東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Integral Equation Methods for the He...

Wang, Jun.

FindBook

Google Book

Amazon

博客來

Integral Equation Methods for the Heat Equation in Moving Geometry.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Integral Equation Methods for the Heat Equation in Moving Geometry./
作者:	Wang, Jun.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2017,
面頁冊數:	109 p.
附註:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:	Dissertation Abstracts International79-02B(E).
標題:	Applied mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10618746
ISBN:	9780355407624

Integral Equation Methods for the Heat Equation in Moving Geometry.
Wang, Jun.

Integral Equation Methods for the Heat Equation in Moving Geometry. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 109 p.

Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.

Thesis (Ph.D.)--New York University, 2017.

Many problems in physics and engineering require the solution of the heat equation in moving geometry. Integral representations are particularly appropriate in this setting since they satisfy the governing equation automatically and, in the homogeneous case, require the discretization of the space-time boundary alone. Unlike methods based on direct discretization of the partial differential equation, they are unconditonally stable. Moreover, while a naive implementation of this approach is impractical, several efforts have been made over the past few years to reduce the overall computational cost. Of particular note are Fourier-based methods which achieve optimal complexity so long as the time step Deltat is of the same order as Deltax, the mesh size in the spatial variables. As the time step goes to zero, however, the cost of the Fourier-based fast algorithms grows without bound. A second difficulty with existing schemes has been the lack of efficient, high-order local-in-time quadratures for layer heat potentials.

ISBN: 9780355407624Subjects--Topical Terms:

2122814
Applied mathematics.

Integral Equation Methods for the Heat Equation in Moving Geometry.
LDR:02539nmm a2200325 4500 001 2155530
005 20180426091049.5
008 190424s2017 ||||||||||||||||| ||eng d
020 $a 9780355407624
035 $a (MiAaPQ)AAI10618746
035 $a (MiAaPQ)nyu:13077
035 $a AAI10618746
040 $a MiAaPQ $c MiAaPQ
100 1 $a Wang, Jun. $3 892864
245 1 0 $a Integral Equation Methods for the Heat Equation in Moving Geometry.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2017
300 $a 109 p.
500 $a Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
500 $a Adviser: Leslie F. Greengard.
502 $a Thesis (Ph.D.)--New York University, 2017.
520 $a Many problems in physics and engineering require the solution of the heat equation in moving geometry. Integral representations are particularly appropriate in this setting since they satisfy the governing equation automatically and, in the homogeneous case, require the discretization of the space-time boundary alone. Unlike methods based on direct discretization of the partial differential equation, they are unconditonally stable. Moreover, while a naive implementation of this approach is impractical, several efforts have been made over the past few years to reduce the overall computational cost. Of particular note are Fourier-based methods which achieve optimal complexity so long as the time step Deltat is of the same order as Deltax, the mesh size in the spatial variables. As the time step goes to zero, however, the cost of the Fourier-based fast algorithms grows without bound. A second difficulty with existing schemes has been the lack of efficient, high-order local-in-time quadratures for layer heat potentials.
520 $a In this dissertation, we present a new method for evaluating heat potentials that makes use of a spatially adaptive mesh instead of a Fourier series, a new version of the fast Gauss transform, and a new hybrid asymptotic/numerical method for local-in-time quadrature. The method is robust and efficient for any Deltat, with essentially optimal computational complexity. We demonstrate its performance with numerical examples and discuss its implications for subsequent work in diffusion, heat flow, solidification and fluid dynamics.
590 $a School code: 0146.
650 4 $a Applied mathematics. $3 2122814
650 4 $a Mathematics. $3 515831
650 4 $a Computer science. $3 523869
690 $a 0364
690 $a 0405
690 $a 0984
710 2 $a New York University. $b Mathematics. $3 1019424
773 0 $t Dissertation Abstracts International $g 79-02B(E).
790 $a 0146
791 $a Ph.D.
792 $a 2017
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10618746