Advanced problems in computational fluid dynamics, finite element structural analysis, and related areas require the solution of large partial differential equations and matrices of large size and dynamic range. This project considers an advanced parallel linear algebra processor and associated novel parallel algorithms for such applications. Research on system fabrication, quantitative performance evaluation and new parallel algorithms are described and considered. Case studies in structural mechanics, dynamics and nonlinear systems, finite element methods, computational fluid dynamics, and partial differential equations are included. The novel utilization of an optical processor for the processing of such problems is the major research given attention.