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Efficient and robust solvers for Mon...

Chen, Ye.

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Efficient and robust solvers for Monge-Ampere equations.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Efficient and robust solvers for Monge-Ampere equations./
Author:	Chen, Ye.
Description:	119 p.
Notes:	Source: Dissertation Abstracts International, Volume: 71-03, Section: B, page: 1788.
Contained By:	Dissertation Abstracts International71-03B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3401445
ISBN:	9781109682793

Efficient and robust solvers for Monge-Ampere equations.
Chen, Ye.

Efficient and robust solvers for Monge-Ampere equations. - 119 p.

Source: Dissertation Abstracts International, Volume: 71-03, Section: B, page: 1788.

Thesis (Ph.D.)--Clarkson University, 2009.

Efficient and robust multigrid method solvers have been developed for Monge-Ampere equations (MAEs), which are second-order nonlinear partial differential equations. The two principal MAEs studied in this dissertation come from atmospheric dynamics.

ISBN: 9781109682793Subjects--Topical Terms:

1669109
Applied Mathematics.

Efficient and robust solvers for Monge-Ampere equations.
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020 $a 9781109682793
035 $a (UMI)AAI3401445
035 $a AAI3401445
040 $a UMI $c UMI
100 1 $a Chen, Ye. $3 626641
245 1 0 $a Efficient and robust solvers for Monge-Ampere equations.
300 $a 119 p.
500 $a Source: Dissertation Abstracts International, Volume: 71-03, Section: B, page: 1788.
500 $a Adviser: Scott R. Fulton.
502 $a Thesis (Ph.D.)--Clarkson University, 2009.
520 $a Efficient and robust multigrid method solvers have been developed for Monge-Ampere equations (MAEs), which are second-order nonlinear partial differential equations. The two principal MAEs studied in this dissertation come from atmospheric dynamics.
520 $a Five specific compact discretizations are investigated for a simple MAE. By doing truncation error analysis and local Fourier analysis, the optimal discretization is chosen. It is shown that there is no fourth-order compact discretization for MAEs. To solve MAEs to fourth-order accuracy, tau-extrapolation is applied.
520 $a The semigeostrophic model (for atmospheric flows with an approximate balance between the wind and mass fields) includes a MAE. For this problem we reproduced results of a previous study by Fulton. In addition, alternate discretizations are applied, and fourth-order accuracy is obtained by using tau-extrapolation.
520 $a The balanced vortex model (for circularly symmetric balanced atmospheric flows) includes a more complicated MAE. The forcing for this problem depends on time; at larger times the forcing is stronger, making the problem more nonlinear and harder to solve. The continuation method is used. The continuation method divides the time into a series of times. At each time the problem is solved on the desired grid, and the final solution is used as the initial approximation for the next time, which will make the method very expensive. The full multigrid method is efficient and cheap, but it cannot solve the problem at a large time. A combination of the continuation and full multigrid methods (C-FMG method) is designed. Two versions of the C-FMG methods have been developed. One is partially adaptive and the other is fully adaptive. Numerical results demonstrate that the fully adaptive C-FMG method is efficient and robust.
590 $a School code: 0049.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Atmospheric Sciences. $3 1019179
690 $a 0364
690 $a 0725
710 2 $a Clarkson University. $3 1020943
773 0 $t Dissertation Abstracts International $g 71-03B.
790 1 0 $a Fulton, Scott R., $e advisor
790 $a 0049
791 $a Ph.D.
792 $a 2009
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3401445