Type: Seminar

Distribution: World

Expiry: 31 Mar 2017

CalTitle1: Solving PDEs on triangles using multivariate orthogonal polynomials

Auth: ega@como.maths.usyd.edu.au

Sheehan Olver (School of Mathematics and Statistics, University of Sydney) Title: Solving PDEs on triangles using multivariate orthogonal polynomials Abstract: Univariate orthogonal polynomials have long history in applied and computational mathematics, playing a fundamental role in quadrature, spectral theory and solving differential equations with spectral methods. Unfortunately, while numerous theoretical results concerning multivariate orthogonal polynomials exist, they have an unfair reputation of being unwieldy on non-tensor product domains. In reality, many of the powerful computational aspects of univariate orthogonal polynomials translate naturally to multivariate orthogonal polynomials, including the existence of Jacobi operators and the ability to construct sparse partial differential operators, a la the ultrapsherical spectral method [Olver & Townsend 2012]. We demonstrate these computational aspects using multivariate orthogonal polynomials on a triangle, including the fast solution of general partial differential equations. http://www.maths.usyd.edu.au/u/SemConf/Applied.html