Random number generators: good ones are hard to find
Communications of the ACM
A New Class of Grid-Free Monte Carlo Algorithms for Elliptic Boundary Value Problems
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Parallel realization of grid-free monte carlo algorithm for boundary value problems
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
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In this work a grid free Monte Carlo algorithm for solving elliptic boundary value problems is investigated. The proposed Monte Carlo approach leads to a random process called a ball process.In order to generate random variables with the desired distribution, rejection techniques on two levels are used.Varied numerical tests on a Sun Ultra Enterprise 4000 with 14 Ultra-SPARC processors were performed. The code which implemented the new algorithm was written in JAVA.The numerical results show that the derived theoretical estimates can be used to predict the behavior of a wide class of elliptic boundary value problems.