Efficient and Accurate Algorithms for Solving the Bethe-Salpeter Eigenvalue Problem for Crystalline Systems

by   Peter Benner, et al.

Optical properties of materials related to light absorption and scattering are explained by the excitation of electrons. The Bethe-Salpeter equation is the state-of-the-art approach to describe these processes from first principles (ab initio), i.e. without the need for empirical data in the model. To harness the predictive power of the equation, it is mapped to an eigenvalue problem via an appropriate discretization scheme. The eigenpairs of the resulting large, dense, structured matrix can be used to compute dielectric properties of the considered crystalline or molecular system. The matrix always shows a 2× 2 block structure. Additionally, certain definiteness properties typically hold. One form can be acquired for crystalline systems, another one is more general and can for example be used to study molecules. In this work, we present new theoretical results characterizing the structure of the two forms in the language of non-standard scalar products. These results enable us to develop a new perspective on the state-of-the-art solution approach for crystalline systems. This new viewpoint is used to develop two new methods for solving the eigenvalue problem. One requires less computational effort while providing the same degree of accuracy. The other one improves the expected accuracy, compared to methods currently in use, with a comparable performance. Both methods are well suited for high performance environments and only rely on basic numerical linear algebra building blocks.



There are no comments yet.


page 1

page 2

page 3

page 4


High Performance Solution of Skew-symmetric Eigenvalue Problems with Applications in Solving the Bethe-Salpeter Eigenvalue Problem

We present a high-performance solver for dense skew-symmetric matrix eig...

Nonlinearization of two-parameter eigenvalue problems

We investigate a technique to transform a linear two-parameter eigenvalu...

Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty

We present a method for linear stability analysis of systems with parame...

Linearizability of eigenvector nonlinearities

We present a method to linearize, without approximation, a specific clas...

Towards optimal boundary integral formulations of the Poisson-Boltzmann equation for molecular electrostatics

The Poisson-Boltzmann equation offers an efficient way to study electros...

Fast Accurate Randomized Algorithms for Linear Systems and Eigenvalue Problems

This paper develops a new class of algorithms for general linear systems...

A weighted global GMRES algorithm with deflation for solving large Sylvester matrix equations

The solution of large scale Sylvester matrix equation plays an important...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.