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Study on the numerical solution of huge boundary value problems in earthquake engineering

地震工程巨边值问题数值求解研究

基本信息

批准号：
10450168
负责人：
NISHIMURA Naoshi
金额：
$ 3.58万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10450168/
关键词：
BIEM BEM FMM elastic wave seismic wave crack fast methods 境界積分方程式法多重極弾性積分方程式波動

项目摘要

In 1998 we have investigated formulations and numerical analyses for elastostatic crack problems. We have shown that a Galerkin formulation allows analyses of three dimensional problems with several hundreds of thousands of DOF with one PC. We have found, however, that the use of the diagonal form originally planned for elastodynamics is not desirable from the point of view of the accuracy. In 1999, we started the investigation with the Helmholtz equation, paying particular attention to the use of the Wigner 3-j symbols. We then proceeded to the FMM formulations in 2 and 3 dimensional elastodynamics. The newly developed formulation uses 2 multipole moments in 2D problems, and 4 in 3D problems, in contrast to the approach with Galerkin's vector which calls for 4 or 6 moments in 2D or 3D problems, respectively. This improvement enabled us to develop more efficient implementations for the elastodynamic FMM, both in 2D and 3D, compared to those proposed earlier. We next considered the parallelisation of the code in statics, using MPI and a PC cluster. The scalability of the code has been proved, and the extension to elastodynamics was attempted. We finally considered the new FMM based on the exponential expansion for Laplace's equation. The new formulation was found to be more efficient than the original FMM when the geometry of the problem is complicated.

1998 年，我们研究了弹性静力裂纹问题的公式和数值分析。我们已经证明，伽辽金公式允许用一台 PC 分析具有数十万个自由度的三维问题。然而，我们发现，从准确性的角度来看，最初计划用于弹性动力学的对角线形式的使用并不可取。 1999年，我们开始对亥姆霍兹方程进行研究，特别关注维格纳3-j符号的使用。然后我们继续研究 2 维和 3 维弹性动力学中的 FMM 公式。新开发的公式在 2D 问题中使用 2 个多极矩，在 3D 问题中使用 4 个多极矩，而伽辽金矢量方法在 2D 或 3D 问题中分别需要 4 个或 6 个多极矩。与之前提出的方案相比，这一改进使我们能够在 2D 和 3D 中开发更高效的弹性动力学 FMM 实现。接下来我们考虑使用 MPI 和 PC 集群来实现静态代码的并行化。代码的可扩展性已被证明，并尝试了弹性动力学的扩展。我们最终考虑了基于拉普拉斯方程指数展开的新 FMM。当问题的几何形状复杂时，新的公式被发现比原始的 FMM 更有效。