Banded Matrix Parallel Optical Processor Architectures and Algorithms

本研究项目关注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，信号处理器采用适合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。并行结构和算法在线性代数信号处理构成了本研究的基础。本文描述了一种新型光学线性代数处理器（OLAP），该处理器利用光学元件实现高速性能和并行性。提出了一种新的数字OLAP结构，该结构对数字二进制编码的数字进行高精度处理。新架构通过光卷积实现数字乘法。具体的问题将被检查，以确定定量性能，误差分析，和最佳算法的发展。其应用包括：用有限差分方法求解偏微分方程，用有限元方法求解结构力学问题，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.