Towards a fast and stable dynamic skeletal muscle model

Abstract

This thesis investigates the possibility to reduce the computational effort of a dynamic skeletal muscle model making use of model order reduction methods. For that purpose, a three-dimensional, nonlinear, dynamic skeletal muscle model based on the theory of incompressible finite hyperelasticity is introduced. After discretisation in space and time, using the mixed Taylor-Hood finite elements and the implicit Euler scheme, respectively, the obtained complex and high-dimensional differential algebraic equation system describing the three fields position, velocity and pressure, is investigated from a theoretical as well as computational point of view. Furthermore, the stability issues, encountered with a reduced-order model, built by projecting each field of the high-dimensional model onto a reduced subspace, are demonstrated. The reason for these problems is additionally investigated and confirmed from the theoretical perspective. In order to propose a suitable approach for obtaining a stable reduced order skeletal muscle model, the well-established technique of combining the reduced basis approximation with the proper orthogonal decomposition needs to be customised. The performance with respect to stability, effciency and accuracy of different reduced-order models, built from various combinations and sizes of subspaces, each of them again constructed from differently calculated POD bases, with and without enrichment by approximate supremizer solutions, is compared.