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Solving Maxwell's equations using FDTD and the Piola transformation

Program in Applied Mathematics Brown Bag Seminar

Solving Maxwell's equations using FDTD and the Piola transformation
Series: Program in Applied Mathematics Brown Bag Seminar
Location: Zoom Meeting
Presenter: Armando Albornoz, Program in Applied Mathematics, University of Arizona

FDTD has proved to be a robust way for numerically solving Maxwell's equations since it was introduced by Kane Yee in 1966. Approximating non rectangular domains with rectangular meshes causes staircasing and as a consequence the accuracy of the numerical solution deteriorates. Madsen and Ziolkowski proposed a way to implement FDTD for general 3D domains that suffers from late time instability. We describe a potential way to repair this instability. For this purpose we employ the Piola transformation which allows us to map cells from the physical space to the reference cell in a manner that preserves fluxes and circulations, a useful property regarding Maxwell's equations. We briefly describe the Piola transformation and also the issue of orienting the edges of the mesh in the 2D case.  Zoom: https://arizona.zoom.us/j/810942010