Unconditionally stable integration of Maxwell’s equations. (English) Zbl 1170.78004
This paper discusses unconditionally stable integration for a general semi-discrete Maxwell system on space grids that exclude the alternating direction implicit (ADI) approach, and addresses the question whether fully implicit and exponential time integration, eliminating any temporal step-size stability restriction, can be feasible and efficient?
For solving the systems of linear algebraic equations arising with implicit integrators , the conjugate gradient iterative method with preconditioning is used, and for exponential integration, Krylov subspace iteration is considered. The paper may be of interest to someone, in the field of Numerical Linear Algebra, working on efficient solvers.
For solving the systems of linear algebraic equations arising with implicit integrators , the conjugate gradient iterative method with preconditioning is used, and for exponential integration, Krylov subspace iteration is considered. The paper may be of interest to someone, in the field of Numerical Linear Algebra, working on efficient solvers.
Reviewer: V. D. Sharma (Mumbai)
MSC:
| 78M25 | Numerical methods in optics (MSC2010) |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65M12 | Stability and convergence of numerical 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 |
Keywords:
Maxwell’s equations; stable integration; alternating direction implicit (ADI) approach; conjugate gradient iterative method; Krylov subspace iterationReferences:
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