MDC: A High-Performance Problem-Solving Environment for Optimization and Control of Chemical and Biological Processes

The primary goal of this research is the development of high-performance problem solving environment (PSE) for the optimization and control of chemical and biological processes, with initial emphasis on bioengineering applications. The optimization and control of such processes requires the repetitive solution of time-dependent partial equations (PDEs) in two or three spatial dimensions. The requirements of this problem, which must be solved interactively, can only be met by the use of massively parallel computers. Such a comprehensive and powerful PSE does not currently exist, and its development presents significant computational and computer science challenges. The initial application is the design and optimization of a small diameter bioartificial artery. Over 600,000 surgical procedures for blood vessel replacement are conducted in the U.S. annually, many involving synthetic polymer substitutes for small diameter blood vessels that fail due to lack of biocompatability, which is not an issue for bioartificial arteries. A PDE model based on continuum mechanical theory that describes the distribution of cells, fibers, and stresses in a tissue will be used to simulate the evolving compaction of a bioartificial artery. Optimization of the ultimate properties of the bioartificial artery is sought, in particular the ability to withstand pulsatile arterial pressure. PDE systems of a similar mathematical structure commonly arise as models for chemical processes with a need for their control and optimization. The project includes collaboration with and input from scientists and engineers at several industrial and government laboratories with applications in processing. To optimize or control a process described by PDEs, the original time interval is divided into subintervals in a multiple- shooting type approach. The PDEs on each subinterval are discretized in space via parallel adaptive finite el ement methods to give a large system of algebraic equations (DAEs). Parameters or control variables are then optimized, subject to state and control variable and continuity constraints (equality and inequality) using large-scale nonlinear programming techniques. Extensive knowledge and research experience in adaptive methods for PDEs, DAEs, large-scale optimization, parallel computing, computing environments, and chemical and biological processes, are required to successfully develop such a PSE. The reaerch team members cover this broad range of expertise, and have a successful record of collaboration with each other.