A Domain Decomposition Method With Lagrange Multipliers For Linear Elasticity
A Domain Decomposition Method With Lagrange Multipliers For Linear Elasticity
复制标题
线弹性拉格朗日乘子域分解方法
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
O. Widlund
中科院分区：
文献类型：
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作者：
A. Klawonn;O. Widlund
引入了一种用于椭圆问题的拉格朗日乘子的新域分解方法。它基于将著名的 FETI 方法重新表述为鞍点问题，原始变量和对偶变量均作为未知数。由此产生的线性系统通过块结构预处理器与合适的 Krylov 子空间方法相结合来求解。这种方法允许使用不精确的子域求解器来解决正定子问题。结果表明，预处理鞍点问题的条件数有界，与子区域的数量无关，并且仅与各个局部子问题的自由度数呈多对数关系。给出了平面应力悬臂膜问题的数值结果。
A new domain decomposition method with Lagrange multipliers for elliptic problems is introduced. It is based on a reformulation of the well--known FETI method as a saddle point problem with both primal and dual variables as unknowns. The resulting linear system is solved with block--structured preconditioners combined with a suitable Krylov subspace method. This approach allows the use of inexact subdomain solvers for the positive definite subproblems. It is shown that the condition number of the preconditioned saddle point problem is bounded independently of the number of subregions and depends only polylogarithmically on the number of degrees of freedom of individual local subproblems. Numerical results are presented for a plane stress cantilever membrane problem.