Fast multiresolution methods for density functional theory in nuclear physics
Fast multiresolution methods for density functional theory in nuclear physics
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DOI：
10.1088/1742-6596/180/1/012080
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发表时间：
2009-07
期刊：
影响因子：
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通讯作者：
G. Fann;J. Pei;J. Pei;R. Harrison;R. Harrison;J. Jia;Judith C. Hill;M. Y. Ou;W. Nazarewicz-W.-Nazarew
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作者：
G. Fann;J. Pei;J. Pei;R. Harrison;R. Harrison;J. Jia;Judith C. Hill;M. Y. Ou;W. Nazarewicz-W.-Nazarew
描述了一种基于实分析的O(N)快速算法，该算法基于函数和算符的多分辨分析和低分离秩次近似，用于求解三维Schrodinger方程和Lippman-Schwinger方程，具有高精度的自旋轨道势。每个运算符和波函数都有其自己的精化结构，以实现并保证所需的有限精度。据我们所知，这是第一次将这种自适应方法用于计算物理，甚至是在一维计算物理中。对于一个样本测试问题，每个波函数都得到了精确的解。自旋轨道势通常存在于半导体、量子化学、分子电子学和核物理的模拟中。以核结构理论为例，将我们的结果与用Hermite基和样条基直接对角化得到的结果进行了比较。
We describe a fast real-analysis based O(N) algorithm based on multiresolution analysis and low separation rank approximation of functions and operators for solving the Schrodinger and Lippman-Schwinger equations in 3-D with spin-orbit potential to high precision for bound states. Each of the operators and wavefunctions has its own structure of refinement to achieve and guarantee the desired finite precision. To our knowledge, this is the first time such adaptive methods have been used in computational physics, even in 1-D. Accurate solutions for each of the wavefunctions are obtained for a sample test problem. Spin orbit potentials commonly occur in the simulations of semiconductors, quantum chemistry, molecular electronics and nuclear physics. We compare our results with those obtained by direct diagonalization using the Hermite basis and the spline basis with an example from nuclear structure theory.