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Space–time variational methods for Maxwell's equations
Author(s) -
Hauser Julia I. M.,
Steinbach Olaf
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900221
Subject(s) - maxwell's equations , discretization , mathematics , laplace's equation , space time , laplace transform , mathematical analysis , wave equation , transformation (genetics) , space (punctuation) , algebraic equation , electromagnetic field solver , spacetime , physics , inhomogeneous electromagnetic wave equation , electromagnetic field , nonlinear system , computer science , partial differential equation , biochemistry , chemistry , quantum mechanics , chemical engineering , engineering , optical field , gene , operating system
The efficient and accurate numerical solution of the time–dependent Maxwell equations is one of the most challenging tasks, see, e.g., [1]. Besides semi–discretization methods such as the method of lines and Laplace transformation approaches, space–time variational formulations became popular in recent years. Here the variational principle is applied simultaneously in space and time, which later requires the solution of the global linear system of algebraic equations. But this can be done in parallel, and the space–time formulation allows for an adaptive resolution of the solution in space and time simultaneously. Following previous work [3,5] on the acoustic wave equation we present two variational formulations for the solution of the electromagnetic wave equation.