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.

提出了一种具有自适应粗糙空间的BDDC预调节器，用于通过稳定有限元方法离散化的对流扩散问题。由于相应变型形式的双线性形式是非对称正定（NSPD），因此一直用于解决对称正定（SPD）问题的自适应BDDC预处理器被扩展来解决非对称问题。通过将原始双线性形式分解为对称部分和偏斜对称部分，设计并分析了针对公共面/边的原始双线性形式的对称部分的一系列局部广义特征值问题，并进行了分析，以形成自适应粗糙成分。数值结果给出了具有不同粘度的模型问题，以显示所提出的预处理器的性能。