Cristin-resultat-ID: 1701943
Sist endret: 15. august 2019, 12:48
NVI-rapporteringsår: 2019
Vitenskapelig artikkel

Level set methods for stochastic discontinuity detection in nonlinear problems

  • Per Pettersson
  • Alireza Doostan og
  • Jan Nordström


Journal of Computational Physics
ISSN 0021-9991
e-ISSN 1090-2716
NVI-nivå 2

Om resultatet

Vitenskapelig artikkel
Publiseringsår: 2019
Volum: 392
Sider: 511 - 531


Scopus-ID: 2-s2.0-85065516445

Beskrivelse Beskrivelse


Level set methods for stochastic discontinuity detection in nonlinear problems


Stochastic problems governed by nonlinear conservation laws are challenging due to solution discontinuities in stochastic and physical space. In this paper, we present a level set method to track discontinuities in stochastic space by solving a Hamilton-Jacobi equation. By introducing a speed function that vanishes at discontinuities, the iso-zeros of the level set problem coincide with the discontinuities of the conservation law. The level set problem is solved on a sequence of successively finer grids in stochastic space. The method is adaptive in the sense that costly evaluations of the conservation law of interest are only performed in the vicinity of the discontinuities during the refinement stage. In regions of stochastic space where the solution is smooth, a surrogate method replaces expensive evaluations of the conservation law. The proposed method is tested in conjunction with different sets of localized orthogonal basis functions on simplex elements, as well as frames based on piecewise polynomials conforming to the level set function. The performance of the proposed method is compared to existing adaptive multi-element generalized polynomial chaos methods.


Per Pettersson

  • Tilknyttet:
    ved NORCE Energi ved NORCE Norwegian Research Centre AS

Alireza Doostan

  • Tilknyttet:
    ved University of Colorado at Boulder

Jan Nordström

  • Tilknyttet:
    ved Linköpings universitet
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