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Materials Research Laboratory
Computer Science: Numerical and Scientific Computing
- Analysis and Improvement of Jacobi-Davidson Type Methods
- Iterative Methods and Matrix Function Approximation in Material Science Simulations
^ Analysis and Improvement of Jacobi-Davidson Type Methods
E. de Sturler,* E. Martinez (Chem.), R. Martin (Physics), A. Najarian (Comput. Sci.), A. Stathopoulos (College of William and Mary)
National Science Foundation, Focused Research Group Grant, DMR-997655
An important new class of eigenvalue solvers for very large, sparse problems is formed by methods of Jacobi-Davidson type. The Jacobi-Davidson method has been introduced only recently, and although it has proven successful for a variety of problems it still may converge slowly. Indeed, under some circumstances the method may not converge at all. In a recent paper, this research team showed why this happens, and offered a solution that remedies the problem. However, to improve the method in an efficient way and improve the convergence more generally, research is needed to better understand the underlying mathematics. These methods have applications in physics, chemistry, and materials science.
^ Iterative Methods and Matrix Function Approximation in Material Science Simulations
E. de Sturler;* D. Johnson, A. Smirnov (Mat. Sci. & Engr.); R. Yu (Theoret. & Appl. Mech.)
National Science Foundation, Focused Research Group Grant, DMR-997655
This research is focused on study of a variety of techniques related to iterative methods for linear systems for problems arising in material science. An important topic is formed by cheap methods to compute selected coefficients of the inverses of matrices.
