524 research outputs found
Beyond the poor man's implementation of unconditionally stable algorithms to solve the time-dependent Maxwell Equations
For the recently introduced algorithms to solve the time-dependent Maxwell
equations (see Phys.Rev.E Vol.64 p.066705 (2001)), we construct a variable grid
implementation and an improved spatial discretization implementation that
preserve the property of the algorithms to be unconditionally stable by
construction. We find that the performance and accuracy of the corresponding
algorithms are significant and illustrate their practical relevance by
simulating various physical model systems.Comment: 18 pages, 16 figure
New numerical methods for solving the time-dependent Maxwell equations
We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeabilitly. 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 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.</p
Chebyshev method to solve the time-dependent Maxwell equations
We present a one-step algorithm to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We compare the results of this algorithm with those obtained from unconditionally stable algorithms and demonstrate that for a range of applications the one-step algorithm may be orders of magnitude more efficient than multiple time-step, finite-difference time-domain algorithms. We discuss both the virtues and limitations of this one-step approach.</p
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