2015, Schlundt, Rainer

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 Maxwells equations we consider academic examples to demonstrate the generality of the approach.

2014, Schlundt, Rainer

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.