Abstract
Two new algorithms for numerical solution of static Hamilton-Jacobi equations are presented. These algorithms are designed to work efficiently on different parallel computing architectures, and numerical results for multicore CPU and GPU implementations are reported and discussed. The numerical experiments show that the proposed solution strategies scale well with the computational power of the hardware. The performance of the new methods are investigate for tow types of static Hamilton-Jacobi formulations are investigated, the isotropic eikonal equation and an anisotropic formulation used to simulate different types of geological folding. Simulations of geological folding is a key component in an industrial software used in oil and gas exploration. In particular, our experiments indicate that the new algorithms would be capable of accelerating an existing industrial simulator substantially. Direct comparison with the current industry code shows that computing times can be reduced from several minutes to a few seconds. The new methods are now being migrated to the industrial software.
Highlights
Two new algorithms for numerical solution of static Hamilton-Jacobi equations are presented
4 Conclusions Two new parallel solvers are presented, together with several numerical experiments conducted on both multicore CPUs and GPUs
list of active subdomains (LAS) places all active subdomains in a list, and updates the subdomains in this list in parallel
Summary
Two new parallel solvers are presented, together with several numerical experiments conducted on both multicore CPUs and GPUs. The conditional upwind stencils first solve for a solution, and thereafter accepts the new estimate only if the associated characteristic originates from within the spatial grid element, defined as the convex hull of the nodes supporting the stencil Both approaches are identical on eikonal formulations but may differ in anisotropic cases [ ]. Due to the isotropic nature of the eikonal problem one can often formulate upwind conditions for the acceptance of a new estimate [ ] These conditions can significantly reduce the amount of computations needed to update a nodal value. A subdomain that is activated receives (at least) one surface with two layers of nodes in the synchronisation Assuming that these ‘thick’ boundary values are correct, the characteristic curves are extrapolated to the rest of the subdomain in the sweeps as new solution values are computed. All authors contributed to the manuscript, and have read and approved the final manuscript
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