Development of large-scale parallel analysis method for contact problem based on domain decomposition method

本研究的目的是建立基于区域分解方法的大尺度接触问题并行求解方案。首先，提出了用有限元方法离散线弹性体无摩擦接触问题的简单解法。A方法是半光滑牛顿方法的一种变体。另一种方法是将内点法与半光滑牛顿法相结合。然后，利用平衡域分解法研究了这些方法在每个迭代步骤中求解具有线性多点约束的线性问题的算法。还研究了GPGPU实现的基本联系人搜索算法。虽然在本研究的提案中计划开发大规模摩擦接触问题的求解方案，但只进行了基础研究，在研究期间无法开发任何实用方案。

A purpose of the present study is to develop parallel solution scheme for large-scale contact problems based on the domain decomposition method. First, simple solution schemes for frictionless contact problems of linear elastic bodies, which are discretized using the finite element method are proposed. A method is a variant of the semismooth Newton method. Another method is combined interior-point method and semismooth Newton method. Then, study on algorithms to solve linear problem with linear multipoint constraints in each iterative step of these methods using the balancing domain decomposition method is conducted. GPGPU implementation of basic contact search algorithms is also studied. Although development of solution schemes for large-scale frictional contact problem was planned in the proposal of the present study, only fundamental studies are conducted, and any practical scheme could not be developed in the research period.