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.在设计流量问题的数值方案时，如何近似会议撕裂是一个关键点。特征有限元近似基于材料衍生物的近似值，这是时间导数项和会议项的总和。到目前为止，已经使用了一阶准确度的特征方法的有限元方案。我们已经开发了一个有限元方案，该方案的时间增量为二阶精度，并获得了最佳可能的误差估计。对于数值集成误差，该方案比一阶方案更强大，并且可以更稳定，准确地解决流量问题。2。我们已经开发了有限的元素方案，并确定了与温度依赖性粘度的热转换问题的误差估计值。热传导问题的粘度，例如地球上的地幔转换以及炉中熔化的玻璃转换很大程度上取决于温度。 …更多的依赖性在对话模式的模具形成中起着重要作用。我们的方案适用于与温度依赖性粘度，导热率和热膨胀系数有关的一般雷利 - 贝纳德问题。使用此方案，我们在三维球形外壳中对地球的地幔对话进行了大规模数值模拟，并成功地获得了复杂的热转换模式。3。在无限精确计算中，我们使用了一个具有10cpu和20GB内存的高性能计算机的大规模平行计算。对于一维边界值问题，已经获得了精确的4995位数字的精确结果。我们已经使用该系统对反问题进行直接的数值模拟，并使反向问题的数值分析成为可能。4。磁性矢量电位和电量表电位中的涡流问题，我们使用层次结构域分解方法解决了它们。在平行计算的环境下，该解决方案已被证明是有效的。通过这种方法，我们对磁性矢量电位中非线性静电问题进行了大规模数值模拟。较少的