Work

Advances in implementation, theoretical motivation, and numerical results for the nested iteration with range decomposition algorithm

Year: 2018

Type: article

Abstract: Summary This paper studies a low‐communication algorithm for solving elliptic PDEs on high‐performance machines, the nested iteration with range decomposition (NIRD) algorithm. Previous work has shown that NIRD converges to a high level of accuracy within a small, fixed number of iterations (usually one or two) when applied to simple elliptic problems. This paper makes some improvements to the NIRD algorithm (including the addition of adaptivity during preprocessing, wider choice of partitioning functions, and modified error measurement) that enhance the method's accuracy and scalability, especially on more difficult problems. In addition, an updated convergence proof is presented based on heuristic assumptions that are supported by numerical evidence. Furthermore, a new performance model is developed that shows increased performance benefits for NIRD when problems are more expensive to solve using traditional methods. Finally, extensive testing on a variety of elliptic problems provides additional insight into the behavior of NIRD and additional evidence that NIRD achieves excellent convergence on a wide class of elliptic PDEs and, as such, should be a very competitive method for solving PDEs on large parallel computers.

Source: Numerical Linear Algebra with Applications

DOI: 10.1002/nla.2149

Authors: Wayne Mitchell, Tom Manteuffel

Institution: University of Colorado Boulder

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: U.S. Department of Energy, Lawrence Livermore National Laboratory

Awards: G1298209411, CENTER FOR EXASCALE RADIATION TRANSPORT (CERT), G5780540008