High-order accurate methods in time-domain computational electromagnetics: A review

Publisher Summary This chapter reviews the Maxwell's equations in the time domain and discusses boundary conditions, various simplifications, and standard normalizations. The chapter provides an overview of the classical phase-error analysis as a way of motivating the need to consider high-order accurate methods in time-domain electromagnetics, particularly as problems increase in size and complexity. The extensions of the Yee scheme and other more complex finite difference schemes are discussed. Higher-order schemes allow a significant reduction of the degrees of freedom with accuracy. For some applications it may be natural to consider the ultimate limit, leading to global or spectral methods. The chapter discusses the elements of spectral multidomain methods, which combine the accuracy of global methods with the geometric flexibility of a multielement formulation. The recent efforts on the development of high-order finite volume methods for the solution of Maxwell's equations are reviewed. The issues related to high-order time stepping and discrete stability are also discussed.

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