报告时间：2023年8月30日下午14:00-15:00
报告地点：红瓦楼726
报告人：钱建良 教授（Michigan State University）
报告摘要：We present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media. For a computational domain discretized with $N_v$ discretization cells, the proposed algorithm first solves and tabulates the phase and HB coefficients via eikonal and transport equations with observation points and point sources located at the Chebyshev nodes using a set of much coarser computation grids, and then butterfly compresses the resulting HB interactions from all $N_v$ cell centers to each other. The overall CPU time and memory requirement scale as $O(N_v\log^2N_v)$ for any bounded 2D domains with arbitrary excitation sources. A direct extension of this scheme to bounded 3D domains yields an $O(N_v^{4/3})$ CPU complexity, which can be further reduced to quasi-linear complexities with proposed remedies. The scheme can also efficiently handle scattering problems involving inclusions in inhomogeneous media. Although the current construction of our HB integrator does not accommodate caustics, the resulting HB integrator itself can be applied to certain sources, such as concave-shaped sources, to produce caustic effects. Compared to finite-difference frequency-domain (FDFD) methods, the proposed HB integrator is free of numerical dispersion and requires fewer discretization points per wavelength.
报告人简介：钱建良，工业与应用数学密歇根中心主任，密歇根州立大学数学系和计算数学、科学和工程系双聘教授。主要研究兴趣是可计算微局部分析，高频波传播的快速算法，反问题，医学成像和地学成像。与一起开发了用于程函方程、 高频波传播、走时断层扫描和势场域反问题的快速算法。在包括Inverse Problems，SIAM J. Numer. Anal. ，SIAM J. Sci. Comput.等国际期刊上发表论文百余篇。
报告邀请人：江渝 教授