Numerical Analysis Seminars: A quasi-Monte Carlo method for the coagulation equation
16 January 2015 14:00 in CM 105
The Monte Carlo method is a powerful tool for solving many problems in the applied sciences. This is a simple, versatile, and robust method but it may suffer from a lack of precision. For improving accuracy, one possibility is to replace the pseudo-random numbers with low discrepancy point sets: this is the principle of quasi-Monte Carlo (QMC) methods.
We propose a quasi-Monte Carlo algorithm for the simulation of the continuous coagulation equation. The mass distribution is approximated by a finite number $N$ of numerical particles. Time is discretized and quasi-random points are used at every time step to determine whether each particle is undergoing a coagulation. Convergence of the scheme is proved when $N$ goes to infinity, if the particles are relabeled according to their increasing mass at each time step. Numerical tests show that the computed
solutions are in good agreement with analytical ones, when available. Moreover, the error of the QMC algorithm is smaller than the error given by a standard Monte Carlo scheme using the same time step and number $N$ of numerical particles.
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