Model Reduction for High Dimensional Micro-FE Models

Three-dimensional serial reconstruction techniques allow us to construct very detailed micro-finite element (micro-FE) model of bones that can represent the porous bone micro-architecture. Solving these models, however, implies solving very large sets of equations (order of millions degrees of freedom), which inhibits dynamic analyses. Previously it was shown for bone models up to 1 million degrees of freedom that formal model order reduction allows us to perform harmonic response simulation for such problems at a computational cost comparable with that of a static solution. However, the main requirement then is that a direct solver is used and there is enough memory to keep the factor. With common serial computers with 4GB of RAM such analyses are limited to bone models with about 1 million degrees of freedom. In order to extend this work to larger models, a parallelizable sparse direct solver needs to be implemented on larger parallel systems, which was the goal of this work. Four bone models have been generated in the range from 1 to 12 million degrees of freedom. They have been used to benchmark the multifrontal massively parallel sparse direct solver MUMPS on SGI Origin 3800 (teras at SARA). The study showed that MUMPS is a good choice to implement model reduction of high dimensional micro-finite element bone models provided that there is enough memory on a high performance computing system. 1