Comparison of high order time integration schemes for second order acoustic wave equations in GPU-CPU simulation
Please login to view abstract download link
In this contribution, we are interested in solving the second order acoustic wave equation using high order methods in GPU-CPU simulation. Assuming that space discretization is already performed with spectral element methods for instance, we obtain the following ODE (Ordinary Differential Equation): $$M_h\frac{\partial^2 p_h(t)}{\partial t^2}+ S_h\frac{\partial p_h(t)}{\partial t}+R_h p_h(t)= F_h(t)$$ where $M_h$ is (diagonal) the mass matrix, $S_h$ is the Damping matrix and $K_h$ the stiffness matrix. Herein, we propose to compare two high order explicit schemes: Modified equation \cite{JolyGilbert} and Runge-Kutta Nystr\"om \cite{HairerNystrom,OptimizedRKN}. We discuss strategies to take into account the Damping term that involve first derivative in time without undermining the order of convergence of the schemes. The proposed approaches are compared regarding the computational time, the memory usage and the data exchange between GPU and CPU. Numerical experiments are conducted in 3D for the acoustic wave equation. The numerical results are obtained with the massively parallel multi-physics simulation code GEOS (https://github.com/GEOS-DEV/GEOS).
