Adaptive Stochastic Numerical Scheme in Parallel Random Walk Models for Transport Problems in Shallow Water

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dc.contributor.authorCharles, Wilson M.
dc.contributor.authorVan den Berg, E.
dc.contributor.authorLin, Hai X.
dc.contributor.authorHeemink, Arnold W.
dc.date.accessioned2016-09-21T12:08:46Z
dc.date.available2016-09-21T12:08:46Z
dc.date.issued2009
dc.description.abstractThis paper deals with the simulation of transport of pollutants in shallow water using random walk models and develops several computation techniques to speed up the numerical integration of the stochastic differential equations (SDEs). This is achieved by using both random time stepping and parallel processing. We start by considering a basic stochastic Euler scheme for integration of the diffusion and drift terms of the SDEs, with a strong order 1 in the strong sense. The errors due to this scheme depend on the location of the pollutant; it is dominated by the diffusion term near boundaries, and by the deterministic drift further away from the boundaries. Using a pair of integration schemes, one of strong order 1.5 near the boundary and one of strong order 2.0 elsewhere, we can estimate the error and approximate an optimal step size for a given error tolerance. The resulting algorithm is developed such that it allows for complete flexibility of the step size, while guaranteeing the correct Brownian behaviour. Modelling pollutants by non-interacting particles enables the use of parallel processing in the simulation. We take advantage of this by implementing the algorithm using the MPI library. The inherent asynchronic nature of the particle simulation, in addition to the parallel processing, makes it difficult to get a coherent picture of the results at any given points. However, by inserting internal synchronisation points in the temporal discretisation, the code allows pollution snapshots and particle counts to be made at times specified by the user.en_US
dc.identifier.citationCharles, W.M., Van Den Berg, E., Lin, H.X. and Heemink, A.W., 2009. Adaptive stochastic numerical scheme in parallel random walk models for transport problems in shallow water. Mathematical and Computer Modelling, 50(7), pp.1177-1187.en_US
dc.identifier.doi10.1016/j.mcm.2009.05.034
dc.identifier.urihttp://hdl.handle.net/20.500.11810/3788
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.subjectWiener processesen_US
dc.subjectStochastic differential equationen_US
dc.subjectRandom walk modelen_US
dc.subjectVariable step sizeen_US
dc.subjectParallel processingen_US
dc.subjectSpeed upen_US
dc.subjectEfficiencyen_US
dc.titleAdaptive Stochastic Numerical Scheme in Parallel Random Walk Models for Transport Problems in Shallow Wateren_US
dc.typeJournal Article, Peer Revieweden_US
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