Name
Title | ||
|---|---|---|
A finite integration method for conformal, structured-grid, electromagnetic simulation |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.jcp.2005.10.032 | J. Comput. Physics |
Keywords | Field | DocType |
discretization method,finite element methods,eigenvalue problems,discrete tensor material equation,discrete differential operator,discrete form,electric field,finite integration technique,compact numerical scheme,finite integration method,discrete matrix eigenvalue equation,jacobi-davidson iteration method,t. weiland,explicit sparse matrix storage,electromagnetic simulation,sparse matrix,linear system,three dimensional,constitutive relation,projection operator,iteration method,scattering matrix,magnetic field,electromagnetic field,finite difference method,differential operators,eigenvalues,function representation,finite element method,frequency domain,time domain | Discretization,Computational electromagnetics,Mathematical analysis,Electromagnetic field solver,Finite element method,Stiffness matrix,Mathematics,Maxwell's equations,Inhomogeneous electromagnetic wave equation,Eigenvalues and eigenvectors | Journal |
Volume | Issue | ISSN |
215 | 1 | Journal of Computational Physics |
Citations | PageRank | References |
2 | 0.51 | 2 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| S. J. Cooke | 1 | 2 | 0.51 |
| R. Shtokhamer | 2 | 2 | 0.51 |
| Mondelli, Alfred A. | 3 | 6 | 1.71 |
| Levush, B. | 4 | 7 | 3.06 |