The study explores the extension of a symplectic numerical scheme to four spacetime dimensions for wave propagation in viscoelastic solids. The authors highlight the advantages of their approach over commercial finite element software solutions, focusing on stability, dissipation error, and dispersion error control. By incorporating thermodynamic principles, they demonstrate how monitoring total energy and entropy production can enhance the reliability of numerical simulations. The research showcases successful applications in one-dimensional and two-dimensional wave propagation problems, providing insights into future developments for more complex systems.
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