Regular triangulation and power diagrams for Maxwell's equations
- Schlundt, Rainer
2010 Mathematics Subject Classification
- 35Q61 65F10 65F15 65N22 65N50
- Maxwell's equations, finite integration technique, linear algebraic equations, eigenvalue problem, optimal triangulations, discrete Hodge star, microcell method
We consider the solution of electromagnetic problems. A mainly orthogonal and locally barycentric dual mesh is used to discretize the Maxwell's equations using the Finite Integration Technique (FIT). The use of weighted duals allows greater flexibility in the location of dual vertices keeping the primal-dual orthogonality. The construction of the constitutive matrices is performed using either discrete Hodge stars or microcells. Hodge-optimized triangulations (HOT) can optimize the dual mesh alone to make it more self-centered while maintaining the primal-dual orthogonality, e.g., the weights are optimized in order to improve one or more of the discrete Hodge stars.