A new parallel algorithm for solving parabolic equations

作者：Xue, Guanyu; Feng, Hui^*

来源：Advances in Difference Equations, 2018, 2018(1): 174.

DOI：10.1186/s13662-018-1617-8

• Parabolic equations
• Finite difference
• Unconditional stability
• Parallelism

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.

• 出版日期2018-5-9
• 单位武汉大学