HODLR3D
A new class of hierarchical matrices for \(N\) body problems in three dimensions
V A Kandappan, Vaishnavi Gujjula and Sivaram Ambikasaran
Department of Mathematics, IIT Madras
Preprint Version of the HODLR3D article will be available soon..
HODLR3D Code
arXiv Version of the article on HODLR3D can be found below:
arXiv Version of the article of our previous work, HODLR2D can be found below:
Purpose
This page is mainly set up in light to provide a set of supplementary images that help understand the Theorem provided n the article. Also, this page serves as a one-stop place for the hierarchical low-rank structure HODLR3D.
Features
In the article,
- We proveTheorem the basis for building the new hierarchical matrix representation.
- We also illustrate numerically the scaling of ranks of different off-diagonal blocks.
- Based on the outcomes of Theorem and the numerical illustrations, we build the HODLR3D representation, wherein we only choose to compress the off-diagonal blocks corresponding to interactions between vertex sharing neighbours and well-separated boxes of the hierarchical tree, to achieve an almost linear complexity algorithm.
- We perform various numerical experiments to illustrate the performance of the HODLR3D matrix-vector product.