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You searched for +publisher:"King Abdullah University of Science and Technology" +contributor:("Huang, Jingfang"). One record found.

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King Abdullah University of Science and Technology

1. Chavez Chavez, Gustavo Ivan. Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2017, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/625172 

This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST's Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption. Advisors/Committee Members: Keyes, David E. (advisor), Moshkov, Mikhail (committee member), Ketcheson, David I. (committee member), Turkiyyah, George (committee member), Huang, Jingfang (committee member).

Subjects/Keywords: hierarchical matrices; cyclic reduction; fast solvers; Direct solvers; preconditioning; Parallel Computing

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Chavez Chavez, G. I. (2017). Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/625172

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Chavez Chavez, Gustavo Ivan. “Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations.” 2017. Thesis, King Abdullah University of Science and Technology. Accessed April 10, 2021. http://hdl.handle.net/10754/625172.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Chavez Chavez, Gustavo Ivan. “Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations.” 2017. Web. 10 Apr 2021.

Vancouver:

Chavez Chavez GI. Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2017. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/10754/625172.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chavez Chavez GI. Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations. [Thesis]. King Abdullah University of Science and Technology; 2017. Available from: http://hdl.handle.net/10754/625172

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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