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A novel multilevel approach for the efficient computation of random hyperbolic conservation laws

In: Multiscale, Nonlinear and Adaptive Approximation II

Author

Listed:
  • Michael Herty

    (RWTH Aachen University, Institut für Geometrie und Praktische Mathematik)

  • Adrian Kolb

    (RWTH Aachen University, Institut für Geometrie und Praktische Mathematik)

  • Siegfried Müller

    (RWTH Aachen University, Institut für Geometrie und Praktische Mathematik)

Abstract

A novel strategy for the efficient computation of moments to solutions of random hyperbolic conservation laws is presented. The random variables are considered as parameters to the equation but understood as additional (stochastic) directions. The key idea is to perform grid adaptation alternatingly in spatial and stochastic directions to compute the moments in stochastic direction and to select deterministically realizations, respectively. New realizations are computed on the adaptive spatial grid. For grid adaptation a multiresolution analysis is employed to perform data compression using different threshold values in spatial and stochastic directions. For proof of concept, the efficiency of the new approach is verified by the 1D–Euler equations with uncertain initial data. The results are compared with the classical Monte–Carlo method showing the improved performance of the proposed method.

Suggested Citation

  • Michael Herty & Adrian Kolb & Siegfried Müller, 2024. "A novel multilevel approach for the efficient computation of random hyperbolic conservation laws," Springer Books, in: Ronald DeVore & Angela Kunoth (ed.), Multiscale, Nonlinear and Adaptive Approximation II, pages 327-346, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-75802-7_15
    DOI: 10.1007/978-3-031-75802-7_15
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