含大量缺陷的多层介质中弹性波传播的奇异边界法研究

Numerical modeling of elastic wave propagation has extensive applications in a broad fields of sciences and engineering, such as aseismic structures design and nondestructive testing. For simulating 3D elastic wave propagation in multilayer media containing multiple defects, e.g., holes, cracks, inclusions, the traditional numerical techniques often encounter such bottleneck problems as a quadratic growth of computational complexity with increasing number of defects, numerical calculation of complex singular or nearly-singular integrals and computational instability of ill-conditioned dense matrix. In recent five years, the applicant has published 15 SCI-indexed journal papers and given 7 international conference presentations on the research areas of boundary meshless methods and numerical simulation of wave propagation. Based on these studies, this proposal is aimed at developing the semi-analytical singular boundary method (SBM), which is easy-to-program, meshless and integration-free. We will investigate the new numerical technique for eliminating the singularity of the fundamental solution of the elastic wave equation at origin, which avoids the numerical calculation of the singular and nearly-singular integrals. This study makes first attemp to apply the SBM to elastic wave propagation. In particular, we will introduce fast multipole methods and precorrected fast Fourier transform to reduce the computational complexity with respect to number of defects from quadratic to linear growth, then investigate preconditioned matrixs and dual iterative techniques to accelerate the converging speed of iterative solvers for the coupled matrix of multilayer problems. Our computational model will be efficient for the elastic wave problems of size up to N=O(10^6) DOFs (degrees of freedom). The purpose of this proposal is to establish a high-performance numerical technique for large-scale elastic wave propagation in complex media to meet growing demands in such important fields as aseismic structures design and nondestructive testing.

弹性波传播数值模拟在结构抗震设计和材料无损检测等领域有着广泛应用。传统数值方法在模拟含大量缺陷(孔洞裂纹夹杂等)的三维多层复杂介质弹性波传播时常遇到计算复杂度随缺陷数量呈平方增长、奇异与近奇异积分计算复杂和病态稠密矩阵计算不稳定等瓶颈。基于申请者近五年的研究工作(15篇SCI论文及7个国际会议报告)，本项目拟发展易于使用、无网格、无数值积分的半解析奇异边界法，研究消除弹性波方程基本解源点奇异性的新数值技术，避免奇异与近奇异积分计算，将奇异边界法首次应用于弹性波传播；引入快速多极子法和预校正傅里叶变换技术，将计算复杂度与缺陷数量的关系从平方增长降低为线性增长；研究预处理矩阵和双重迭代技术，加快多层介质耦合矩阵迭代收敛速度，快速有效求解上百万自由度的弹性波问题。本项目的目标是建立一类模拟大规模复杂介质弹性波传播的高性能数值方法，以满足结构抗震设计和材料无损检测等领域日益增长的应用需求。

弹性波传播数值模拟在结构抗震设计和材料无损检测等领域有着广泛应用。传统数值方法在模拟含大量缺陷(孔洞裂纹夹杂等)的三维多层复杂介质弹性波传播时常遇到计算复杂度随缺陷数量呈平方增长、奇异与近奇异积分计算复杂和病态稠密矩阵计算不稳定等瓶颈。本项目发展精确求解三维弹性波方程源点强度因子的数值技术，将奇异边界法首次应用于弹性波传播；引入快速多极子法和快速傅里叶变换技术，将计算复杂度与缺陷数量的关系从平方增长降低为线性增长，实现上百万自由度的弹性波传播数值模拟；研究预处理矩阵和双重迭代技术，加快多层介质耦合矩阵迭代收敛速度；同时开发基于Matlab的计算波传播数值软件包。成果方面，团队成员基于上述研究内容，发表了学术论文17篇，其中SCI检索论文15篇,合作出版一本中文学术专著，成功申请国家授权软件著作权3项，获得2016年度江苏省高等学校科学技术奖-自然科学奖三等奖和2016年度“江苏力学科学技术奖”一等奖。人才培养方面，依托项目培养了博士研究生5名，硕士研究生2名，其中3名研究生已顺利获得博士学位、1名研究生已顺利获得硕士学位。本项目也极大地促进了项目组成员的学术交流，举办1次小型学术研讨会，组织2次专题研讨会，参加国内外学术会议并做学术报告14次，出国访学4人次、合作来访9人次。综上所述，项目在含大量缺陷的多层介质中弹性波传播的奇异边界法研究方面达到了预期目标，促进了科研团队的发展，培养了科研人才。

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