solved on the mesh by a coupled finite-element/integral-equation technique.