Finite-element method for electronic structure.
Finite-element method for electronic structure.
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DOI：
10.1103/physrevb.39.5819
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发表时间：
1989-03
期刊：
影响因子：
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通讯作者：
Steven R. White;John W. Wilkins;M. Teter
中科院分区：
文献类型：
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作者：
Steven R. White;John W. Wilkins;M. Teter
讨论了有限元法在电子结构计算中的应用。利用正交或非正交一维有限元形状函数的乘积在三次网格上形成三维基函数。这些函数的严格局部性意味着任何局部算子的矩阵都非常稀疏，使得计算次数与基函数(N)的数量成正比成为可能。通过减小网格间距可以提高全局基的完备性，通过增加每个站点基函数的数量可以提高局部基的完备性。我们讨论了在O(N)时间内求解泊松方程和单粒子薛定谔方程基态的算法，包括高效的多重网格法。给出了H、H/sub 2//sup +/、He和H/sub 2/使用多达50万个基函数的试验计算结果。
We discuss the use of the finite-element method in electronic-structure calculations. Products of orthogonal or nonorthogonal one-dimensional (1D) finite-element shape functions are used to form 3D basis functions on a cubic grid. The strict locality of these functions means that the matrix for any local operator is very sparse, making calculation times proportional to the number of basis functions (N) possible. The completeness of the basis can be increased globally by decreasing the grid spacing and locally by increasing the number of basis functions per site. We discuss algorithms, including the highly efficient multigrid method, for solving the Poisson equation and for the ground state of the single-particle Schroedinger equation in O(N) time. Results are presented for test calculations of H, H/sub 2//sup +/, He, and H/sub 2/ using as many as 500 000 basis functions.