Development of Verified Methods for Numerical Simulations with Domain Decompsition Methods

项目实施三年来，取得了许多成果。主要研究成果如下：1.本文的主要研究成果。数值模拟方法的发展矢量化快速数值计算的新方法。并行计算模拟。无限精度的数值模拟。新的前置条件方法。数值积分分析。混凝土材料的介观模拟。非线性问题的应用和数值分析。相分离系统的分析。有限元方法的误差估计。地幔对流的有限元方法代码。反应扩散系统的分析。带摩擦型边界条件的N-S方程。自由边界问题的数值方法。用多重网格方法分析微波问题。几种流体动力学的数值模拟：两相流、Navier-Stokes流、脑内血液流动

In the term of the project (three years) many results are obtained. Important results are shown as follows.1. Development of methods fot numerical simulationNew method of a fast numerical computation by vectorization.Simulation by paralel computaions.Numerical simulation in Infinite precisions.New pre-condition methods.Analysis of numerical integrations.Mesoscopic simulation of concrete materials.2. Applied and numerical analysis of nonlinear problems.Analysis of the system of phase separations.Error estimates for finite element methods.Code of finite element methods for mandtle convections.Analysis of reaction-diffusion systems.Navier-Stokes equations with friction type boundary conditions.Numerical methods for free boundary problems.Analysis microwave problems using multi grids methods.3. Numerical simulations of several fluid dynamics.Two-phase flows.Navier-Stokes flows.Blood flow in brain