Banded Matrix Parallel Optical Processor Architectures and Algorithms

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This research project is concerned with the match of algorithms for signal processing with architectures to solve complex large-scale problems in a variety of engineering applications. Modern signal processing algorithms are normally described in terms of linear algebra and signal processors employ matrix-vector techniques suitable for various linear algebra computations. Both architectures and algorithms are inherently parallel in nature. Parallel architectures and algorithms in linear algebra for signal processing forms the basis of this research. This research describes a new type of optical linear algebra processor (OLAP) that uses optical elements to achieve high speed performance and parallelism. A novel digital OLAP architecture is proposed which operates on digital binary-encoded numbers for high-accuracy. The new architecture achieves digital multiplication by optical convolution. Specific problems will be examined to determine quantitative performance, error analysis, and optimum algorithm development. The applications to be addressed include: the solution of partial differential equations by finite differencing methods, the solution of structural mechanics problems using finite element methods, and computational fluid mechanics problems.