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PRECONDITIONERS FOR PDE-CONSTRAINED OPTIMIZATION PROBLEMS

Alqarni, Mohammed Zaidi A.
http://rave.ohiolink.edu/etdc/view?acc_num=kent1573148003180191

Abstract Details

2019, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Finding the solution for PDE-Constrained Optimization Problems can be accomplished in two ways: optimize-then-discretize and discretize-then-optimize. Both techniques lead to either a linear or non-linear system of equations. To obtain the optimal solution (to solve the system of equations), it's more practical to use numerical methods than analytical ones. Numerical methods can be direct or iterative. Generally, direct solvers tend to be more costly than iterative ones in terms of memory utilization and computational time. Moreover, they are less flexible in taking advantage of multiple processors in parallel computers than iterative methods. Preconditioners are essential for the performance of iterative methods. They are beneficial in diminishing the overall computational time as a reduction in iteration counts and ideally their computing cost. Over the past few decades, a stack of preconditioners has been developed. Here, we propose preconditioners that reduce both the number of iterations and the computational time for a specific type of PDE-Constrained Optimization problems, that is optimal control problems. Subsequently, for the sake of clarity, we apply those preconditioners to these problems.
Jing Li (Advisor)
Reichel Lothar (Committee Member)
Xiaoyu Zheng (Committee Member)
Qiang Guan (Committee Member)
Jong-Hoon Kim (Committee Member)
86 p.
Applied Mathematics; Mathematics
PRECONDITIONERS; PDE-CONSTRAINED OPTIMIZATION PROBLEMS; PDE; OVERLAPPING SCHWARZ; DOMAIN DECOMPOSITION; FEM

Recommended Citations

Citations

  • Alqarni, M. Z. A. (2019). PRECONDITIONERS FOR PDE-CONSTRAINED OPTIMIZATION PROBLEMS [Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1573148003180191

    APA Style (7th edition)

  • Alqarni, Mohammed. PRECONDITIONERS FOR PDE-CONSTRAINED OPTIMIZATION PROBLEMS. 2019. Kent State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1573148003180191.

    MLA Style (8th edition)

  • Alqarni, Mohammed. "PRECONDITIONERS FOR PDE-CONSTRAINED OPTIMIZATION PROBLEMS." Doctoral dissertation, Kent State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=kent1573148003180191

    Chicago Manual of Style (17th edition)

kent1573148003180191
409
© 2019, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.