An analytic pseudo-spectral method to generate a regular 4-sided PDE surface patch

Authors:
M. I. G. Bloor;M. J. Wilson
Affiliations:
School of Mathematics, The University of Leeds, Leeds LS2 9JT, UK;School of Mathematics, The University of Leeds, Leeds LS2 9JT, UK
Venue:
Computer Aided Geometric Design
Year:
2005

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Abstract

We describe a pseudo-spectral method for rapidly calculating an analytic approximation to a 4-sided PDE surface patch. The method generates an approximate solution consisting of three parts: an eigenfunction solution and a polynomial solution, both of which satisfy the generating partial differential equation exactly, and a third function, or 'remainder' term that ensures that the boundary conditions are satisfied exactly. Being analytic, the approximation allows an arbitrary degree of surface refinement thereby facilitating physical analysis.