We are particularly interested in nonlinear optimization problems, which involve computationally intensive function evaluations. The comparability among the various techniques for numerical approximation through optimization algorithms is very important. We are developing object-oriented computational tools for the analysis of material microstructure. The goal is to predict the macroscopic behavior of a material from knowledge of its microscopic geometry. Starting from a digitized micrograph, the program identifies features in the image, assigns material properties to them, generates a finite element mesh, and performs virtual measurements to determine the effect of the microstructure on the macroscopic properties of the system.
Opportunities exist in image analysis, materials science, physics, and computer science.
50.89.11.B4451 Boulder, Colorado Algorithm Development for Modeling Communication Systems B.K. Alpert Problems arising in modeling communication systems, including antennas, microwave guides, and opto-electronic devices, are attacked with tools from scientific computation, numerical analysis, and applied mathematics. Particular emphasis is placed on high-order convergent and reduced computational complexity techniques for numerical solution of integral equations and partial differential equations, including quadrature methods, fast multipole methods, and wavelet methods. Recently we have also explored coding issues arising in communication protocols, using analytical methods to understand issues of noise resilience and communication security.