Distance descending ordering method: An O(n) algorithm for inverting the mass matrix in simulation of macromolecules with long branches

Xiankun Xu, Peiwen Li

Research output: Contribution to journalArticlepeer-review

Abstract

Fixman's work in 1974 and the follow-up studies have developed a method that can factorize the inverse of mass matrix into an arithmetic combination of three sparse matrices|one of them is positive definite and need to be further factorized by using the Cholesky decomposition or similar methods. When the molecule subjected to study is of serial chain structure, this method can achieve O(n) computational complexity. However, for molecules with long branches, Cholesky decomposition about the corresponding positive definite matrix will introduce massive fill-in due to its nonzero structure, which makes the calculation in scaling of O(n3). Although several methods have been used in factorizing the positive definite sparse matrices, no one could strictly guarantee for no fill-in for all molecules according to our test, and thus O(n) efficiency cannot be obtained by using these traditional methods. In this paper we present a new method that can guarantee for no fill-in in doing the Cholesky decomposition, and as a result, the inverting of mass matrix will remain the O(n) scaling, no matter the molecule structure has long branches or not.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Jun 29 2017

Keywords

  • Cholesky decomposition
  • Internal coordinates
  • Inverse of mass matrix
  • Molecular dynamics
  • Sparse matrix

ASJC Scopus subject areas

  • General

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