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Reduced rank extrapolation applied to electronic structure computations. (English) Zbl 1287.65040

Summary: This paper presents a new approach for accelerating the convergence of a method for solving a nonlinear eigenvalue problem that arises in electronic structure computations. Specifically, we seek to solve the Schrödinger equation using the Kohn-Sham formulation. This requires the solution of a nonlinear eigenvalue problem. The currently prevailing method for determining an approximate solution is the self-consistent field method accelerated by Anderson’s iterative procedure or a Broyden-type method. We propose to formulate the nonlinear eigenvalue problem as a nonlinear fixed point problem and to accelerate the convergence of fixed-point iteration by vector extrapolation. We revisit the reduced rank extrapolation method, a polynomial-type vector extrapolation method, and apply it in the real-space density functional theory software.

MSC:

65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)

Software:

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