An adaptive BDDC algorithm in variational form for mortar discretizations

作者：Peng, Jie; Shu, Shi; Wang, Junxian^*

来源：Journal of Computational and Applied Mathematics, 2018, 335: 185-206.

DOI：10.1016/j.cam.2017.11.031

• Elliptic problems
• Mortar methods
• BDDC algorithm
• Adaptive primal constraints

A balancing domain decomposition by constraints (BDDC) algorithm with adaptive primal constraints in variational form is introduced and analyzed for high-order mortar discretization of two-dimensional elliptic problems with high varying and random coefficients. Some vector-valued auxiliary spaces and operators with essential properties are defined to describe the variational algorithm, and the coarse space is formed by using a transformation operator on each interface. Compared with the adaptive BDDC algorithms for conforming Galerkin approximations, our algorithm is simpler, because there have not any continuity constraints at subdomain vertices in the mortar method involved in this paper. The condition number of the preconditioned system is proved to be bounded above by a user defined tolerance and a constant which is dependent on the maximum number of interfaces per subdomain, and independent of the mesh size and the contrast of the given coefficients. Numerical results show the robustness and efficiency of the algorithm for various model problems.

• 出版日期2018-6
• 单位湘潭大学