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

C++

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.