An efficient parallel algorithm for solving viscoelastic wave equations

The high computational complexity of time-fractional viscoelastic wave equations limits their practical applications in seismic exploration and medical imaging. To address this challenge, this paper proposes a parallelized algorithm to address the practical application demands of viscoelastic wave equations. The method leverages the rapid decay property of cubic B-spline local wavelets in their dual space and designs perfectly matched boundary conditions (PMBCs) to achieve closure of local spline coefficients. This approach enables accurate global spline reconstruction with only localized communication between adjacent patches. Furthermore, by integrating the distributed-parallel local spline simulator (DPLS) with a short-memory operator splitting (SMOS) scheme, we develop an efficient solver for viscoelastic wave equations. Numerical examples in one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) viscoelastic wave propagation scenarios validate the convergence, accuracy, and computational efficiency of the proposed method.