Applied Maths Seminar: Olver -- Solving PDEs on triangles using multivariate orthogonal polynomials

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