A finite integration method for conformal, structured-grid, electromagnetic simulation

Journal Article · Sat Jun 10 00:00:00 EDT 2006 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2005.10.032· OSTI ID:20767050

Cooke, S J ^[1]; Shtokhamer, R ^[2]; Mondelli, A A ^[2]; Levush, B ^[1]

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1. Naval Research Laboratory, Code 6841, 4555 Overlook Avenue S.W., Washington, DC 20375 (United States)
2. SAIC, McLean, VA 22102 (United States)

We describe a numerical scheme for solving Maxwell's equations in the frequency domain on a conformal, structured, non-orthogonal, multi-block mesh. By considering Maxwell's equations in a volume parameterized by dimensionless curvilinear coordinates, we obtain a set of tensor equations that are a continuum analogue of common circuit equations, and that separate the metrical and metric-free parts of Maxwell's equations and the material constitutive relations. We discretize these equations using a new formulation that treats the electric field and magnetic induction using simple basis-function representations to obtain a discrete form of Faraday's law of induction, but that uses finite integral representations for the displacement current and magnetic field to obtain a discrete form of Ampere's law, as in the finite integration technique [T. Weiland, A discretization method for the solution of Maxwell's equations for six-component fields, Electron. Commun. (AE U) 31 (1977) 116; T. Weiland, Time domain electromagnetic field computation with finite difference methods, Int. J. Numer. Model: Electron. Netw. Dev. Field 9 (1996) 295-319]. We thereby derive new projection operators for the discrete tensor material equations and obtain a compact numerical scheme for the discrete differential operators. This scheme is shown to exhibit significantly reduced numerical dispersion when compared to the standard linear finite element method. We take advantage of the mesh structure on a block-by-block basis to implement these numerical operators efficiently, and achieve computational speed with modest memory requirements when compared to explicit sparse matrix storage. Using the Jacobi-Davidson [G.L.G. Sleijpen, H.A. van der Vorst, A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl. 17 (2) (1996) 401-425; S.J. Cooke, B. Levush, Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi-Davidson algorithm, J. Comput. Phys. 157 (1) (2000) 350-370] and quasi-minimal residual [R.W. Freund, N.M. Nachtigal, QMR: a quasi-minimal residual method for non-Hermitian linear systems, Numer. Math. 60 (1991) 315-339] iterative matrix solution algorithms, we solve the resulting discrete matrix eigenvalue equations and demonstrate the convergence characteristics of the algorithm. We validate the model for three-dimensional electromagnetic problems, both cavity eigenvalue solutions and a waveguide scattering matrix calculation.

• OSTI ID: 20767050
• Journal Information: Journal of Computational Physics, Vol. 215, Issue 1; Other Information: DOI: 10.1016/j.jcp.2005.10.032; PII: S0021-9991(05)00490-0; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
CONVERGENCE
CURVILINEAR COORDINATES
EIGENVALUES
ELECTRIC FIELDS
ELECTROMAGNETIC FIELDS
FINITE DIFFERENCE METHOD
FINITE ELEMENT METHOD
INDUCTION
MAGNETIC FIELDS
MAXWELL EQUATIONS
PROJECTION OPERATORS
SCATTERING
SIMULATION
TENSORS
THREE-DIMENSIONAL CALCULATIONS
VELOCITY
WAVEGUIDES