Improved dual meshes using Hodge-optimized triangulations for electromagnetic problems
- Schlundt, Rainer
2010 Mathematics Subject Classification
- 35Q61 65F10 65F15 65N22 65N50
- Optimal triangulations, discrete Hodge star, Maxwell's equations, finite integration technique, microcell method, linear algebraic equations
Hodge-optimized triangulations (HOT) can optimize the dual mesh alone or both the primal and dual meshes. They make them more self-centered while keeping the primal-dual orthogonality. The weights are optimized in order to improve one or more of the discrete Hodge stars. Using the example of Maxwell's equations we consider academic examples to demonstrate the generality of the approach.