A fast algorithm for particle simulations
Journal of Computational Physics
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
The fast multipole method: numerical implementation
Journal of Computational Physics
Fast and Efficient Algorithms in Computational Electromagnetics
Fast and Efficient Algorithms in Computational Electromagnetics
The Fast Illinois Solver Code: Requirements and Scaling Properties
IEEE Computational Science & Engineering
A Prescription for the Multilevel Helmholtz FMM
IEEE Computational Science & Engineering
Computing in Science and Engineering
A study of mlfma for large-scale scattering problems
A study of mlfma for large-scale scattering problems
Nyström method for elastic wave scattering by three-dimensional obstacles
Journal of Computational Physics
Efficiency improvement of the frequency-domain BEM for rapid transient elastodynamic analysis
Computational Mechanics
A fast and high-order method for the three-dimensional elastic wave scattering problem
Journal of Computational Physics
Hi-index | 31.45 |
Multilevel fast multipole algorithm (MLFMA) is developed for solving elastic wave scattering by large three-dimensional (3D) objects. Since the governing set of boundary integral equations (BIE) for the problem includes both compressional and shear waves with different wave numbers in one medium, the double-tree structure for each medium is used in the MLFMA implementation. When both the object and surrounding media are elastic, four wave numbers in total and thus four FMA trees are involved. We employ Nystrom method to discretize the BIE and generate the corresponding matrix equation. The MLFMA is used to accelerate the solution process by reducing the complexity of matrix-vector product from O(N^2) to O(NlogN) in iterative solvers. The multiple-tree structure differs from the single-tree frame in electromagnetics (EM) and acoustics, and greatly complicates the MLFMA implementation due to the different definitions for well-separated groups in different FMA trees. Our Nystrom method has made use of the cancellation of leading terms in the series expansion of integral kernels to handle hyper singularities in near terms. This feature is kept in the MLFMA by seeking the common near patches in different FMA trees and treating the involved near terms synergistically. Due to the high cost of the multiple-tree structure, our numerical examples show that we can only solve the elastic wave scattering problems with 0.3-0.4 millions of unknowns on our Dell Precision 690 workstation using one core.