Efficient solution of mechanical and biomechanical problems by domain decomposition (Q2760374)

This paper shows the ability of domain decomposition method with a Neumann-Neumann preconditioner to solve industrial and biomechanical problems. After introducing the main features of decomposition and preconditioner technique, the authors present a large scale engineering problem stemming from an anisotropic non-homogeneous three-dimensional slender structure. Next, a three-dimensional model of human liver is in the focus of attention. First, a linear elasticity model is considered and solved by Neumann-Neumann approach, by a direct method, and by the preconditioned conjugate gradient method with different preconditioners. Then a nonlinear hyperelastic model is treated by the Neumann-Neumann domain decomposition algorithm. In all instances, the proposed method appears to be more reliable than standard iterative methods and more efficient than direct methods. The algorithm has been implemented on different parallel computers in the framework of the general purpose finite element library Modulef.