A Framework for Grid Solvers

The design and implementation of an object-oriented framework for grid solvers is presented. Unlike conventional sparse solvers, a grid solver solves the sparse linear system embedded in a computational grid without creating the sparse matrix explicitly at any stage of the solution process. This allows it to take advantage of additional information about the problem that is available within the grid data structure. Such an approach leads to an optimal parallel algorithm for matrix reordering by cartesian nested dissection. It also facilitates the efficient computation of the elimination tree and factorization of the sparse system by the multi-frontal method in a high-performance computing environment. In addition, it enables the construction of a structural preconditioner that is highly effective in accelerating the rates of convergence of iterative methods. The problem of non-universality of grid data structures is addressed by designing and implementing the grid solver as an object-oriented framework that can be used by a wide variety of applications through instantiation and customization. Such a framework can encompass diverse grid representations in different spatial dimensions without any loss of functionality.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Vidwans, Akhil Jayant

Contributors dc:contributor

• Heath, Michael T.

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9953169

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/81967