Return to Colloquia & Seminar listing
Fast Numerical Methods for Electronic Structure CalculationsPDE and Applied Math Seminar
|Speaker: ||Chao Yang, Lawrence Berkeley Lab|
|Location: ||2112 MSB|
|Start time: ||Tue, Apr 14 2015, 4:10PM|
The Kohn-Sham density functional theory (KSDFT) is the most widely used
theory for studying electronic properties of molecules and solids.
It allows us to reduce the need to solve a many-body Schrodinger's equation
to the task of solving a system of single electron equations coupled
by the electron density. These equations can be viewed as a nonlinear
eigenvalue problem. Although they contain far fewer degrees of freedom,
they are more difficult to solve due to their nonlinear properties.
In this talk, I will give an overview on efficient algorithms for solving
this type of problem. I will describe discretization techniques that can
potentially reduce the number of degrees of freedom required to represent
the Kohn-Sham Hamiltonian. I will also present recently developed algebraic
techniques for reducing the computational complexity of the Kohn-Sham DFT
calculation. A key concept that is important for understanding these
algorithms is a nonlinear map known as the Kohn Sham map. The ground state electron density is a fixed point of this map. I will examine properties
of this map and its Jacobian. These properties can be used to develop
effective strategies for accelerating Broyden's method for finding the
optimal solution. They can also be used to reduce the computational
complexity associated with the evaluation of the Kohn Sham map, which
is often the most expensive step in a Broyden iteration.