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Direct and Line Based Iterative Methods for Solving Sparse Block Linear Systems

Yang, Xiaolin
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543921330763997

Abstract Details

2018, MS, University of Cincinnati, Engineering and Applied Science: Aerospace Engineering.
Solving sparse linear system of equations represents the major computation cost in many scientific and engineering areas. There are two major approaches for solving large sparse linear system: direct method and iterative method. Both methods have their own advantages for certain type of problem. In general, the direct method is more robust and the iterative method has better scalability. High-order Discontinuous Galerkin (DG) Method has gained growing interest in Computation Fluid Dynamics (CFD) community. The Jacobian matrices that arise in the application of the DG method are sparse and block-structured. This thesis summarizes the development of direct and iterative solvers for sparse block linear system. Block capability is achieved by using Intel CPU library or Nvidia GPU based libraries. The direct solver uses left-looking method with fill-reducing ordering to factorize the matrices into lower/upper triangular parts. The iterative solver uses line-based Successive Over-Relaxation method (SLOR) and Alternating Direction Implicit method (ADI), which exploit the characteristic of structured grid. The direct and iterative solvers are tested with matrices from the simulation of a flow channel using DG method. The grid dimension is 6×2×2. The results show that direct solver performs better on these small matrices. However, the iterative solver using ADI method demonstrates better scalability with respect to the degree of polynomial used in DG scheme. This work advances the development of linear solver for DG method.
Mark Turner, Sc.D. (Committee Chair)
Shaaban Abdallah, Ph.D. (Committee Member)
Donald French, Ph.D. (Committee Member)
72 p.
Engineering
sparse matrix; direct method; line-based iterative method; Discontinuous Galerkin Method

Recommended Citations

Citations

  • Yang, X. (2018). Direct and Line Based Iterative Methods for Solving Sparse Block Linear Systems [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543921330763997

    APA Style (7th edition)

  • Yang, Xiaolin. Direct and Line Based Iterative Methods for Solving Sparse Block Linear Systems. 2018. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543921330763997.

    MLA Style (8th edition)

  • Yang, Xiaolin. "Direct and Line Based Iterative Methods for Solving Sparse Block Linear Systems." Master's thesis, University of Cincinnati, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543921330763997

    Chicago Manual of Style (17th edition)

ucin1543921330763997
271
© 2018, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.