A fully separated space-time decomposition for the simulation of viscoelastic structures

A space-time decomposition based on the Proper Generalized Decomposition for viscoelastic structures is presented. The displacement field and the field of the internal variable are each represented by a sum of products of space and time modes. Due to the linearity of the evolution equation of the internal variable in the strains, the calculation of space and time modes can be fully separated. In contrast to earlier studies on the subject, this work presents a fully separated framework throughout the entire algorithm. Nevertheless, the strong coupling of balance of linear momentum equation and evolution equation is kept intact. Therefore, the resulting scheme resembles classical schemes easing the implementation. The efficiency and robustness of the method are investigated for a variety of boundary value problems. For problems with more than 20 time steps, the presented method is often more efficient. The source code is available at https://github.com/ikm-luh/SpaceTimeDecomp_SourceCode.