Recent results on a thermodinamically 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. Concerning the scheme, what is nontrivial is the arrangement of which quantity is represented where in discretized spacetime, including the question of  realizing the boundary conditions appropriately . In parallel, placing the problem in the thermodynamical framework proves beneficial regarding 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  presented here advantageous above commercial finite element software solutions.
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.
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