A Hierarchical O(N) Force Calculation Algorithm

This article deals with the solution of integral equations using collocation methods with almost linear complexity. Methods such as fast multipole, panel clustering and H-matrix methods gain their efficiency from approximating the kernel function. The proposed algorithm which uses the H-matrix format, in contrast, is purely algebraic and relies on a small part of the collocation matrix for its blockwise approximation by low-rank matrices. Furthermore, a new algorithm for matrix partitioning that significantly reduces the number of blocks generated is presented.

/pdf/adaptive-low-rank-approximation-of-collocation-matrices-508qkfl7eu.pdf

Adaptive low-rank approximation of collocation matrices

https://repository.upenn.edu/cgi/viewcontent.cgi?article=1001&context=meam_papers

A kernel-independent adaptive fast multipole algorithm in two and three dimensions

Fast multipole accelerated boundary integral equation methods

1. Introduction 2. Conventional BEM for potential problems 3. Fast multipole BEM for potential problems 4. Elastostatic problems 5. Stokes flow problems 6. Acoustic wave problems.

/pdf/fast-multipole-boundary-element-method-theory-and-41w29r2035.pdf

H. Cheng

Papers

Regular Article: A Fast Adaptive Multipole Algorithm in Three Dimensions