Rapidly-convergent, high-performance PDE solvers for materials-science and engineering applications: theory, implementation and applications.

California Institute Of Technology, Pasadena CA

Investigators

Abstract

Bruno 0707564 The investigator seeks development and analysis of accurate, rapidly convergent, high performance solvers for the types of challenging partial differential equations that arise in present-day materials science applications, as well as use of such solvers for design of concrete devices and prediction of properties of realistic systems. He creates algorithms to treat certain types of problems related to potential theory and wave propagation, composite materials and optical devices, elasticity, acoustics, and electromagnetism. Significant difficulties arise in these classical fields of numerical analysis and computational science in the context of the materials science problems considered, which require treatment of microstructures, non-coercive systems, geometric singularities, resonant structures, high frequencies, multiple scattering, etc. These are mathematical problems that, in spite of significant efforts and progress over the last century, remain elusive in a wide range of important instances. The combination of a number of such challenges often arises in the treatment of materials science configurations, which has made materials problems difficult to tackle. In particular, most algorithms available for the types of materials science applications considered in the project lack in either accuracy, computational efficiency, or both -- a circumstance that has hindered progress in the field. The investigator develops effective, high-performance computational methods for solving partial differential equations that model the properties and behaviors of various physical systems, emphasizing features important for materials. The project has consequences for several areas of societal interest, including the medical field (tomography, imaging), electrical engineering (optics, electronics), military and civilian remote sensing (radar, sonar, stealth), communications (antennas), atmospheric science, etc. The project also provides training for students at both graduate and undergraduate levels, as well as for postdoctoral associates.