Alternating block Crank-Nicolson method for the 3-D heat equation
Recently, there has been growing interest in the parallel implementation of implicit methods. The alternating segment Crak-Nicolson and the alternating band and block Crank-Nicolson methods have been developed for one- and two-dimensional diffusion equations, respectively. In this paper the author extends the alternating block technique to a 3-dimensional problem and proposes a new numerical scheme called alternating block Crank-Nicolson (ABkC-N) method for the 3-dimensional linear heat equation in the unit cube. The Crank-Nicolson (C-N) scheme is an implicit form and is difficult to arrange for computation in sequence or in parallel. Out of consideration for parallelism, stability and accuracy, the author constructs the ABkC-N method by dividing the net region into finite blocks on which the computations are independent from each other. The ABkC-N scheme is unconditionally stable and is suitable to an MIMD computer. The numerical experiments show that the scheme is a little more accurate than the C-N scheme itself.
alternating band and block Crank- Nicolson methods
scientific article; zbMATH DE number 753926