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Integral Equation Methods for the He...

Wang, Jun.

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Integral Equation Methods for the Heat Equation in Moving Geometry.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Integral Equation Methods for the Heat Equation in Moving Geometry./
Author:	Wang, Jun.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2017,
Description:	109 p.
Notes:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:	Dissertation Abstracts International79-02B(E).
Subject:	Applied mathematics. -
Online resource:	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.
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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
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710 2 $a New York University. $b Mathematics. $3 1019424
773 0 $t Dissertation Abstracts International $g 79-02B(E).
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