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Numerical studies on Helmholtz equat...

Li, Guangrui.

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Numerical studies on Helmholtz equation and traveling wave.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Numerical studies on Helmholtz equation and traveling wave./
Author:	Li, Guangrui.
Description:	89 p.
Notes:	Source: Dissertation Abstracts International, Volume: 71-01, Section: B, page: 0405.
Contained By:	Dissertation Abstracts International71-01B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NR55821
ISBN:	9780494558218

Numerical studies on Helmholtz equation and traveling wave.
Li, Guangrui.

Numerical studies on Helmholtz equation and traveling wave. - 89 p.

Source: Dissertation Abstracts International, Volume: 71-01, Section: B, page: 0405.

Thesis (Ph.D.)--University of Alberta (Canada), 2009.

Waves are interesting phenomena with important practical applications. A wave is a disturbance that propagates through space and time, usually with transference of energy. Physicists and engineers are interested in the reliable simulation of processes in which waves are scattered from obstacles.

ISBN: 9780494558218Subjects--Topical Terms:

1669109
Applied Mathematics.

Numerical studies on Helmholtz equation and traveling wave.
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008 130515s2009 ||||||||||||||||| ||eng d
020 $a 9780494558218
035 $a (UMI)AAINR55821
035 $a AAINR55821
040 $a UMI $c UMI
100 1 $a Li, Guangrui. $3 1669369
245 1 0 $a Numerical studies on Helmholtz equation and traveling wave.
300 $a 89 p.
500 $a Source: Dissertation Abstracts International, Volume: 71-01, Section: B, page: 0405.
502 $a Thesis (Ph.D.)--University of Alberta (Canada), 2009.
520 $a Waves are interesting phenomena with important practical applications. A wave is a disturbance that propagates through space and time, usually with transference of energy. Physicists and engineers are interested in the reliable simulation of processes in which waves are scattered from obstacles.
520 $a In the Part I, we deal with the linear mathematical models for wave propagation and scattering. Assuming time-harmonic behavior, the model becomes the helmholtz equation Du+k2u=0, where k, the wave number, is a physical parameter. My interest will be mainly in the numerical computation for the Helmholtz problem, including designing the novel finite difference schemes and efficient linear solvers.
520 $a In the Part II, we put the focus on the travelling wavefront, which can be treated as biological wave. For the population of a single species with age-structure, it is described as the time delayed reaction-diffusion partial differential equation 6v6t=d6 2v6x2+ae -gtvx,t-t -bv2. By using the weighted-energy method and comparison principle, the nonlinear stability is achieved with the initial perturbation decaying to zero exponentially. The exponential convergent rate (in time) of the solution is obtained. Numerical simulations are carried out to confirm the theoretical results, and the traveling wavefronts with a large delay term in the model are reported.
520 $a The conclusions and future works are given in the Part III.
590 $a School code: 0351.
650 4 $a Applied Mathematics. $3 1669109
690 $a 0364
710 2 $a University of Alberta (Canada). $3 626651
773 0 $t Dissertation Abstracts International $g 71-01B.
790 $a 0351
791 $a Ph.D.
792 $a 2009
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NR55821