Parallel Multi-Core and Multi-Processor Methods on Point-Value Multiresolution Algorithms for Hyperbolic Conservation Laws.

The underlying sequential behavior of the multiresolution (MR) method has been exploited for parallel computing by introducing a concept of multiresolution forest structures (MFS) along with two new load-balancing algorithms. Another easy-to-implement multithreading approach has also been introduced for the multicore architectures. Tests were conducted using an Euler solver based on a fifth-order shock capturing WENO scheme and a third-order Runge–Kutta algorithm. The methods have been rigorously analyzed in terms of speedup ratio and parallel efficiency to bring forth their benefits as well as limitations. The performance yielded through these methods indicates that the MFS is a new headway for the MR method in parallel computing that has a potential to harness better scalability.