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，我们研究了弹性裂纹问题的配方和数值分析。我们已经表明，Galerkin公式可以用一台PC分析数十万个DOF的三个维度问题。但是，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是不可取的。 1999年，我们开始使用Helmholtz方程进行调查，特别注意使用Wigner 3-J符号。然后，我们在2和3维弹性动力学中进行了FMM配方。与Galerkin的向量分别在2D或3D问题中要求4或6时，新开发的配方在2D问题中使用了2个多极矩，在3D问题中使用了4个。与较早提议的弹性动力FMM相比，这种改进使我们能够为弹性动力FMM开发更有效的实现。接下来，我们使用MPI和PC群集考虑了静态代码的并行化。已经证明了代码的可扩展性，并尝试了弹性动力学的扩展。我们最终根据拉普拉斯方程的指数扩展考虑了新的FMM。当问题的几何形状复杂时，发现新的配方比原始FMM更有效。