Keywords: distributed parallel, multi-core, computational techniques, domain decomposition, finite element analysis.

Finite element analysis is the foundation of engineering simulations in many industries. Subjects for industrial simulations are, for example, the behavior of a car body traveling over a rough road in the auto industry, or the opening of the landing gear of an airplane in the aircraft industry. Practical applications of such complexity require significant computing time and immense computational resources. Dedicated techniques well suited to modern distributed hardware architectures are needed to complete these analyses.

The first element of such techniques involves subdividing very large problems into smaller partition problems. Various geometry domain decomposition methods may be applied directly to a finite element graph or the graph of finite element matrices. The most commonly used method based on spectral bisection is presented in this chapter.

The second component is the implementation of various analysis computations in a distributed form. Physical solution computations in geometry partitions are connected through their common boundaries. Partition solutions must be executed in a certain order and with a strategy applicable to the hardware at hand. As an example, the commonly used normal modes analysis procedure in a recursive distributed fashion is discussed at length.

Finally, the numerically intensive computational kernels that provide the interior of finite element computations must be efficiently executed in parallel on the emerging multi-core hardware architectures. The premier, industry standard factorization technique in finite element analysis, the multi-frontal method is explained in detail.

To demonstrate the effect of the above technologies, the results of two analyses are presented. One was the analysis of a car body. The model had all major components of the car structure, chassis, windows, doors, etc. incorporated. The finite element model had 1.3 million node points and approximately 1.2 million shell elements. The resulting matrix size after the elimination of constraints was 7.9 million degrees of freedom. Normal modes were computed for various frequency ranges; for example, the range of 0 to 200 Hz contained about 1000 normal modes. The model was solved using 512 partitions.

The second example presented was the analysis of an engine block. The finite element model had approximately 3.6 million node points due to the richness of geometric details. The model had 2.3 million solid, specifically tetrahedral finite elements and the resulting degrees of freedom were 10.8 million. For such a model, the frequency range of interest from the engineer is also wider, reaching into the tens of thousands of Hz. This model was solved using 256 partitions.

The chapter shows that difficult industrial finite element analysis problems may be solved by a recursively partitioned and distributed solution technique. The technique, coupled with computational kernels executing linear algebraic operations on multicore processors, produced spectacular results in various auto industry applications. The technology, however, is not limited to a specific industry; similar applications in other industries also produce excellent results.

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