Efficient GPU-Based Solver for Acoustic Wave Equation

We present an efficient algorithm to solve the acoustic wave equation that is used to model the propagation of sound waves through a material medium. Our approach assumes that the speed of sound is constant in the medium and computes an adaptive rectangular decomposition(ARD) of the environment. We map the algorithm to many-core GPU architectures by performing discrete cosine transforms (DCTs) inside each rectangular volume along with a sixth order interface handling at the boundaries. The entire solution to the second order PDE is computed on the GPU and we highlight many techniques to accelerate its performance by exploiting the features of GPU architectures. We highlight the performance of our algorithm in terms of computing impulse responses and sound propagation in complex 3D models. In practice, we observe a performance gain of more than 500X over finite-difference time-domain(FDTD) methods. The use of GPUs also results in almost one order of magnitude improvement over CPU-based ARD algorithms. To the best of our knowledge, this is the fastest method for solving the acoustic wave equation.