We present a method for numerically modelling viscoelastic wave propagation using domain decomposition combined with a pseudospectral method based on Legendre-Gauss-Lobatto nodes defined on a structured quadrilateral mesh. The physics of the method is modelled using the Kelvin-Voigt equation for the time-dependent relation of stress and strain. Here we derive a coupled system of first-order equations for the particle velocities and accelerations which only doubles the number of required equations as opposed to the increase from 2 to 5 in the 2D case and 3 to 9 in the 3D case required when modelling the velocities and stresses. Working with the first order system also allows us to incorporate absorbing boundary conditions by modifying the damping matrix at the boundary elements in a way that further increases the sparsity of the damping matrix and allows us to maintain the use of a low-storage explicit Runge-Kutta time-stepping algorithm.
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