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A novel domain decomposition method for coupled semilinear elliptic equation
Author(s) -
Yue Meiling,
Xu Fei,
Ma Hongkun
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7415
Subject(s) - domain decomposition methods , mathematics , domain (mathematical analysis) , elliptic curve , nonlinear system , decomposition method (queueing theory) , finite element method , smoothness , mathematical analysis , elliptic partial differential equation , algorithm , partial differential equation , discrete mathematics , physics , quantum mechanics , thermodynamics
This study presents a new framework to solve the coupled semilinear elliptic equation by the domain decomposition algorithm. Unlike the traditional domain decomposition algorithm, the coupled semilinear elliptic equation doesn't need to be solved directly. The strategy is to construct a set of nested finite element spaces, and subsequently solve some decoupled linear elliptic equations by using the domain decomposition method in each level space. Additionally, a small‐scale coupled semilinear elliptic equation in a specially designed correction space will be solved. As the large‐scale coupled semilinear elliptic equation doesn't need to be solved directly, there will be an improved efficiency as compared to the traditional domain decomposition method. Furthermore, as the domain decomposition method is only used to solve decoupled linear elliptic equations, any efficient algorithms designed for the associated linear elliptic equations can be incorporated in the proposed algorithm framework. Thus, the algorithm is highly flexible. Additionally, it can be theoretically proven that the proposed algorithm has very low requirements for the smoothness of nonlinear terms.