论文标题
均等质量矩阵的易于有效的预处理
Easy and Efficient preconditioning of the Isogeometric Mass Matrix
论文作者
论文摘要
本文介绍了与质量矩阵相关的线性系统的快速解决方案，在同几何分析的背景下。我们提出了一个基于单变量参数质量矩阵的对角线尺度的Kronecker产品，该预处理既有效又易于实现。它的应用比涉及质量基质本身的矩阵矢量产物快。我们证明，随着较小的网格尺寸降低，即预处理矩阵的条件数会收敛到1，也就是说，预处理器在渐近上等同于确切的反向。此外，我们给出了其相对于样条学位和（可能是单数）几何参数化的良好行为的数值证据。我们还通过添加剂Schwarz方法将预处理扩展到了多捕获案例。
This paper deals with the fast solution of linear systems associated with the mass matrix, in the context of isogeometric analysis. We propose a preconditioner that is both efficient and easy to implement, based on a diagonal-scaled Kronecker product of univariate parametric mass matrices. Its application is faster than a matrix-vector product involving the mass matrix itself. We prove that the condition number of the preconditioned matrix converges to 1 as the mesh size is reduced, that is, the preconditioner is asymptotically equivalent to the exact inverse. Moreover, we give numerical evidence of its good behaviour with respect to the spline degree and the (possibly singular) geometry parametrization. We also extend the preconditioner to the multipatch case through an Additive Schwarz method.
