Algorithms, analyses, and model reductions for a class of parametrized systems

Colorado School Of Mines, Golden CO

Investigators

Abstract

The main aim of the project is to develop, implement, and analyze innovative fast and highly accurate algorithms for simulation, model reduction, and quantification of interactions and radiation induced by parametrized configurations comprising a large number of three dimensional particles. The focus is specifically on large systems with hundreds or even thousands of particles in multiscale configurations that arise in atmospheric and biological sciences applications. Even for a fixed set of parameters describing a large configuration,standard iterative algorithms (and acceleration techniques) suffer from computational complexity (and slow convergence). The innovative preconditioned and accelerated iterative algorithms and analyses in this project facilitate a practical approach to efficiently simulate scattering and absorption by (and interactions of) large numbers of particles occurring in atmospheric and biological sciences. Development of very efficient algorithms for electromagnetic scattering and absorption by a single three dimensional particle is essential to simulate interactions in large configurations. Atmospheric aerosols affect Earth's energy budget directly by scattering and absorbing radiation, and indirectly by modifying the amount of cloud and the radiative properties of clouds. One of the highest priority tasks is to advance the ability to model aerosol-cloud-precipitation interaction in climate models. The key to quantifying and reducing uncertainty about the impact of aerosols is to understand the scattering, absorption, and interaction properties of large configurations of particles well enough to accurately replicate them in the full climate models. A technically related problem arises in medical diagnostics where a high priority task is to understand how a laser beam interacts with a large number of red blood cells (erythrocytes). The focus of the project is to implement the computational mathematics component of these high priority recommendations. The project includes training of graduate and undergraduate students.