search query: @supervisor Eirola, Timo / total: 16
reference: 5 / 16
« previous | next »
Author:Koskela, Antti Herman
Title:Structure preserving Krylov integrators for Hamiltonian systems
Rakenteen säilyttäviä Krylov-integroijia Hamiltonin systeemeille
Publication type:Master's thesis
Publication year:2010
Pages:vi + 70      Language:   eng
Department/School:Informaatio- ja luonnontieteiden tiedekunta
Main subject:Matematiikka   (Mat-1)
Supervisor:Eirola, Timo
Instructor:
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
Instructions

Reading digital theses in the closed network of the Aalto University Harald Herlin Learning Centre

In the closed network of Learning Centre you can read digital and digitized theses not available in the open network.

The Learning Centre contact details and opening hours: https://learningcentre.aalto.fi/en/harald-herlin-learning-centre/

You can read theses on the Learning Centre customer computers, which are available on all floors.

Logging on to the customer computers

  • Aalto University staff members log on to the customer computer using the Aalto username and password.
  • Other customers log on using a shared username and password.

Opening a thesis

  • On the desktop of the customer computers, you will find an icon titled:

    Aalto Thesis Database

  • Click on the icon to search for and open the thesis you are looking for from Aaltodoc database. You can find the thesis file by clicking the link on the OEV or OEVS field.

Reading the thesis

  • You can either print the thesis or read it on the customer computer screen.
  • You cannot save the thesis file on a flash drive or email it.
  • You cannot copy text or images from the file.
  • You cannot edit the file.

Printing the thesis

  • You can print the thesis for your personal study or research use.
  • Aalto University students and staff members may print black-and-white prints on the PrintingPoint devices when using the computer with personal Aalto username and password. Color printing is possible using the printer u90203-psc3, which is located near the customer service. Color printing is subject to a charge to Aalto University students and staff members.
  • Other customers can use the printer u90203-psc3. All printing is subject to a charge to non-University members.
Location:P1 Ark Aalto  205   | Archive
Keywords:Hamiltonian systems
numerical time integration
Krylov subspace
highly oscillatory systems
Hamiltonin systeemit
numeerinen aikaintegrointi
Krylov-aliavaruus
nopeasti oskilloivat systeemit
Abstract (eng): The topic of the thesis is the numerical time integration of Hamiltonian PDEs.
The time integration of the PDEs is done by applying different time integration methods on Hamiltonian ODEs, which are obtained as a result of a semidiscretization of PDEs.
Specifically nonlinear hyperbolic equations which give rise to highly oscillatory ODEs are considered.

When considering the methods two points will be emphasized.
First is the successful resolving of the high frequencies, and the second is the preservation of the structure.
For the first issue the so called exponential integrators are applied, and to approximate the matrix functions Krylov subspace methods are used.
To enhance the convergence of the Krylov approximations, so called rational Krylov methods are considered.

For the issue of the structure preservation, the Krylov subspace methods are performed in a way that a symplectic basis is produced.
For the resulting reduced systems we numerically experiment also some higher order structure preserving Runge-Kutta methods.

The thesis concludes with several numerical experiments with the methods discussed.
Abstract (fin): Työssä tarkastellaan eri aikaintegroijien soveltamista Hamiltonin differentiaaliyhtälöihin, jotka saadaan paikkadiskretoimalla Hamiltonin osittaisdifferentiaaliyhtälöitä.
Erityisesti tarkastellaan integrointia epälineaarisille hyperbolisille osittaisdifferentiaaliyhtälöille, joita diskretoimalla saadaan nopeasti oskilloivia tavallisia differentiaaliyhtälöitä.

Tarkasteltavilta menetelmiltä vaaditaan kahta ominaisuutta.
Ensimmäinen on ratkaisuissa aktiivisena olevien korkeataajuisten moodien tarkka ratkaiseminen, ja toinen on yhtälöiden struktuurin säilyttäminen.
Ensimmäinen ominaisuus yritetään saavuttaa käyttämällä niin sanottuja eksponentiaalisia integroijia.
Näiden laskemiseen käytetään Krylov-aliavaruus-menetelmiä.
Approksimaatioiden tehostamiseksi työssä sovelletaan myös niin sanottuja rationaali-Krylov-menetelmiä.

Struktuurin säilyttämiseksi Krylov-aliavaruus menetelmiä sovelletaan siten, että iteraatiossa muodostetaan symplektinen kanta.
Tämän seurauksena saataviin redusoituihin systeemeihin sovelletaan myös korkeampiasteisia struktuurin säilyttäviä Runge-Kutta menetelmiä.

Lopuksi menetelmien vertailemiseksi suoritetaan useita numeerisia testejä.
ED:2010-11-16
INSSI record number: 41312
+ add basket
« previous | next »
INSSI