Name
Abstract | ||
|---|---|---|
Explicit local time-stepping methods are derived for time dependent Maxwell equations in conducting and non-conducting media. By using smaller time steps precisely where smaller elements in the mesh are located, these methods overcome the bottleneck caused by local mesh refinement in explicit time integrators. When combined with a finite element discretisation in space with an essentially diagonal mass matrix, the resulting discrete time-marching schemes are fully explicit and thus inherently parallel. In a non-conducting source-free medium they also conserve a discrete energy, which provides a rigorous criterion for stability. Starting from the standard leap-frog scheme, local time-stepping methods of arbitrarily high accuracy are derived for non-conducting media. Numerical experiments with a discontinuous Galerkin discretisation in space validate the theory and illustrate the usefulness of the proposed time integration schemes. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.cam.2010.04.028 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
local mesh refinement,non-conducting source-free medium,maxwell's equations 2000 msc: 65n30,local time-stepping,smaller time step,electromagnetic waves,proposed time integration scheme,explicit local time-stepping method,explicit time integrator,discontinuous galerkin discretisation,non-conducting media,finite element methods,local time-stepping method,discrete energy,discontinuous galerkin methods,explicit time integration,finite element,discontinuous galerkin method,maxwell equation,finite element method,discontinuous galerkin,local time,discrete time,maxwell s equations | Discontinuous Galerkin method,Stability criterion,Discretization,Mathematical analysis,Galerkin method,Finite element method,Discrete time and continuous time,Numerical analysis,Mathematics,Maxwell's equations | Journal |
Volume | Issue | ISSN |
234 | 12 | 0377-0427 |
Citations | PageRank | References |
16 | 0.85 | 14 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcus J. Grote | 1 | 401 | 51.61 |
| Teodora Mitkova | 2 | 37 | 3.20 |