Development of Verified Methods for Numerical Simulations with Domain Decompsition Methods

使用域分解方法开发数值模拟的验证方法

• 批准号: 13555021
• 负责人: NAKAMURA Masaaki
• 金额: $ 8.64万
• 依托单位: Nihon University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13555021/
• 关键词: domain decomposition; parallel computing; FEM and FDM; precondition; simulation; fluid dynamics; phase separation; nonlinear problems; interative method; precondiion; Navier -Stokes equation; spinodal decomposition; infinnite precision; compu

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

在项目期间（三年）取得了许多成果。重要结果如下：1。数值模拟方法的发展矢量化快速数值计算的新方法。通过并行计算进行仿真。无限精度的数值模拟。新的前置条件方法。数值积分分析。混凝土材料的细观模拟。非线性问题的应用与数值分析。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规范。反应扩散系统分析。具有摩擦型边界条件的Navier-Stokes方程。自由边界问题的数值方法。用多网格法分析微波问题。几种流体力学的数值模拟。两相流。n - s流动。脑部血流

项目成果

Y.Fujita, K.Ohmori: "A comparison theorem for Bellman equation of ergodic control"Differential and Integral Equation. vol.16. 641-651 (2003)

Y.Fujita，K.Ohmori：“遍历控制贝尔曼方程的比较定理”微分方程和积分方程。

M.Tabata, A.Suzuki: "Mathematical modeling and numerical simulation of Earth's mantle convection"Springer Lecture Note in computational Science and Engineering. vol.19. 161-177 (2002)

M.Tabata、A.Suzuki：“地球地幔对流的数学建模和数值模拟”计算科学与工程施普林格讲义。

T.Tanaka: "Solutions of radiative transfer in aniis6tropic plane-parallel atmosphere"J.Quantitaive Specroscopy & Radiattive Transfer. vol.83. 557-577 (2004)

T.Tanaka：“各向异性平面平行大气中辐射传输的解决方案”J.定量光谱学

H.Fujita: "Non-stationary Stokes flows under leak boundary conditions of friction type"Journal of computing Mathematics. vol.19,No.1. 1-8 (2001)

H.Fujita：“摩擦型泄漏边界条件下的非平稳斯托克斯流”计算数学杂志。

T.Hanada, N.Ishimura, M.Nakamura: "On a stable finite difference scheme for a model equation of phase separation."Proceedings of the Third International Workshop on Scientific Computing and Applications. (to appear). (2004)

T.Hanada、N.Ishimura、M.Nakamura：“关于相分离模型方程的稳定有限差分格式。”第三届国际科学计算与应用研讨会论文集。