Orthogonal collocation revisited

By L. Young. Computer Methods in Applied Mechanics and Engineering, 2019

51 citations recorded by the source corpus.

Abstract 2018 marked the 80th anniversary of Lanczos (1938) and 2017 was the 50th anniversary of Villadsen and Stewart (1967), both seminal works in development of the Orthogonal Collocation Method, also known as the Pseudospectral Method and Differential Quadrature Method. Due to these milestones, a retrospective on development of the method seems appropriate. The method’s development as a Method of Weighted Residuals (MWR), with numerical integration, is reviewed. It is placed into historical perspective and developments in disparate disciplines are reconciled. We show the equivalence of methods that were thought by many to be different. Guidance in navigating the minefield of terminology is also provided. In addition to reviewing the development of the method, we show some refinements which are not known to most practitioners. Chief amongst these are the correct treatment of boundary conditions involving fluxes. We demonstrate that a proper treatment of flux boundary conditions can sometimes reduce errors by several orders of magnitude.

Subfields: Materials Chemistry, Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/3ff7799dcf5ff86aba1fc0693349fde26091e7e1