A Grid Free Monte Carlo Algorithm for Solving Elliptic Boundary Value Problems

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 UltraSPARC 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.

• Type: Conference
• Year: 2000
• Where: NAA
• Authors: Todor V. Gurov, Paula A. Whitlock, Ivan Dimov
• Keywords: Boundary Value Problems, Elliptic Boundary Value, Mathematics, Monte Carlo, NAA 2000