极点展开法用于电子结构计算中一类参数化线性系统的求解
Pole expansion for solving a type of parametrized linear systems in electronic structure calculations
AI总结：
本文提出了一种求解参数化线性系统的新方法，通过线性组合少量固定参数的线性系统解来近似所有参数的解，适用于需大量不同参数或右端向量的情况，且易于并行化，已在苯分子和DNA分子的响应函数计算中验证。
摘要：
我们提出了一种求解参数化线性系统的新方法。在某些参数化假设下，所有参数的线性系统解可通过少量固定参数线性系统解的线性组合准确近似。结合直接求解器或预条件迭代求解器处理每个固定参数的线性系统，该方法特别适用于需要大量不同参数或右端向量解的情况。该方法也易于并行化。我们展示了该方法在电子结构理论中响应函数计算中的应用，并通过苯分子和DNA分子的数值性能验证了该方法。
英文摘要：
We present a new method for solving parametrized linear systems. Under certain assumptions on the parametrization, solutions to the linear systems for all parameters can be accurately approximated by linear combinations of solutions to linear systems for a small set of fixed parameters. Combined with either direct solvers or preconditioned iterative solvers for each linear system with a fixed parameter, the method is particularly suitable for situations when solutions to a large number of distinct parameters or a large number of right hand sides are required. The method is also simple to parallelize. We demonstrate the applicability of the method to the calculation of the response functions in electronic structure theory. We demonstrate the numerical performance of the method using a benzene molecule and a DNA molecule.
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