DESIGN OPTIMIZATION OF SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS

ALGORITHMS WILL BE DEVELOPED FOR THE AUTOMATED DESIGN OPTIMIZATION OF PHYSICAL SYSTEMS (MODELS) GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS (PDE'S) IN TWO AND THREE DIMENSIONS. THE IMMEDIATE MOTIVATION IS THE PROBLEM OF ELECTRODE DESIGN OPTIMIZATION FOR LASERS AND SWITCHES. THIS WORK WILL BUILD ON THE ELF CODES, USER-INTERACTIVE DESIGN CODES WHICH ACCURATELY CALCULATE THE FIELDS IN LASERS AND PULSED POWER SWITCHES. THIS WORK IS DIRECTLY OF INTEREST TO SDI PULSED POWER PROJECTS, AND IS ALSO APPLICABLE TO OTHER HIGHLY INTEGRATED DESIGN PROBLEMS GOVERNED BY SYSTEMS OF PDE'S, NOTABLY THE NATIONAL AEROSPACE PLANE. THE NUMERICAL SOLUTION OF THE PDE'S IS DEMANDING ON THE EFFICIENCY, ROBUSTNESS, ACCURACY, AND ACCURACY ESTIMATION OF THE SOLUTION METHODS, AND WILL BUILD ON PREVIOUSLY FUNDED AFOSR AND AFWL WORK ON ADAPTIVE GRID GENERATION AND MULTIGRID METHODS. THE OPTIMIZATION PROBLEM IS A NON-CLASSICAL ONE OF NONLINEARLY SOLUTIONCONSTRAINED OPTIMIZATION; IT WILL UTILIZE THE METHODS AND ALGORITHMS OF E. POLAK.