Umeå universitets logga

umu.sePublikationer
Ändra sökning
Avgränsa sökresultatet
1 - 5 av 5
RefereraExporteraLänk till träfflistan
Permanent länk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Träffar per sida
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sortering
  • Standard (Relevans)
  • Författare A-Ö
  • Författare Ö-A
  • Titel A-Ö
  • Titel Ö-A
  • Publikationstyp A-Ö
  • Publikationstyp Ö-A
  • Äldst först
  • Nyast först
  • Skapad (Äldst först)
  • Skapad (Nyast först)
  • Senast uppdaterad (Äldst först)
  • Senast uppdaterad (Nyast först)
  • Disputationsdatum (tidigaste först)
  • Disputationsdatum (senaste först)
  • Standard (Relevans)
  • Författare A-Ö
  • Författare Ö-A
  • Titel A-Ö
  • Titel Ö-A
  • Publikationstyp A-Ö
  • Publikationstyp Ö-A
  • Äldst först
  • Nyast först
  • Skapad (Äldst först)
  • Skapad (Nyast först)
  • Senast uppdaterad (Äldst först)
  • Senast uppdaterad (Nyast först)
  • Disputationsdatum (tidigaste först)
  • Disputationsdatum (senaste först)
Markera
Maxantalet träffar du kan exportera från sökgränssnittet är 250. Vid större uttag använd dig av utsökningar.
  • 1.
    Berg, André
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Numerical analysis and simulation of stochastic partial differential equations with white noise dispersion2023Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This doctoral thesis provides a comprehensive numerical analysis and exploration of several stochastic partial differential equations (SPDEs). More specifically, this thesis investigates time integrators for SPDEs with white noise dispersion. 

    The thesis begins by examining the stochastic nonlinear Schrödinger equation with white noise dispersion (SNLSE), see Paper 1. The investigation probes the performance of different numerical integrators for this equation, focusing on their convergences, L2-norm preservation, and computational efficiency. Further, this thesis thoroughly investigates a conjecture on the critical exponent of the SNLSE, related to a phenomenon known as blowup, through numerical means. 

    The thesis then introduces and studies exponential integrators for the stochastic Manakov equation (SME) by presenting two new time integrators - the explicit and symmetric exponential integrators - and analyzing their convergence properties, see Paper 2. Notably, this study highlights the flexibility and efficiency of these integrators compared to traditional schemes. The narrative then turns to the Lie-Trotter splitting integrator for the SME, see Paper 3, comparing its performance to existing time integrators. Theoretical proofs for convergence in various senses, alongside extensive numerical experiments, shed light on the efficacy of the proposed numerical scheme. The thesis also deep dives into the critical exponents of the SME, proposing a conjecture regarding blowup conditions for this SPDE.

    Lastly, the focus shifts to the stochastic generalized Benjamin-Bona-Mahony equation, see Paper 4. The study introduces and numerically assesses four novel exponential integrators for this equation. A primary finding here is the superior performance of the symmetric exponential integrator. This thesis also offers a succinct and novel method to depict the order of convergence in probability.

    Ladda ner fulltext (pdf)
    fulltext
    Ladda ner (pdf)
    spikblad
    Ladda ner (png)
    preview image
  • 2.
    Berg, André
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Numerical simulations of stochastic generalized Benjamin-Bona-Mahony equationsManuskript (preprint) (Övrigt vetenskapligt)
  • 3.
    Berg, André
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cohen, David
    Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 41296 Gothenburg, Sweden.
    Dujardin, Guillaume
    Univ. Lille, Inria, CNRS, UMR 8524 - Laboratoire Paul Painlevé, F-59000 Lille, France.
    Approximated exponential integrators for the stochastic Manakov equation2023Ingår i: Journal of Computational Dynamics, ISSN 2158-2491, Vol. 10, nr 2, s. 323-344Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This article presents and analyzes an approximated exponential integrator for the (inhomogeneous) stochastic Manakov system. This system of SPDE occurs in the study of pulse propagation in randomly birefringent optical fibers. For a globally Lipschitz-continuous nonlinearity, we prove that the strong order of the time integrator is 1/2. This is then used to prove that the approximated exponential integrator has convergence order 1/2 in probability and almost sure order 1/2−, in the case of the cubic nonlinear coupling which is relevant in optical fibers. Finally, we present several numerical experiments in order to support our theoretical findings and to illustrate the efficiency of the approximated exponential integrator as well as a modified version of it.

  • 4.
    Berg, André
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cohen, David
    Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden.
    Dujardin, Guillaume
    Univ. Lille, Inria, CNRS, UMR 8524 - Laboratoire Paul Painlevé, Villeneuve-d’Ascq, France.
    Lie–Trotter Splitting for the Nonlinear Stochastic Manakov System2021Ingår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 88, nr 1, artikel-id 6Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This article analyses the convergence of the Lie–Trotter splitting scheme for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optical fibers. First, we prove that the strong order of the numerical approximation is 1/2 if the nonlinear term in the system is globally Lipschitz. Then, we show that the splitting scheme has convergence order 1/2 in probability and almost sure order 12- in the case of a cubic nonlinearity. We provide several numerical experiments illustrating the aforementioned results and the efficiency of the Lie–Trotter splitting scheme. Finally, we numerically investigate the possible blowup of solutions for some power-law nonlinearities.

  • 5.
    Berg, André
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cohen, David
    Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden.
    Dujardin, Guillaume
    Inria Lille Nord-Europe and Laboratoire Paul Painlevé UMR CNRS 8524, Villeneuve d’Asq Cedex, France.
    Numerical study of nonlinear Schrödinger equations with white noise dispersionManuskript (preprint) (Övrigt vetenskapligt)
1 - 5 av 5
RefereraExporteraLänk till träfflistan
Permanent länk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf