Reconfigurable architecture for the efficient solution of large-scale non-Hermitian eigenvalue problems

The solution of large eigensystems has numerous applications in engineering and science, including circuit simulation, mechanical structure stability, and quantum physics. In particular, many optics and photonics applications, such as the design of photonic crystal slab devices, dispersion engineering, and other iterative-based design techniques, require an eigenvalue solver. Unfortunately, brute force solutions exhibit a computational complexity of O(n 3 ), rendering them entirely impractical for medium to large matrices. Although techniques have been developed to reduce this complexity to O(n 2 ), these algorithms are restricted to special cases such as real, symmetric, or sparse matrices, limiting the applicability of these solutions. Thus, there is a clear need for a high-performance eigenvalue solver for large, non-hermitian matrices. To this end, we are developing a novel, hardware-based platform for the analysis of eigenvalue problems. In this paper, we describe this platform and its application to eigenvalue problems, as well as our progress to date.