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Institute for Research in Computer Science and Random Systems |  |
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Institute for Research in Computer Science and Random Systems | |
| HAL: hal-00649170, version 2 |
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| Available versions | v1 (2011-12-07) | v2 (2012-05-21) | v3 (2012-08-20) |
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| Simulating diffusion processes in discontinuous media: a numerical scheme with constant time steps |
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| Antoine Lejay 1, 2Géraldine Pichot 3 |
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| For the TOSCA ; SAGE collaboration(s) |
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| (2011-12-02) |
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| In this article, we propose new Monte Carlo techniques for moving a diffusive particle in a discontinuous media. In this framework, we characterize the stochastic process that governs the positions of the particle. The key tool is the reduction of the process to a Skew Brownian Motion (SBM). In a zone where the coefficients are locally constant on each side of the discontinuity, the new position of the particle after a constant time step is sampled from the exact distribution of the SBM process at the considered time. To do so, we propose two different but equivalent algorithms: a two-steps simulation with a stop at the discontinuity and a one-step direct simulation of the SBM dynamic. Some benchmark tests illustrate their effectiveness. |
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| 1: | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| 2: | TOSCA (INRIA Sophia Antipolis / INRIA Lorraine / IECN) |
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INRIA – CNRS : UMR7502 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| 3: | SAGE (INRIA - IRISA) |
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CNRS : UMR6074 – INRIA – Université de Rennes 1 |
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| Probabilités et statistiques |
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| Domain | : | Mathematics/Probability Physics/Physics/Geophysics Sciences of the Universe/Earth Sciences/Geophysics Environmental Sciences/Global Changes |
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| divergence form operators – stochastic differential equation – skew Brownian motion – Monte Carlo simulation – Euler scheme – geophysics – diffusive media with interfaces |
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| Attached file list to this document: | |||||
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| hal-00649170, version 2 | |
| http://hal.inria.fr/hal-00649170 | |
| oai:hal.inria.fr:hal-00649170 | |
| From: Antoine Lejay | |
| Submitted on: Monday, 21 May 2012 14:55:12 | |
| Updated on: Thursday, 31 May 2012 14:55:33 | |
