Variable Time Stepping In Parallel
Particle Models For Transport Problems In
Shallow Waters
Author(s)
W. M. Charles, E. van den Berg, H.X. Lin & A. W. Heemink
Abstract
Stochastic differential equations (SDEs) are stochastic in nature. The SDEs under
consideration are often called particle models (PMs). PMs in this article model
the simulation of transport of pollutants in shallow waters. The main focus is
the derivation and efficient implementation of an adaptive scheme for numerical
integration of the SDEs in this article. The error determination at each integration
time step near the boundary where the diffusion is dominant is done by a pair of
numerical schemes with strong order 1 of convergence and that of strong order 1.5.
When the deterministic is dominantwe use the aforementioned order 1 scheme and
another scheme of strong order 2. An optimal stepsize for a given error tolerance
is estimated. Moreover, the algorithm is developed in such a way that it allows
for a completely flexible change of the time stepsize while guaranteeing correct
Brownian paths. The software implementation uses the MPI library and allows
for parallel processing. By making use of internal synchronisation points it allows
for snapshots and particle counts to be made at given times, despite the inherent
asynchronicity of the particles with regard to time.
Keywords: adaptive schemes, Wiener processes, SDEs, particle model, variable
stepsize, parallel computing, speed up.
Keywords
adaptive schemes, Wiener processes, SDEs, particle model, variable
stepsize, parallel computing, speed up.
Related Book
Other papers in this volume
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