Quasi-random Walks on Balls Using C.U.D. Sequences

摘要

This paper presents work on solving elliptic BVPs problems based on quasi-random walks, by using a subset of uniformly distributed sequences—completely uniformly distributed (c.u.d.) sequences. This approach is novel for solving elliptic boundary value problems. The enhanced uniformity of c.u.d. sequences leads to faster convergence. We demonstrate that c.u.d. sequences can be a viable alternative to pseudorandom numbers when solving elliptic boundary value problems. Analysis of a simple problem in this paper showed that c.u.d. sequences achieve better numerical results than pseudorandom numbers, but also have the potential to converge faster and so reduce the computational burden.