Transient elastic wave analysis of 3-D large-scale cavities by fast multipole BEM using implicit Runge-Kutta convolution quadrature
Transient elastic wave analysis of 3-D large-scale cavities by fast multipole BEM using implicit Runge-Kutta convolution quadrature
复制标题
使用隐式龙格-库塔卷积求积法通过快速多极边界元法对 3D 大型空腔进行瞬态弹性波分析
DOI：
10.1016/j.cma.2016.02.002
复制
发表时间：
2016
影响因子：
7.2
通讯作者：
and Sohichi Hirose
中科院分区：
文献类型：
--
作者：
Taizo Maruyama;Takahiro Saitoh;Tinh Quoc Bui;and Sohichi Hirose
现有的边界元方法（BEM）已被证明是有效的数值技术，特别是在模拟波传播问题，但仍然存在局限性，在解决大规模问题。主要缺点可能是由几个问题引起的，包括高成本和用于计算的大量计算机存储器。一个时域边界元法，其中的配置方法用于时间离散也显示数值不稳定的小CFL（Courant-Friedrichs-Lewy）数。在这项工作中，我们提出了一个新的三维（3-D）的方法来解决瞬态弹性波传播问题的大规模的球形和椭球形腔的快速多极方法（FMM）加速卷积求积边界元法使用隐式龙格库塔格式（简称为IRK-based CQ-FMBEM）。两个特殊的技术有关的FMM，包括修改的球面贝塞尔函数的缩放和截断方法被用来提高我们所提出的方法的效率和稳定性。该方法具有精度高、时间推进过程稳定、计算效率高等优点，特别适用于三维大规模问题。这些属性随后通过处理3-D单球形和椭球形腔和多个相等和不规则球形腔的大规模波动问题的数值例子来说明。本配方的准确性进行了验证，通过比较所得结果与文献中可用的参考解决方案。数值方面的时间增量，尺寸和拓扑形状的空腔，以及它们对变形和波形的影响进行了研究。此外，我们提出的方法，如CPU时间，所需的内存等的计算效率的详细调查。所有的实施任务都是使用东京技术进行的。这台超级计算机被称为TSUBAME 2.5 [42]。
Existing boundary element methods (BEMs) have been proven to be efficient numerical techniques particularly in modeling wave propagation problems but still remain limitations in solving large-scale problems. The main disadvantages may be caused by several problems, including high cost and large amount of computer memory for the computation. A time-domain BEM in which a collocation method is used for the time discretization also shows numerical instability for small CFL (Courant–Friedrichs–Lewy) number. In this work, we propose a new three-dimensional (3-D) approach for solving transient elastic wave propagation problems of large-scale spherical and spheroidal cavities by the convolution quadrature BEM accelerated by fast multipole method (FMM) using an implicit Runge–Kutta scheme (in abbreviation, we name it as IRK-based CQ-FMBEM). Two special techniques pertaining to the FMM including the scaling of modified spherical Bessel functions and the truncation method are used to enhance the efficiency and stability of our proposed method. This approach is found to be particularly suitable for 3-D large-scale problems as its high accuracy, stability of time-marching process, and computational efficiency. These properties are subsequently illustrated through numerical examples dealing with large-scale wave problems of 3-D single spherical and spheroidal cavities and multiple equally and irregularly spherical cavities. The accuracy of the present formulation is verified by comparing the obtained results with available reference solutions in the literature. Some numerical aspects of time increments, sizes and topological shapes of cavities, and their influences on the deformations and the waveforms are investigated. Also, detailed investigation of the computational efficiency of our proposed method, such as CPU time, required memory, etc. is presented. All the implementation tasks are carried out using the Tokyo Tech. supercomputer which is called TSUBAME 2.5 [42].