Multimethod Solvers: Algorithms, Application And Software

Open Access
Author:
Bhowmick, Sanjukta
Graduate Program:
Computer Science and Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
August 26, 2004
Committee Members:
  • Padma Raghavan, Committee Chair
  • Mahmut Taylan Kandemir, Committee Member
  • Lyle Norman Long, Committee Member
  • Lois Curfman Mc Innes, Committee Member
  • Paul Plassmann, Committee Member
  • Raj Acharya, Committee Member
Keywords:
  • Iterative Linear Solvers
  • High Reliability
  • Composite Solvers
  • Adaptive Solvers
Abstract:
The solution of large sparse linear systems is a fundamental problem in scientific computing. A variety of solution schemes are available reflecting a wide range of performance and quality trade-offs. The ``best' solution method can vary across application domains and often even across different phases in a single application. As noted by Ern et al. ``The impossibility of uniformly ranking linear system solvers in any order of effectiveness....is widely appreciated.' In this thesis, we attempt to deliver the benefits of the variety of sparse linear solution techniques to the application community, by developing multimethod solvers, i.e. solvers that use more than one basic sparse solution scheme. More specifically, the thesis concerns the development of two types of multimethod sparse linear solvers, namely, composite and adaptive solvers. We develop a composite solver to provide highly reliable solution with low memory requirements by applying a sequence of limited memory iterative solution schemes to the same linear system. We develop an adaptive solver to dynamically select a linear solution scheme to match changing linear system attributes and thus reduce the time required for linear system solution.