Performance of iterative algorithms for the solution of the shallow-water equations

Manuel Gonzalez, Manuel Espino, Santiago Chumbe, Marc Garcia, Agustin Sanchez-Arcilla

Research output: Contribution to conferencePaper

Abstract

We discuss the performance of iterative solution methods implemented in a 3D model of the shallow water equations used to simulate the propagation of tidal waves in stratified ocean domains. The model uses a harmonic approach by means of which the transient problem is transformed into a number of steady-state nonlinear problems (one per each tidal frequency considered). For the vertical interpolation of the model variables, a spectral decomposition in terms of an orthogonal set of basis functions is applied. A Picard iteration is used to solve the nonlinear systems of equations, and a preconditioned conjugate gradient method is used to solve the intermediate linear systems. We report 3D numerical results of the tidal circulation in the Strait of Gibraltar, and we compare the performance of different conjugate gradient methods implemented in the model with the performance obtained with classical direct methods.
Original languageEnglish
Pages381-386
Publication statusPublished - 8 Jan 1998
Event10th International Conference on Finite Elements in Fluids - Tucson, United States
Duration: 5 Jan 19988 Jan 1998

Conference

Conference10th International Conference on Finite Elements in Fluids
CountryUnited States
CityTucson
Period5/01/988/01/98

Fingerprint

shallow-water equation
interpolation
strait
decomposition
method
ocean

Keywords

  • OCEAN DYNAMICS
  • ITERATIVE SOLUTION
  • ; THREE DIMENSIONAL MODELS; WAVE PROPAGATION; TIDES; CONJUGATE GRADIENT METHOD; NONLINEAR EQUATIONS
  • INTERPOLATION
  • ALGORITHMS

Cite this

Gonzalez, M., Espino, M., Chumbe, S., Garcia, M., & Sanchez-Arcilla, A. (1998). Performance of iterative algorithms for the solution of the shallow-water equations. 381-386. Paper presented at 10th International Conference on Finite Elements in Fluids, Tucson, United States.
Gonzalez, Manuel ; Espino, Manuel ; Chumbe, Santiago ; Garcia, Marc ; Sanchez-Arcilla, Agustin. / Performance of iterative algorithms for the solution of the shallow-water equations. Paper presented at 10th International Conference on Finite Elements in Fluids, Tucson, United States.
@conference{a340b492c7834c42a602b819b50fdbf5,
title = "Performance of iterative algorithms for the solution of the shallow-water equations",
abstract = "We discuss the performance of iterative solution methods implemented in a 3D model of the shallow water equations used to simulate the propagation of tidal waves in stratified ocean domains. The model uses a harmonic approach by means of which the transient problem is transformed into a number of steady-state nonlinear problems (one per each tidal frequency considered). For the vertical interpolation of the model variables, a spectral decomposition in terms of an orthogonal set of basis functions is applied. A Picard iteration is used to solve the nonlinear systems of equations, and a preconditioned conjugate gradient method is used to solve the intermediate linear systems. We report 3D numerical results of the tidal circulation in the Strait of Gibraltar, and we compare the performance of different conjugate gradient methods implemented in the model with the performance obtained with classical direct methods.",
keywords = "OCEAN DYNAMICS, ITERATIVE SOLUTION, ; THREE DIMENSIONAL MODELS; WAVE PROPAGATION; TIDES; CONJUGATE GRADIENT METHOD; NONLINEAR EQUATIONS , INTERPOLATION, ALGORITHMS",
author = "Manuel Gonzalez and Manuel Espino and Santiago Chumbe and Marc Garcia and Agustin Sanchez-Arcilla",
note = "http://md1.csa.com/partners/viewrecord.php?requester=gs&collection=TRD&recid=A9821877AH&q=&uid=791800457&setcookie=yes link doesn't work; 10th International Conference on Finite Elements in Fluids ; Conference date: 05-01-1998 Through 08-01-1998",
year = "1998",
month = "1",
day = "8",
language = "English",
pages = "381--386",

}

Gonzalez, M, Espino, M, Chumbe, S, Garcia, M & Sanchez-Arcilla, A 1998, 'Performance of iterative algorithms for the solution of the shallow-water equations', Paper presented at 10th International Conference on Finite Elements in Fluids, Tucson, United States, 5/01/98 - 8/01/98 pp. 381-386.

Performance of iterative algorithms for the solution of the shallow-water equations. / Gonzalez, Manuel; Espino, Manuel; Chumbe, Santiago; Garcia, Marc; Sanchez-Arcilla, Agustin.

1998. 381-386 Paper presented at 10th International Conference on Finite Elements in Fluids, Tucson, United States.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Performance of iterative algorithms for the solution of the shallow-water equations

AU - Gonzalez, Manuel

AU - Espino, Manuel

AU - Chumbe, Santiago

AU - Garcia, Marc

AU - Sanchez-Arcilla, Agustin

N1 - http://md1.csa.com/partners/viewrecord.php?requester=gs&collection=TRD&recid=A9821877AH&q=&uid=791800457&setcookie=yes link doesn't work

PY - 1998/1/8

Y1 - 1998/1/8

N2 - We discuss the performance of iterative solution methods implemented in a 3D model of the shallow water equations used to simulate the propagation of tidal waves in stratified ocean domains. The model uses a harmonic approach by means of which the transient problem is transformed into a number of steady-state nonlinear problems (one per each tidal frequency considered). For the vertical interpolation of the model variables, a spectral decomposition in terms of an orthogonal set of basis functions is applied. A Picard iteration is used to solve the nonlinear systems of equations, and a preconditioned conjugate gradient method is used to solve the intermediate linear systems. We report 3D numerical results of the tidal circulation in the Strait of Gibraltar, and we compare the performance of different conjugate gradient methods implemented in the model with the performance obtained with classical direct methods.

AB - We discuss the performance of iterative solution methods implemented in a 3D model of the shallow water equations used to simulate the propagation of tidal waves in stratified ocean domains. The model uses a harmonic approach by means of which the transient problem is transformed into a number of steady-state nonlinear problems (one per each tidal frequency considered). For the vertical interpolation of the model variables, a spectral decomposition in terms of an orthogonal set of basis functions is applied. A Picard iteration is used to solve the nonlinear systems of equations, and a preconditioned conjugate gradient method is used to solve the intermediate linear systems. We report 3D numerical results of the tidal circulation in the Strait of Gibraltar, and we compare the performance of different conjugate gradient methods implemented in the model with the performance obtained with classical direct methods.

KW - OCEAN DYNAMICS

KW - ITERATIVE SOLUTION

KW - ; THREE DIMENSIONAL MODELS; WAVE PROPAGATION; TIDES; CONJUGATE GRADIENT METHOD; NONLINEAR EQUATIONS

KW - INTERPOLATION

KW - ALGORITHMS

M3 - Paper

SP - 381

EP - 386

ER -

Gonzalez M, Espino M, Chumbe S, Garcia M, Sanchez-Arcilla A. Performance of iterative algorithms for the solution of the shallow-water equations. 1998. Paper presented at 10th International Conference on Finite Elements in Fluids, Tucson, United States.