dorsal/arxiv
View SchemaNumerical methods for solving the time-dependent Maxwell equations
| Authors | H. De Raedt, J. S. Kole, K. F. L. Michielsen, M. T. Figge |
|---|---|
| Categories | |
| ArXiv ID | physics/0210035 |
| URL | https://arxiv.org/abs/physics/0210035 |
Abstract
We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We show that the Suzuki product-formula approach can be used to construct a family of unconditionally stable algorithms, the conventional Yee algorithm, and two new variants of the Yee algorithm that do not require the use of the staggered-in-time grid. We also consider a one-step algorithm, based on the Chebyshev polynomial expansion, and compare the computational efficiency of the one-step, the Yee-type, the alternating-direction-implicit, and the unconditionally stable algorithms. For applications where the long-time behavior is of main interest, we find that the one-step algorithm may be orders of magnitude more efficient than present multiple time-step, finite-difference time-domain algorithms.
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"abstract": "We review some recent developments in numerical algorithms to solve the\ntime-dependent Maxwell equations for systems with spatially varying\npermittivity and permeability. We show that the Suzuki product-formula approach\ncan be used to construct a family of unconditionally stable algorithms, the\nconventional Yee algorithm, and two new variants of the Yee algorithm that do\nnot require the use of the staggered-in-time grid. We also consider a one-step\nalgorithm, based on the Chebyshev polynomial expansion, and compare the\ncomputational efficiency of the one-step, the Yee-type, the\nalternating-direction-implicit, and the unconditionally stable algorithms. For\napplications where the long-time behavior is of main interest, we find that the\none-step algorithm may be orders of magnitude more efficient than present\nmultiple time-step, finite-difference time-domain algorithms.",
"arxiv_id": "physics/0210035",
"authors": [
"H. De Raedt",
"J. S. Kole",
"K. F. L. Michielsen",
"M. T. Figge"
],
"categories": [
"physics.comp-ph",
"physics.optics"
],
"title": "Numerical methods for solving the time-dependent Maxwell equations",
"url": "https://arxiv.org/abs/physics/0210035"
},
"schema_id": "dorsal/arxiv",
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