Overlapping and non-overlapping domain decomposition methods for large-scale meshless EFG simulations

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Meshless methods have a number of virtues in problems concerning crack growth and propagation, strain localization, dynamic shear band propagation, projectile penetration, among others. The main drawback of such methods is that the resulting matrices are more densely populated and the computational cost for the formulation and solution of the problem is much higher than the conventional FEM. This is the reason for their limited application to academic and small-scale problems until now. In this paper, we introduce a novel approach for reducing the computational cost of meshless element free Galerkin (EFG) methods by employing domain decomposition techniques on the physical as well as on the algebraic domains. Specifically, we propose the implementation of the dual domain decomposition FETI family of methods that have been successfully used with FEM in many problems in computational mechanics. We address the issues of dividing an overlapping meshfree EFG domain to several overlapping subdomains, following the algebraic decomposition of the FETI method and alternatively on non-overlapping subdomains by modifying the required displacement compatibility conditions and by improving the accuracy of the solution through a stress update procedure.