Iterative solution of elliptic problems by approximate factorization

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:85

Article

Giladi, E ; Keller, JB

关键词: defect correction iteration;    asymptotic factorization;    preconditioners;   

DOI  :  10.1016/S0377-0427(97)00132-5

来源: Elsevier

【 摘 要 】

An iterative method for the numerical solution of singularly perturbed second-order linear elliptic problems is presented. It is a defect correction iteration in which the approximate operator is the product of two first-order operators, which is readily inverted numerically. The approximate operator is generated by formal asymptotic factorization of the original operator. Hence this is a QUasi Analytic Defect correction iteration (QUAD). Both its continuous and discrete versions are analyzed in one dimension. The scheme is extended to a variety of two dimensional operators and it is analyzed for a model advection-diffusion equation. Numerical calculations show the effectiveness of the scheme over a wide range of values of the small parameter.

【 授权许可】

Free