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.

翻译：本文推广了近期基于热力学构思的数值格式在黏弹性/流变固体中波传播问题的应用，既包括将该格式扩展至四维时空维度，也涉及热力学方法的优势特性。在格式设计方面，离散化时空中物理量表达位置的排布方案（包括边界条件合理实现问题）具有非平凡性。同时，将问题置于热力学框架下，对监测与控制数值伪像（不稳定性、耗散误差及色散误差）展现出显著优势。加之该方案在计算精度、速度及资源友好性方面的优异表现，本文提出的热力学扩展辛方法相比商用有限元软件解决方案更具优越性。