M. Ammann

Distributed point objects: a new concept for parallel finite elements applied to a geomechanical problem

We present a new concept for the realization of finite element computations on parallel machines which is based on a dynamic data structure address by points. All geometric objects (cells, faces, edges) are referenced by its midpoint, and all algebraic data structures (vectors and matrices) are tied to the nodal points of the finite elements. Together, they build Distributed Point Objects (DPO), where the parallel distribution is made transparent by processor lists assigned to the points. All objects are stored in hash tables (where the keys are points) so that pointers can be completely avoided.Then, we consider the application of the parallel programming model to a geomechanical porous media problem. This work complements our previous work [C. Wieners, M. Ammann, S. Diebels, W. Ehlers, Parallel 3-D simulations for porous media models in soil mechanics, Comput. Mech. 29 (2002) 75-87], where the geomechanical model, the interface of the finite element code and the parallel solver is described in detail. Here, we discuss the parallel data structure and the parallel performance for a characteristic application. Together, this demonstrates that demanding 3-D non-linear and time-dependent engineering applications on unstructured meshes can be parallelized very efficiently within a very small overhead for the parallel implementation.

Non-linear behaviour in the deformation and localization analysis of unsaturated soil

Deformation and localization analysis is a crucial issue and has thus been intensively investigated in the last decades. In particular, geotechnical applications do not only concern a single solid material but they also affect the interaction with the pore-fluids, water and air. As a result, both the deformation and the localization analysis must be applied to a triphasic material consisting of a materially incompressible elasto-plastic or elasto-viscoplastic skeleton saturated by two viscous pore-fluids, a materially incompressible pore-liquid and a materially compressible pore-gas. Based on a continuum mechanical approach, unsaturated soil can be described within the well-founded framework of the Theory of Porous Media (TPM). The numerical computations proceed from weak formulations of the momentum balance of the overall triphasic material together with the mass balance equations of the pore-fluids. The resulting system of strongly coupled differential-algebraic equations (DAE) is solved by use of the finite element tool PANDAS. Furthermore, several initial boundary-value problems are presented demonstrating the efficiency of the overall formulation.

h -Adaptive Strategies Applied to Multi-phase Models

Based on the error estimator of Zienkiewicz and Zhu, a new error estimator is presented which is especially designed for multi-phase problems. Furthermore, efficient h-adaptive strategies concerning the generation of a new mesh and data transfer between different meshes are pointed out. The efficiency of these tools is demonstrated using a shear banding problem as a numerical example.