Dynamic load balance strategy: application to nonlinear optics
High performance scientific and engineering computing
Dynamic Load Balancing Computation of Pulses Propagating in a Nonlinear Medium
The Journal of Supercomputing
DSC time-domain solution of Maxwell's equations
Journal of Computational Physics
High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
Journal of Computational Physics
Journal of Computational Physics
Frequency Optimized Computation Methods
Journal of Scientific Computing
High order Hybrid central-WENO finite difference scheme for conservation laws
Journal of Computational and Applied Mathematics
Numerical simulations of acoustic fields on boundary-fitted grids
Mathematics and Computers in Simulation
A new combined stable and dispersion relation preserving compact scheme for non-periodic problems
Journal of Computational Physics
Journal of Computational Physics
A linear focusing mechanism for dispersive and non-dispersive wave problems
Journal of Computational Physics
Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
SIAM Journal on Numerical Analysis
Multistep and Multistage Convolution Quadrature for the Wave Equation: Algorithms and Experiments
SIAM Journal on Scientific Computing
Certain numerical issues of wave propagation modelling in rods by the Spectral Finite Element Method
Finite Elements in Analysis and Design
Journal of Computational Physics
The Nonconvergence of $$h$$h-Refinement in Prolate Elements
Journal of Scientific Computing
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This paper analyzes a number of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, and elastic waves. The spatial operators analyzed include compact schemes, noncompact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods include Runge--Kutta methods, Adams--Bashforth methods, and the leapfrog method. In addition, the following fully-discrete finite-difference methods are studied: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. The results provide a clear understanding of the relative merits of the methods compared, especially the trade-offs associated with the use of optimized methods. A numerical example is given which shows that the benefits of an optimized scheme can be small if the waveform has broad spectral content.