13.5. Summary

The applications of finite element analysis are boundless, and analysts use FEA to model such diverse systems as astrophysics, structural engineering, and the movement of pollution in the atmosphere. In each case, analysts approximate the differential equations with linear equations, and because of the many zeros, these equations are solved as sparse matrices. The goal of this chapter has been to explain what these matrices are and how they can be solved in OpenCL.

Rather than generate sparse matrices using random values, this chapter has relied on a real matrix from NIST’s Harwell-Boeing collection. This 153-by-153 matrix, BCSSTK05, corresponds to the structural analysis of a transmission tower. The first section of this chapter explained how to find the characteristics of this matrix through its Matrix Market file and then read its nonzero values. With minimal modification, the example code can be used to access any matrix in the Harwell-Boeing collection or any of the other matrices in NIST’s Matrix Market site, http://math.nist.gov/MatrixMarket.