Banded Matrix Parallel Optical Processor Architectures and Algorithms

这项研究项目关注的是信号处理算法与体系结构的匹配，以解决各种工程应用中的复杂大规模问题。现代信号处理算法通常用线性代数来描述，而信号处理器使用适合于各种线性代数计算的矩阵-向量技术。架构和算法本质上都是并行的。信号处理的线性代数并行体系结构和算法构成了本研究的基础。本研究描述了一种新型的光学线性代数处理器(OLAP)，它利用光学元件来实现高速性能和并行性。提出了一种新的数字OLAP体系结构，该体系结构对数字二进制编码的数字进行操作以获得高精度。新结构通过光学卷积实现数字乘法。将检查具体问题，以确定量化性能、误差分析和最佳算法开发。要解决的应用包括：用有限差分法求解偏微分方程组，用有限元方法解决结构力学问题，以及计算流体力学问题。

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.