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Construction of Numerical Analysis for High-performance Large-Scale Computation

高性能大规模计算数值分析的构建

基本信息

批准号：
13304007
负责人：
TABATA Masahisa
金额：
$ 26.12万
依托单位：
Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
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

项目摘要

1.In devising numerical schemes for flow problems, how to approximate the convection torn is a crucial point. Characteristic finite element approximation is based on the approximation of the material derivative, which is the sum of the time derivative term and the convection term. So far finite element schemes of characteristic method of the first-order accuracy in time increment have been used. We have developed a finite element scheme of the second-order accuracy in time increment and obtained the best possible error estimate. This scheme is more robust than the first-order scheme with respect to numerical integration error and can solve flow problems more stably and accurately.2.We have developed a finite element scheme and established an error estimate for heat convection problems with temperature-dependent viscosity. The viscosity of heat conduction problems such as mantle convection in the Earth and melting glass convection in the furnace is strongly dependent on the temperature. … More The dependence plays an important role in die formation of convection patterns. Our scheme is applicable for the general Rayleigh-Benard problems with temperature-dependent viscosity, thermal conductivity, and thermal expansion coefficient. Using this scheme we have carried out large-scale numerical simulation of Earth's mantle convection in three-dimensional spherical shell and succeeded in obtaining complex heat convection patterns.3.In the infinite precision computation we have succeeded a large-scale parallel computation using a cluster of high-performance computers with 10CPU and 20GB memory. For one-dimensional boundary-value problems very precise results with precision 4995 digits have been obtained. We have used this system to perform direct numerical simulation of inverse problems and made possible a numerical analysis of inverse problems.4.Formulating eddy current problems in magnetic vector potential and electric scalar potential, we have solved them using a hierarchical domain decomposition method. This solution has been shown to be effective under the environment of parallel computation. By this method we have carried out large-scale numerical simulation of nonlinear static magnetic problems in magnetic vector potential. Less

1.在设计流动问题的数值格式时，如何逼近对流撕裂是一个关键问题。特征有限元近似是基于物质导数的近似，它是时间导数项和对流项的和。目前采用的是时间增量一阶精度特征法的有限元格式。我们建立了一种时间增量二阶精度的有限元格式，得到了可能的最佳误差估计。该格式在数值积分误差方面比一阶格式具有更强的鲁棒性，可以更稳定、更准确地求解流动问题。我们开发了一个有限元格式，并建立了一个误差估计的热对流问题的温度依赖粘度。地球上地幔对流和炉内熔融玻璃对流等热传导问题的黏性对温度有很强的依赖性。这种依赖关系在对流模式的模形形成中起着重要作用。我们的方案适用于具有温度依赖性粘度、导热系数和热膨胀系数的一般瑞利-贝纳德问题。利用该方案对三维球壳中地幔对流进行了大规模数值模拟，成功地获得了复杂的热对流模式。在无限精度计算中，我们成功地使用10CPU和20GB内存的高性能计算机集群进行了大规模并行计算。对于一维边值问题，得到了精度为4995位的非常精确的结果。利用该系统对反问题进行了直接的数值模拟，使反问题的数值分析成为可能。提出磁矢量势和电标量势中的涡流问题，用层次域分解方法求解。该方法在并行计算环境下是有效的。用该方法对磁矢量势下的非线性静磁问题进行了大规模数值模拟。少