  The recent results attained from a thermodynamically conceived numerical
scheme applied on wave propagation in viscoelastic/rheological solids are
generalized here, both in the sense that the scheme is extended to four
spacetime dimensions and in the aspect of the virtues of a thermodynamical
approach. Regarding the scheme, the arrangement of which quantity is
represented where in discretized spacetime, including the question of
appropriately realizing the boundary conditions, is nontrivial. In parallel,
placing the problem in the thermodynamical framework proves to be beneficial in
regards to monitoring and controlling numerical artefacts - instability,
dissipation error, and dispersion error. This, in addition to the observed
preciseness, speed, and resource-friendliness, makes the thermodynamically
extended symplectic approach that is presented here advantageous above
commercial finite element software solutions.
