Tensor Product Generalized ADI Methods for Elliptic Problems

We collsider IlOlving separable, second order. linear elliptic partial differential equations. If an elliptic problem is separable, then, for certain discretizations. the matrices involved in the corresponding discrete problem can be expressed in terms of tensor products of lower order matrices. In the most general case. the discrete problem can be written in the form (Al@Bz +81i&lA,2)C ==F. We present a new Tensor Product Generalized AltematLog Dirc~c. tion Implicit (TPGADI) iterative method for solving such discrete problems. We prove convergence and establish computational etriciency. The TPGADI method is applied to the Hermite bicubic collocation equations. We conclude that the TPGADI method is an effecti.ve tool for solving the discrete elliptic problems arising from a large class o[ elliptic problems. Tensor Product Generalized ADI Methods for Elliptie Problems