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Mimetic Discretizations for Maxwell's Equations

By James M. Hyman and Mikhail Shashkov


This paper is a part of our attempt to develop a discrete analog of vector and tensor calculus that can be used to accurately approximate continuum models for a wide range of physical processes on logically rectangular, nonorthogonal, nonsmooth grids. These mimetic FDMs mimic fundamental properties of the original continuum differential operators and allow the discrete approximations of partial differential equations (PDEs) to preserve critical properties including conservation laws and symmetries in the solution of the underlying physical problem. In particular, we have constructed discrete analogs of first-order differential 881 0021-9991/99 operators, such as div, grad, and curl, that satisfy the discrete analogs of theorems of vector and tensor calculus [10--13]. This approach has also been used to construct high-quality mimetic FDMs for the divergence and gradient in approximating the diffusion equation [15, 38, 39

Year: 1999
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