On optimizing Jacobi-Davidson method for calculating eigenvalues in low dimensional structures using eight band k . p model
On optimizing Jacobi-Davidson method for calculating eigenvalues in low dimensional structures using eight band k . p model
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DOI：
10.1016/j.jcp.2013.04.003
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发表时间：
2013-09-15
影响因子：
4.1
通讯作者：
Andrzejewski, Janusz
中科院分区：
文献类型：
--
作者：
Andrzejewski, Janusz
本文提出了两种改进Jacobi-Davidson法计算八带k描述的特征值和特征向量的方法。量子点和其他低维结构的p模型。首先，通过应用时间反演对称算子，对该方法进行了推广。这种扩展允许有效的计算存在于多频带k的双重简并。p模型和其他内部特征值。第二，八阶k离散化后不定矩阵的预条件子。p哈密顿量。这种预条件子的构造是基于对k中能带结构的物理考虑。p模型。基于两个真实的例子，结果表明，尽管预处理器和Hamilton的内存使用量相当，但预处理器可以显着缩短计算内部特征值所需的时间。最后介绍了实现八频段k . p哈密顿量和本征解。(c)2013 Elsevier Inc. All rights reserved.
The paper presents two ways of improving the Jacobi-Davidson method for calculating the eigenvalues and eigenvectors described by eight-band k . p model for quantum dots and other low dimensional structures. First, the method is extended by the application of time reversal symmetry operator. This extension allows efficient calculations of the twofold degeneracy present in the multiband k . p model and other interior eigenvalues. Second, the preconditioner for the indefinite matrix which comes from the discretization of the eight band k . p Hamiltonian is presented. The construction of this preconditioner is based on physical considerations about energy band structure in the k . p model. On the basis of two real examples, it is shown that the preconditioner can significantly shorten the time needed to calculate the interior eigenvalues, despite the fact that the memory usage of the preconditioner and Hamiltionian is comparable. Finally, some technical details for implementing the eight band k . p Hamiltonian and the eigensolver are provided. (c) 2013 Elsevier Inc. All rights reserved.