Abstract
In this paper, a new parallel algorithm for solving parabolic equations is proposed. The new algorithm includes two domain decomposition methods, each method is applied to compute the values at (n+1)st time level by use of known numerical solutions at nth time level, respectively. Then the average of two above values is chosen to be the numerical solutions at (n+1)st time level. The new algorithm obtains satisfactory accuracy while maintaining parallelism and unconditional stability. This algorithm can be extended to solve two-dimensional parabolic equations by alternating direction implicit (ADI) technique. Both error analysis and numerical experiments illustrate the accuracy and efficiency of the new algorithm.
Highlights
With the development of large-scale scientific and engineering computations, the parallel difference method for parabolic equations has been studied rapidly
Inspired by the alternating segment algorithm, we present a new parallel algorithm for parabolic equations in this paper
We focus on a model problem, namely one-dimensional parabolic equations
Summary
With the development of large-scale scientific and engineering computations, the parallel difference method for parabolic equations has been studied rapidly. An alternating segment algorithm is a form of the domain decomposition method, which is suitable for parallel computation and unconditionally stable. Inspired by the alternating segment algorithm, we present a new parallel algorithm for parabolic equations in this paper.
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