Optimization and large scale computation of an entropy-based moment closure

We present computational advances and results in the implementation of an entropy-based moment closure, M_N, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as P_N, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. These results show, in particular, load balancing issues in scaling the M_N algorithm that do not appear for the P_N algorithm. We also observe that in weak scaling tests, the ratio in time to solution of M_N to P_N decreases.