Evaluation of the Intel Xeon Phi 7120 and NVIDIA K80 as accelerators for two-dimensional panel codes

Abstract

To optimize the geometry of airfoils for a specific application is an important engineering problem. In this context genetic algorithms have enjoyed some success as they are able to explore the search space without getting stuck in local optima. However, these algorithms require the computation of aerodynamic properties for a significant number of airfoil geometries. Consequently, for low-speed aerodynamics, panel methods are most often used as the inner solver. In this paper we evaluate the performance of such an optimization algorithm on modern accelerators (more specifically, the Intel Xeon Phi 7120 and the NVIDIA K80). For that purpose, we have implemented an optimized version of the algorithm on the CPU and Xeon Phi (based on OpenMP, vectorization, and the Intel MKL library) and on the GPU (based on CUDA and the MAGMA library). We present timing results for all codes and discuss the similarities and differences between the three implementations. Overall, we observe a speedup of approximately 2.5 for adding an Intel Xeon Phi 7120 to a dual socket workstation and a speedup between 3.4 and 3.8 for adding a NVIDIA K80 to a dual socket workstation.

A $μ$-mode integrator for solving evolution equations in Kronecker form

“…However, as opposed to the case in section 4.2, the resulting ODE cannot be integrated exactly in time. For the time discretization, we will then use the order two Magnus integrator (18). We call the resulting scheme Hermite Kronecker Magnus Pseudospectral method (HKMP).…”

“…It has increasingly been realized that in order to fully exploit present and future highperformance computing systems we require algorithms that parallelize well and which can be implemented efficiently on accelerators, such as GPUs [5]. In particular, for GPU computing much research effort has been undertaken to obtain efficient implementations (see, e.g., [6,8,17,18,19,31,34,39,41,44]).…”

An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs

“…The original REXI scheme and the differences to REXII The original REXI scheme was developed for matrices A with real entries. It is based on (15) where τ A is substituted for ix. A further simplification comes from the fact that e τ A is real which suggests to neglect the imaginary part of (15).…”

“…If A = iB, where B is a real diagonalizable matrix, then the transformation matrix V is real. If moreover f 0 is real, the use of (15) for approximating e τ A is justified, and we end up with the following scheme:…”

“…Therefore, methods which are highly parallelizable and work well on these new computer architectures are needed to take advantage of their computational power. A significant body of research has been accumulated in recent years that considers numerical methods that are well suited for such systems (see, e.g., [15,16,21,27,28]). More specifically, in the context of exponential integrators we refer to [17,18].…”