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Higher order explicit time integration schemes for Maxwell's equations
Author(s) -
Spachmann Holger,
Schuhmann Rolf,
Weiland Thomas
Publication year - 2002
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.467
Subject(s) - discretization , runge–kutta methods , integrator , mathematics , stability (learning theory) , convergence (economics) , finite difference time domain method , spacetime , maxwell's equations , mathematical analysis , computer science , numerical analysis , physics , computer network , bandwidth (computing) , quantum mechanics , machine learning , economics , economic growth
The finite integration technique (FIT) is an efficient and universal method for solving a wide range of problems in computational electrodynamics. The conventional formulation in time‐domain (FITD) has a second‐order accuracy with respect to spatial and temporal discretization and is computationally equivalent with the well‐known finite difference time‐domain (FDTD) scheme. The dispersive character of the second‐order spatial operators and temporal integration schemes limits the problem size to electrically small structures. In contrast higher‐order approaches result not only in low‐dispersive schemes with modified stability conditions but also higher computational costs. In this paper, a general framework of explicit Runge–Kutta and leap‐frog integrators of arbitrary orders N is derived. The powerful root‐locus method derived from general system theory forms the basis of the theoretical mainframe for analysing convergence, stability and dispersion characteristics of the proposed integrators. As it is clearly stated, the second‐ and fourth‐order leap‐frog scheme are highly preferable in comparison to any other higher order Runge–Kutta or leap‐frog scheme concerning stability, efficiency and energy conservation. Copyright © 2002 John Wiley & Sons, Ltd.