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Level set methods for stochastic discontinuity detection in nonlinear problems
NORCE Norwegian Research Centre, Norway.
Aerospace Engineering Sciences, University of Colorado Boulder, USA.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2019 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 392, p. 511-531Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 392, p. 511-531
Keywords [en]
Uncertainty quantification, Discontinuity tracking, Level set methods, Polynomial chaos, Hyperbolic PDEs
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-156834DOI: 10.1016/j.jcp.2019.04.053ISI: 000470110700028OAI: oai:DiVA.org:liu-156834DiVA, id: diva2:1315457
Note

Funding agencies: Research Council of Norway through CLIMIT program [244035/E20 CONQUER]; U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research [DE-SC0006402]; NSF [CMMI-1454601]

Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-07-03

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The full text will be freely available from 2021-05-03 09:13
Available from 2021-05-03 09:13

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Nordström, Jan

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  • apa
  • harvard1
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