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LopamudraChakravarty_Dissertation.pdf (1.9 MB)

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Scalable Hybrid Schwarz Domain Decomposition Algorithms to Solve Advection-Diffusion Problems

Chakravarty, Lopamudra
http://rave.ohiolink.edu/etdc/view?acc_num=kent1523325804305835

Abstract Details

2018, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
The solution of the linear system of algebraic equations that arise from the finite element discretization of the advection-diffusion equation is considered here. In this dissertation, we study three hybrid Schwarz domain decomposition algorithms to solve this non-symmetric problem. We use the GMRES and BiCGStab methods to solve the resulting preconditioned system. In each iteration step, we solve a coarse finite element problem and a number of local problems depending on the algorithm. Local problems are solved in non-overlapping subdomains and ring-shaped overlapping subdomains into which the original domain is subdivided. These three algorithms combine the advantages of additive and multiplicative methods. We show that these algorithms are scalable in the sense that the rate of convergence is independent of the mesh size and the number of subdomains. The performance of these algorithms in two dimensions is illustrated by numerical experiments.
Jing Li (Advisor)
Lothar Reichel (Committee Member)
Chuck Gartland (Committee Member)
Arden Ruttan (Committee Member)
Ye Zhao (Committee Member)
132 p.
Applied Mathematics
domain decomposition; hybrid algorithm; scalable algorithm; Schwarz algorithm; advection-diffusion equation; numerical analysis

Recommended Citations

Citations

  • Chakravarty, L. (2018). Scalable Hybrid Schwarz Domain Decomposition Algorithms to Solve Advection-Diffusion Problems [Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1523325804305835

    APA Style (7th edition)

  • Chakravarty, Lopamudra. Scalable Hybrid Schwarz Domain Decomposition Algorithms to Solve Advection-Diffusion Problems. 2018. Kent State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1523325804305835.

    MLA Style (8th edition)

  • Chakravarty, Lopamudra. "Scalable Hybrid Schwarz Domain Decomposition Algorithms to Solve Advection-Diffusion Problems." Doctoral dissertation, Kent State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=kent1523325804305835

    Chicago Manual of Style (17th edition)

kent1523325804305835
585
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This open access ETD is published by Kent State University and OhioLINK.