标题： 平面波电子结构计算中线性响应的高效 Krylov 方法 显示英文标题

标题： Efficient Krylov methods for linear response in plane-wave electronic structure calculations

摘要： 我们提出了一种基于不精确GMRES方法的新算法，用于密度泛函理论中的线性响应计算。 此类计算需要迭代求解嵌套的线性问题$\mathcal{E} \delta\rho = b$以获得电子密度$\delta \rho$的变化。 值得注意的是，每次应用介电算子$\mathcal{E}$需要依次迭代求解多个线性系统，即Sternheimer方程。 我们开发了可计算的界限来估计给定Sternheimer方程求解精度时的密度变化准确性。 基于此结果，我们建议可靠的策略以自适应地选择Sternheimer方程的收敛容差，使得每次应用$\mathcal{E}$不会比所需更准确。 在实际相关的具有挑战性的材料系统上的实验表明，我们的策略实现了超线性收敛，并且减少了大约40\%的计算时间。 我们的算法可以无缝地与来自自洽场问题上下文的标准预处理方法结合，使其成为基于Krylov子空间技术的有效响应求解器的一个有前景的框架。 显示英文摘要

摘要： We propose a novel algorithm based on inexact GMRES methods for linear response calculations in density functional theory. Such calculations require iteratively solving a nested linear problem $\mathcal{E} \delta\rho = b$ to obtain the variation of the electron density $\delta \rho$. Notably each application of the dielectric operator $\mathcal{E}$ in turn requires the iterative solution of multiple linear systems, the Sternheimer equations. We develop computable bounds to estimate the accuracy of the density variation given the tolerances to which the Sternheimer equations have been solved. Based on this result we suggest reliable strategies for adaptively selecting the convergence tolerances of the Sternheimer equations, such that each applications of $\mathcal{E}$ is no more accurate than needed. Experiments on challenging materials systems of practical relevance demonstrate our strategies to achieve superlinear convergence as well as a reduction of computational time by about 40% while preserving the accuracy of the returned response solution. Our algorithm seamlessly combines with standard preconditioning approaches known from the context of self-consistent field problems making it a promising framework for efficient response solvers based on Krylov subspace techniques.