Analysis of Block Preconditioners for Models of Coupled Magma/Mantle Dynamics
Analysis of Block Preconditioners for Models of Coupled Magma/Mantle Dynamics
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DOI：
10.1137/130946678
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发表时间：
2013-11
期刊：
影响因子：
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通讯作者：
S. Rhebergen;G. N. Wells;R. Katz;A. Wathen
中科院分区：
文献类型：
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作者：
S. Rhebergen;G. N. Wells;R. Katz;A. Wathen
本文讨论了岩浆动力学方程有限元离散的迭代解法。在简化形式下，岩浆动力学方程具有Stokes方程的某些特征。因此，我们制定，分析和数值测试的Elman，西尔维斯特，和Wathen型块预处理岩浆动力学。我们证明解析和数值证明的预条件的最优性。所提出的分析突出了预条件的岩浆动力学方程中的参数，可以影响迭代线性求解器的收敛性的依赖。通过一系列二维和三维非结构化网格的数值例子，从简单的说明性问题，通过大型问题俯冲带的几何形状的分析进行验证。复制所有数值例子的计算机代码可作为辅助材料免费获得。
This article considers the iterative solution of a finite element discretization of the magma dynamics equations. In simplified form, the magma dynamics equations share some features of the Stokes equations. We therefore formulate, analyze, and numerically test an Elman, Silvester, and Wathen-type block preconditioner for magma dynamics. We prove analytically and demonstrate numerically the optimality of the preconditioner. The presented analysis highlights the dependence of the preconditioner on parameters in the magma dynamics equations that can affect convergence of iterative linear solvers. The analysis is verified through a range of two- and three- dimensional numerical examples on unstructured grids, from simple illustrative problems through to large problems on subduction zone-like geometries. The computer code to reproduce all numerical examples is freely available as supporting material.