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

摘要

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. (C) 2004 Elsevier B.V. All rights reserved.