An adapted coarse space for Balancing domain decomposition method to solve nonlinear elastodynamic problems

This work is devoted to present a scalable domain decomposition method to solve nonlinear elastodynamic problems. Large non linear elastodynamic problems represent an appropriate application field for substructuring methods which are efficient on parallel computer with the proviso of using specific preconditioner techniques well adapted to the mechanical modeling. According to this reason, we develop an adapted Balancing domain decomposition method [Man93, LeT94] appropriated to solve this kind of systems. By using the theoretical framework of Schwarz additive decomposition method [LeT94, LMV98] and by using arguments developed in [ABLV00], we propose a two level Neumann-Neumann preconditioner based on the construction of a coarse space of "lower energy" modes adapted to finite deformations problems with dynamic process. In section 1, nonlinear elastodynamic problems and domain decomposition frameworks are recalled. The section 2 is devoted to present the definition of an adapted coarse space by using Schwarz additive formulation. The construction of the two level Neumann-Neumann preconditioner is detailled in section 3. In last section 4, we test the efficiency of this updated Balancing domain decomposition method on numerical solutions of an academic non linear dynamic problem.