New point and group iterative methods for solving three-dimensional elliptic equations

Abstract

In this paper we construct a rotated finite differnce formula in 3-dimensions analogous to the rotated finite difference formula in 2-dimensions (Dahlquist and Bjorck, 1974; Vichnevetsky, 1981). Further, an explicit 2×2×2 de-coupled group (EDG) iterative method for the solution of problems arising in 3-dimensional elliptic partial differential equations is developed.Performance results for the two algorithms are presented and a comparison with the 7 point S.O.R. scheme in 3-dimensions confirm the new methods to be computationally superior.

Keywords:

• 3d finite difference formula
• Laplace's eqn
• explicit group methods

C.R. Categories:

• G1.8
• G1.3