To overcome some of the limitations described above, two techniques have been recently derived: the first-passage Green’s function and synchronous parallel KMC. The first-passage Green’s function approach has been successfully used in various sub­areas ofcomputational science but so far has escaped the widespread attention of materials scientists. Pre­liminary work indicates that constructive use of the first-passage Green’s function approach for modeling radiation microstructures is possible46,47 but will re­quire considerable effort to develop a time-dependent formulation of the method. However, the potential payoff is well worth it: preliminary estimates show that it should be possible to boost the effective perfor­mance of the (exact) Monte Carlo simulations by several orders ofmagnitude. The speedup ofthe sim­ulation with the first-passage Green’s function ap­proach can be estimated from a rough argument based on the number of events required to process the diffusion of a vacancy from one void to another in Oswald coarsening. For example, voids in irradiated alloys are separated by ^0.2 mm. But as the atomic jump distance is typically on the order of 0.25 nm, the ratio between the required diffusion length and the atomic jump distance is around 103. The ripening process consists mainly of vacancies detaching from one void and diffusing to a neighbor. If this is done with a direct hop simulation, then ^106 random walk diffusion hop events would be required, from vacancy emission to absorption. Each such event requires the generation of one or more random numbers and changes in bookkeeping tables that store current posi­tions for each defect. Using the first-passage Green’s function algorithm, the vacancy in most cases will reach the vicinity of a void in several (10-30) steps, each of which will require <10 times the number of calculations for a simple hop. Thus, it is possible to conclude that the simulation of the ripening of voids (which is similar to modeling radiation-induced pre­cipitation processes) at this spacing would require about three orders of magnitude less computer time than the current KMC programs.

At the moment, the first-passage Green’s function KMC appears to work very well for some specific cases such as the one mentioned above, but when one tries to model a more realistic case such as the con­tinuous introduction of displacement cascades in which all the defects are very close to each other and diffuse with very different diffusivities, the pos­sible ‘protective domains’ become very small and the technique is not very efficient.

One additional difficulty with KMC simulations is the fact that the current state-of-the-art simulation codes utilize serial computing only. Thus, there exists a critical need to accelerate the maturation of multi­scale modeling of fusion reactor materials, namely the development of advanced and highly efficient Monte Carlo algorithms for the simulation of materi­als evolution when controlling processes occur with characteristic time scales between 10_ 2 and ^10°s. There has recently been some activity associated with synchronous parallel KMC48; however, the problem of dealing with highly inhomogeneous regions and species diffusing at rates that are disparate by many of orders of magnitude tends to greatly reduce the par­allel algorithm performance. Clearly, more effort is needed on the development of advanced algorithms for KMC simulations. Further, it is imperative that the algorithms developed be highly efficient in today’s massively parallel computing architectures.

At the moment, no single KMC method can efficiently treat the complex microstructures and kinetic evolution associated with radiation effects in multi-component materials, nor efficiently balance the computational requirements to treat inhomoge­neous domains consisting of very different defect densities. It is possible that a combination of different techniques in the course of a single simulation will be the most efficient pathway.