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Level set methods f...
Level set methods for stochastic discontinuity detection in nonlinear problems
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- Pettersson, Per (författare)
- NORCE Norwegian Research Centre, Norway
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- Doostan, Alireza (författare)
- Aerospace Engineering Sciences, University of Colorado Boulder, USA
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- Nordström, Jan, 1953- (författare)
- Linköpings universitet,Beräkningsmatematik,Tekniska fakulteten
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(creator_code:org_t)
- Elsevier, 2019
- 2019
- Engelska.
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Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 392, s. 511-531
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Uncertainty quantification
- Discontinuity tracking
- Level set methods
- Polynomial chaos
- Hyperbolic PDEs
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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