NASC Seminar: Maxwell in a cylinder via orthogonal polynomials for the de Rham complex

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Speaker: Sheehan Olver (Imperial College London) Abstract: We construct vector-valued multivariate orthogonal polynomials that capture the structure of the de Rham complex (i.e., the gradient, curl and divergence) with boundary conditions in disks and cylinders (both periodic and finite) in a way that respects rotational symmetry. This construction naturally gives bases in cylinders with simple recurrences relating their gradient, curl and divergence, which leads to an optimal complexity solverfor Maxwell and Hodge-Laplacian equations in a cylinder. The approach extends to other classical elements like balls and tetrahedra.