An a posteriori verification method for generalized Hermitian eigenvalue problems in large-scale electronic state calculations
An a posteriori verification method for generalized Hermitian eigenvalue problems in large-scale electronic state calculations
复制标题
大规模电子态计算中广义埃尔米特特征值问题的后验验证方法
DOI：
10.1016/j.cam.2020.112830
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发表时间：
2020
影响因子：
2.4
通讯作者：
Takeo Hoshi,Takeshi Ogita,Katsuhisa Ozaki,Takeshi Terao
中科院分区：
文献类型：
--
作者：
Tanaka K.;Hoshi T.;Mochizuki I.;Hanada T.;Ichimiya A.;Hyodo T.;Takeo Hoshi,Takeshi Ogita,Katsuhisa Ozaki,Takeshi Terao
针对广义实对称特征值问题提出了一种后验验证方法，并将其应用于大规模电子态计算中的密集聚类特征值问题。该方法通过两阶段过程实现，其中通过现有数值库计算近似解，然后在适度的计算时间内进行验证。该过程返回每个区间中包含一个精确特征值的区间。对有机器件材料进行了测试计算，验证方法证实了所有精确的特征值在获得的区间内得到了很好的分离。该验证方法将集成到 EigenKernel (https://github.com/eigenkernel/) 中，EigenKernel 是用于广义特征值问题的各种并行求解器的中间件。这种事后验证方法在未来的计算科学中将非常重要。
An a posteriori verification method is proposed for the generalized real-symmetric eigenvalue problem and is applied to densely clustered eigenvalue problems in large-scale electronic state calculations. The proposed method is realized by a two-stage process in which the approximate solution is computed by existing numerical libraries and is then verified in a moderate computational time. The procedure returns intervals containing one exact eigenvalue in each interval. Test calculations were carried out for organic device materials, and the verification method confirms that all exact eigenvalues are well separated in the obtained intervals. This verification method will be integrated into EigenKernel (https://github.com/eigenkernel/), which is middleware for various parallel solvers for the generalized eigenvalue problem. Such an a posteriori verification method will be important in future computational science.