A new Monte Carlo approach for conservation laws and relaxation systems

Lorenzo Pareschi; Mohammed Seaïd

doi:10.1007/978-3-540-24687-9_35

A new Monte Carlo approach for conservation laws and relaxation systems

Lorenzo Pareschi
, Mohammed Seaïd

University of Ferrara
Technische Universität Darmstadt

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We present a Monte Carlo method for approximating the solution of conservation laws. A relaxation method is used to transform the conservation law to a kinetic form that can be interpreted in a probabilistic manner. A Monte Carlo algorithm is then used to simulate the kinetic approximation. The method we present in this paper is simple to formulate and to implement, and can be straightforwardly extended to higher dimensional conservation laws. Numerical experiments are carried out using Burgers equation subject to both smooth and nonsmooth initial data.

Original language	English
Pages (from-to)	276-283
Number of pages	8
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3037
DOIs	https://doi.org/10.1007/978-3-540-24687-9_35
State	Published - 2004
Externally published	Yes

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AB - We present a Monte Carlo method for approximating the solution of conservation laws. A relaxation method is used to transform the conservation law to a kinetic form that can be interpreted in a probabilistic manner. A Monte Carlo algorithm is then used to simulate the kinetic approximation. The method we present in this paper is simple to formulate and to implement, and can be straightforwardly extended to higher dimensional conservation laws. Numerical experiments are carried out using Burgers equation subject to both smooth and nonsmooth initial data.

UR - https://www.scopus.com/pages/publications/34547173822

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SN - 0302-9743

VL - 3037

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JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -

A new Monte Carlo approach for conservation laws and relaxation systems

Abstract

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