Efficient computation on physics and engineering problems not only requires robust and high order numerical schemes, but also intelligent implementation on advancing computer technology. In this paper, we report three applications using the graphics processing units (GPUs)-based algorithms for high performance computation of mathematical models with the FronTier++ code. We present a detailed discussion on how to optimize execution resources allocation in these applications according to the nature of the problems. In the first set of simulations, the system of one-dimensional gas dynamics equations is solved by the fifth order weighted essentially non-oscillatory (WENO) scheme, we achieved 7-20 times speedup for different mesh sizes on one GPU device. In the second case, the spring model for fabric dynamics is studied. The GPU code is about 6 times faster than the pure CPU code for different mesh sizes. In the last case, a GPU enhanced numerical algorithm for American option pricing under the generalized hyperbolic distribution is explored. Using one GPU device, we have achieved 11 times speedup for the pricing of single option and 400 times speedup for multiple options.

GPGPU, gas dynamics, spring model, American option pricing.