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Parallel ILU Preconditioning for Structured Grid Matrices

Eisenlohr, John Merrick

Abstract Details

2015, Master of Science, Ohio State University, Computer Science and Engineering.
Many scientific simulation codes represent physical systems by storing data at a set of discrete points. For example, a weather modeling software application may store data representing temperature, wind velocity, air pressure, humidity, etc. at a set of points in the atmosphere over a portion of the Earth's surface. Similarly, Computational Fluid Dynamics (CFD) software stores data representing fluid velocity, pressure, etc. at discrete points in the domain of the particular problem being solved. In many simulations, this set of discrete points is a structured grid; i.e., a finite n-dimensional regular lattice. One of the most important steps in many scientific simulations is the solution of a system of linear equations, where the unknowns of the system correspond to data elements at each of the discrete points used to model the system. If the simulation is based on a structured grid, this linear system will often have a special structure itself, and this structure may lead to more efficient techniques for solving the system than can be used for general sparse linear systems. Scientific simulations most often use an iterative technique such as the Conjugate Gradient Method or GMRES for solving linear systems.. It is well known that these iterative techniques converge much more quickly if a preconditioner is used. The ILU, or Incomplete LU Factorization, preconditioner is a good choice but it is not parallelizable is a straightforward way. This thesis examines techniques for parallelizing the application of the ILU preconditioner to linear systems arising from scientific simulations on structured grids. Various techniques are tested and timing results are recorded for different types and sizes of linear systems on structured grids.
P Sadayappan (Advisor)
Atanas Rountev (Committee Member)
65 p.

Recommended Citations

Citations

  • Eisenlohr, J. M. (2015). Parallel ILU Preconditioning for Structured Grid Matrices [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429820221

    APA Style (7th edition)

  • Eisenlohr, John. Parallel ILU Preconditioning for Structured Grid Matrices. 2015. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1429820221.

    MLA Style (8th edition)

  • Eisenlohr, John. "Parallel ILU Preconditioning for Structured Grid Matrices." Master's thesis, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429820221

    Chicago Manual of Style (17th edition)