Parallel hierarchical linear solvers and fast multipole methods with applications
Abstract/Contents
- Abstract
- With the advent of modern ever more powerful supercomputers, it is desired to carry out existing numerical simulations faster and to larger scales. This thesis contributes to the goal with newly developed algorithms and their implementations using tools from both numerical analysis and parallel computing. The common theme behind all algorithms presented in this thesis is the so-called hierarchical-matrix theory (HMT), which states from a high-level perspective that discretization matrices of elliptic partial differential equations have low-rank off-diagonal blocks. The applications studied here include fluid/solid/structural mechanics, climate simulation and dislocation dynamics. The three main parts of this thesis are the following. The first part (chapter 2) presents a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. The second part (chapter 3) introduces a hierarchical solver for solving sparse ill-conditioned linear systems in parallel and its applications to ice sheet modeling. The third part (chapter 4) is about an algorithm commonly used in computational physics, namely, the fast multipole method (FMM), of which the HMT is an algebraic generalization. The application of FMM in dislocation dynamics simulations is also studied. In conclusion, this thesis presents (1) parallel hierarchical linear solvers with applications in ice sheet modeling, and (2) ``black-box'' FMMs with applications in dislocation dynamics.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2018; ©2018 |
| Publication date | 2018; 2018 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Chen, Chao |
|---|---|
| Degree supervisor | Darve, Eric |
| Thesis advisor | Darve, Eric |
| Thesis advisor | Poulson, Jack Lesly |
| Thesis advisor | Ying, Lexing |
| Degree committee member | Poulson, Jack Lesly |
| Degree committee member | Ying, Lexing |
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Chao Chen. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2018. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2018 by Chao Chen
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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