2007 PIMS-CSC Seminar - 03

In today's product development and engineering process, usage of computer aided design (CAD) platform is an obvious choice. It allows creating of quite realistic models, precisely describing not only the geometry of the developed prototype, but also its physical properties. These models, usually referred as parts, are brought together (assembled) into assemblies, like it occurs in real world. The final digital prototype consists sometimes of thousands of parts and sub-assemblies. Thus, its finite element based optimization is limited by computing architectures that cannot hold and process large models in a timely way. It is therefore desirable to use multiprocessor parallel computers to solve large mathematical systems.

We propose to apply domain decomposition methodology (DDM) to run numerical simulation of CAD large assemblies. Instead of exporting a complex assembly as a single component, and later dividing it into numerous, randomly created sub-domains, we propose to use assembly topology, which was previously created by designer while modelling process period. Thus, each part represents an independent sub-domain, and could be analyzed simultaneously with other parts, by sharing only the contact information. One of the main goals of this research is to handle various types of nonconformities on the adjacent sub-domains. In
order to enforce the matching of the local solutions, interface conditions and projection operators have to be written on the boundaries between sub-domains. These terms and conditions are imposed iteratively. The convergence rate is very sensitive to these interface conditions. The classical Schwarz algorithm without overlap, the mortar element method as well as FETI-based methods are presented.

A brief presentation of the finite element open-source FreeFem3D software could be initiated.