First - and Last - Passage Algorithms in Di usion Monte

This paper provides a review of a new method of addressing problems in di usion Monte Carlo: the Green's function rst-passage method (GFFP). In particular, we address four new strands of thought and their interaction with the GFFP method: the use of angle-averaging methods to reduce vector or tensor Laplace equations to scalar Laplace equations; the use of the simulation-tabulation (ST) method to dramatically expand the range of the GFFP method; the use of the Feynman-Kac formula, combined with GFFP to actually perform path integrals, one patch at a time; and the development of last-passage di usion methods; these drastically improve the eÆciency of di usion Monte Carlo methods. All of these techniques are described in detail, with speci c examples.