New Approaches in Solving Saddle Point Problems

The research will focus on two areas: solving saddle-point problems and discretization on non-matching grids. To build new and efficient algorithms, the PI will combine his new ideas on solving saddle-point problems with already known methods from distinctive fields of numerical analysis such as iterative methods, multilevel methods, and adaptive methods for elliptic PDEs. The main technique will be based on the new spectral results for saddle-point systems found by the PI. The proposed work for solving saddle-point systems has scientific and technical applications in optimization, optimal control, computational fluid dynamics, linear elasticity, electromagnetism, electrical networks, linear models in statistics, and image restoration. A second area of research will be to investigate multilevel discretizations and multilevel preconditioning techniques in the context of discretizations on nonmatching grids based on the Partition of Unity method. The applications are to modeling fluid and gas flow near complex objects and fluid flow in porous media.

Article created: August 27, 2007