An adaptive BDDC preconditioner for advection-diffusion problems with a stabilized finite element discretization

A BDDC preconditioner with adaptive coarse space for advection-diffusion problems discretized by stabilized finite element method is proposed. Since the bilinear form of the corresponding variational form is nonsymmetric and positive definite (NSPD), the adaptive BDDC preconditioner, which is always used for solving the symmetric and positive definite (SPD) problems, is extended to solve the nonsymmetric problems. By decomposing the original bilinear form to the symmetric part and the skew-symmetric part, a series of local generalized eigenvalue problems with respect to the symmetric part of the original bilinear form for the common faces/edges are designed and analyzed to form the adaptive coarse components. Numerical results are presented for model problems with various viscosities to show the performance of the proposed preconditioner. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

An adaptive BDDC preconditioner is proposed for advection-diffusion problems, which extends the method to solve nonsymmetric and positive definite bilinear forms. By decomposing the original form and designing local generalized eigenvalue problems, adaptive coarse components are formed for improved performance. Published by Elsevier B.V. with all rights reserved.