Simulating Diffusion Processes in Discontinuous Media: Benchmark Tests

Antoine Lejay 1, 2 Géraldine Pichot 3
1 Probabilités et statistiques
IECL - Institut Élie Cartan de Lorraine
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : We present several benchmark tests for Monte Carlo methods simulating diffusion in one-dimensional discontinuous media. These benchmark tests aim at studying the potential bias of the schemes and their impact on the estimation of micro- or macroscopic quantities (repartition of masses, fluxes, mean residence time,...). These benchmark tests are backed by a statistical analysis to filter out the bias from the unavoidable Monte Carlo error. We apply them on four different algorithms. The results of the numerical tests give a valuable insight of the fine behavior of these schemes, as well as rules to choose between them.
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Submitted on : Friday, March 18, 2016 - 11:21:57 AM
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Antoine Lejay, Géraldine Pichot. Simulating Diffusion Processes in Discontinuous Media: Benchmark Tests. Journal of Computational Physics, Elsevier, 2016, 314, pp.348-413. ⟨10.1016/j.jcp.2016.03.003⟩. ⟨hal-01003853v3⟩

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