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Integral Equation Methods for the Heat Equation in Moving Geometry.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Integral Equation Methods for the Heat Equation in Moving Geometry./
Author:	Wang, Jun.
Description:	1 online resource (109 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:	Dissertation Abstracts International79-02B(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355407624

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

Integral Equation Methods for the Heat Equation in Moving Geometry. - 1 online resource (109 pages)

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

Thesis (Ph.D.)

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355407624Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

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.
264 0 $c 2017
300 $a 1 online resource (109 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
500 $a Adviser: Leslie F. Greengard.
502 $a Thesis (Ph.D.) $c New York University $d 2017.
504 $a Includes bibliographical references
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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
650 4 $a Mathematics. $3 527692
650 4 $a Computer science. $3 573171
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
690 $a 0405
690 $a 0984
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a New York University. $b Mathematics. $3 1180487
773 0 $t Dissertation Abstracts International $g 79-02B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10618746 $z click for full text (PQDT)