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Random Sampling Algorithms for Multiscale Partial Differential Equations
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Random Sampling Algorithms for Multiscale Partial Differential Equations. |
| 개인저자 | Chen, Ke. |
| 단체저자명 | The University of Wisconsin - Madison. Mathematics. |
| 발행사항 | [S.l.]: The University of Wisconsin - Madison., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 163 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-02B. Dissertation Abstract International |
| ISBN | 9781085673051 |
| 학위논문주기 | Thesis (Ph.D.)--The University of Wisconsin - Madison, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
Advisor: Li, Qin. |
| 이용제한사항 | This item must not be sold to any third party vendors.This item must not be added to any third party search indexes. |
| 요약 | In this dissertation, we present a general framework to solve linear multiscale partial differential equations (PDEs) and demonstrate our numerical methods in two examples: elliptic equations with rough media and radiative transfer equations in various limiting regimes.Numerical computation for multiscale problems is challenging due to the large degrees of freedom stemmed from their fine scale nature. The link between the fine scale and the coarse scale description of these multiscale problems is often employed to relax the computation restriction. Unfortunately, such link is only available for certain scenarios and usually hard to derive in most cases. Delicate analysis and expensive computation are usually needed to identify the coarse model from the fine model.Randomized sampling, originally from the data science, is an efficient strategy to find low rank structure of a matrix based on a small number of samplings. By integrating this idea into the domain decomposition framework, we propose both randomized direct and iterative solvers for multiscale PDEs. In particular, we perform a model reduction of multiscale PDEs through offline computations with random inputs, and use the low rank structures to compute multiscale PDEs in the online stage. Our algorithms are efficient, easy to implement and does not rely on detailed analytic understanding of the multiscale PDEs. A criterion to analyze and compare different random sampling strategies is provided at the end. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
