Abstract
We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric and magnetic field. Special emphasis is placed on an efficient implementation which is achieved by taking advantage of recurrence properties and the tensor-product structure of the chosen shape functions. These recurrences have been derived symbolically with computer algebra methods reminiscent of the holonomic systems approach.
| Original language | English |
|---|---|
| Title of host publication | Numerical and Symbolic Scientific Computing: Progress and Prospects |
| Place of Publication | Wien |
| Publisher | Springer |
| Pages | 105-121 |
| Number of pages | 18 |
| Volume | 1 |
| ISBN (Print) | 978-3-7091-0793-5 |
| Publication status | Published - 2012 |
Fields of science
- 101001 Algebra
- 101002 Analysis
- 101 Mathematics
- 102 Computer Sciences
- 102011 Formal languages
- 101009 Geometry
- 101013 Mathematical logic
- 101020 Technical mathematics
- 101025 Number theory
- 101012 Combinatorics
- 101005 Computer algebra
- 101006 Differential geometry
- 101003 Applied geometry
- 102025 Distributed systems
JKU Focus areas
- Computation in Informatics and Mathematics