Singularity-free evaluation of collapsed-coordinate orthogonal polynomials

Author:
Open Access
Publisher website
Google Scholar
Abstract
The L 2 -orthogonal polynomials used in finite and spectral element methods on nonrectangular elements may be defined in terms of collapsed coordinates, wherein the shapes are mapped to a square or cube by means of a singular change of variables. The orthogonal basis is a product of specific Jacobi polynomials in these new coordinates. Implementations of these polynomials require special handling of the coordinate singularities. We derive new recurrence relations for these polynomials on triangles and tetrahedra that work directly in the original coordinates. These relations, also applicable to pyramids and prisms, do not require any special treatment of singular points. These recurrences are seen to speed up both symbolic and numerical computation of the orthogonal polynomials.

This publication has 13 references indexed in Scilit: