Sequential function approximation for the solution of differential equations

作     者：Meade, AJ Kokkolaras, M Zeldin, BA 

作者机构：Rice Univ Dept Mech Engn & Mat Sci Houston TX 77251 USA 

出 版 物：《COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING》 (工程数值法快报)

年 卷 期：1997年第13卷第12期

页      面：977-986页

核心收录：

学科分类：08[工学] 09[农学] 0901[农学-作物学] 0836[工学-生物工程] 0701[理学-数学] 090102[农学-作物遗传育种] 

主　　题：sequential function approximation interpolation functions optimization parallel direct search 

摘      要：A computational method for the solution of differential equations is proposed. With this method an accurate approximation is built by incremental additions of optimal local basis functions. The parallel direct search software package (PDS), that supports parallel objective function evaluations, is used to solve the associated optimization problem efficiently. The advantage of the method is that, although it resembles adaptive methods in computational mechanics, an a priori grid is not necessary. Moreover, the traditional matrix construction and evaluations are avoided. Computational cost is reduced while efficiency is enhanced by the low-dimensional parallel-executed optimization and parallel function evaluations. In addition, the method should be applicable to a broad class of interpolation functions. Results and global convergence rates obtained for one-and two-dimensional boundary value problems are satisfactorily compared to those obtained by the conventional Galerkin finite element method. (C) 1997 John Wiley & Sons, Ltd.