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Some experiments with massively parallel computation for Monte Carlo simulation of stochastic dynamical systems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Johnson, Eric Wojtkiewicz, Steven F. Bergman, Lawrence A. |
| Copyright Year | 1994 |
| Abstract | The evolution of stochastic dynamical systems is governed by Fokker–Planck equations if the response process is Markovian. Analytical solutions for the transient response do not exist for all but the simplest of systems. The evolution of the transition probability density function over the phase space has been solved numerically for various two-dimensional systems subjected to additive and multiplicative random excitation using the finite element method (Spencer and Bergman 1993). Systems of higher order, however, pose significant difficulty when using standard finite element formulations due to memory requirements and computational expense. Direct Monte Carlo simulation (MCS), while often regarded as less elegant than other methods, can indeed be used to solve problems of significantly higher complexity. Low order systems are often more efficiently solved by other methods ( e.g. , the finite element method, cell mapping, path integral methods, etc.). For example, a standard finite element solution with a grid of n points in each spatial dimension and a uniform time step requires a single reduction to upper triangular form of equations followed by forward and backward substitution at each time step for a -dimensional problem. Thus, the required number of computations and memory allocation grow exponentially with the dimennd |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www2.aae.uiuc.edu/~lbergman/csdg/papers/athens94mcs.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
