Optimized compact-difference-based finite-volume schemes for linear wave phenomena. (English) Zbl 0898.65055
The aim of this paper is to obtain more efficient techniques for the time integration of the classical Maxwell’s equations than available hitherto. These new methods are based on a space discretization with finite-volume schemes that use compact-difference methods. Compact-difference schemes are a special class of centered schemes and use a very small stencil support; they allow to compute derivatives in a coupled fashion along an entire line and have a smaller truncation error.
The classical single-step multistage Runge-Kutta method for fourth-order accuracy RK4 is chosen for the time integration step.
The authors establish stability bounds for their method and readjust the coefficients of the spatial discretization for optimal performance. Several calculations are given to illustrate the properties of the method.
The classical single-step multistage Runge-Kutta method for fourth-order accuracy RK4 is chosen for the time integration step.
The authors establish stability bounds for their method and readjust the coefficients of the spatial discretization for optimal performance. Several calculations are given to illustrate the properties of the method.
Reviewer: W.Govaerts (Gent)
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 78A25 | Electromagnetic theory (general) |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
time evolution; numerical examples; Maxwell’s equations; finite-volume schemes; compact-difference methods; Runge-Kutta method; stability; performanceReferences:
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