An adaptive BDDC preconditioner for advection-diffusion problems with a stabilized finite element discretization
An adaptive BDDC preconditioner for advection-diffusion problems with a stabilized finite element discretization
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DOI：
10.1016/j.apnum.2021.02.012
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发表时间：
2021-02
影响因子：
2.8
通讯作者：
J. Peng;S. Shu;Junxian Wang;L. Zhong
中科院分区：
文献类型：
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作者：
J. Peng;S. Shu;Junxian Wang;L. Zhong
针对稳定化有限元离散的对流扩散问题，提出了一种具有自适应粗空间的BDDC预处理器。由于相应的变分形式的双线性形式是非对称正定的，因此将求解对称正定问题的自适应BDDC预条件子推广到求解非对称问题.通过将原双线性形式分解为对称部分和反对称部分，设计并分析了一系列关于原双线性形式对称部分的公共面/边的局部广义特征值问题，从而形成自适应粗分量.数值结果与各种粘度的模型问题，以显示所提出的预处理器的性能。
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.