Fast computation of close-coupling exchange integrals using polynomials in a tree representation

Wallerberger M.; Igenbergs K.; Schweinzer J.; Aumayr F.

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Fast computation of close-coupling exchange integrals using polynomials in a tree representation

机译：在树形表示中使用多项式的近耦合交换积分的快速计算

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The semi-classical atomic-orbital close-coupling method is a well-known approach for the calculation of cross sections in ion-atom collisions. It strongly relies on the fast and stable computation of exchange integrals. We present an upgrade to earlier implementations of the Fourier-transform method. For this purpose, we implement an extensive library for symbolic storage of polynomials, relying on sophisticated tree structures to allow fast manipulation and numerically stable evaluation. Using this library, we considerably speed up creation and computation of exchange integrals. This enables us to compute cross sections for more complex collision systems.

机译：半古典原子轨道近耦合方法是用于计算离子原子碰撞中的横截面的众所周知的方法。它强烈依赖于交换积分的快速和稳定计算。我们升级到傅立叶变换方法的早期实现。为此目的，我们实现了一个广泛的文库，用于多项式的符号存储，依赖于复杂的树结构来允许快速操作和数值稳定的评估。使用此库，我们相当加快了Exchange积分的创建和计算。这使我们能够计算更复杂的碰撞系统的横截面。

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来源
《Computer physics communications》 |2011年第3期|共4页
作者
Wallerberger M.; Igenbergs K.; Schweinzer J.; Aumayr F.;
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作者单位

Institute of Applied Physics TU Wien - Vienna Univ. of Technology Association Euratom-?AW 1040 Vienna Austria;

Institute of Applied Physics TU Wien - Vienna Univ. of Technology Association Euratom-?AW 1040 Vienna Austria;

Max-Planck-Institut für Plasmaphysik Association Euratom 85748 Garching Germany;

Institute of Applied Physics TU Wien - Vienna Univ. of Technology Association Euratom-?AW 1040 Vienna Austria;

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原文格式 PDF
正文语种 eng
中图分类计算机的应用;
关键词
Close-coupling; Exchange integral; Polynomial; Symbolic manipulations;

机译：近耦合;交换积分;多项式;象征性操纵;

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1. Fast computation of close-coupling exchange integrals using polynomials in a tree representation [J] . Wallerberger M., Igenbergs K., Schweinzer J., Computer physics communications . 2011,第3期

机译：在树形表示中使用多项式的近耦合交换积分的快速计算
2. Precise and fast computation of generalized Fermi-Dirac integral by parameter polynomial approximation [J] . Fukushima Toshio Applied mathematics and computation . 2015,第Null期

机译：通过参数多项式逼近精确快速计算广义Fermi-Dirac积分
3. Integral Representations for the Lagrange Polynomials, Shively's Pseudo-Laguerre Polynomials, and the Generalized Bessel Polynomials [J] . H. M. Srivastava, Shy-Der Lin, Shuoh-Jung Liu, Russian journal of mathematical physics . 2012,第1期

机译：Lagrange多项式，Shively的伪Laguerre多项式和广义Bessel多项式的积分表示
4. Faster Steiner Tree Computation in Polynomial-Space [C] . Fedor V. Fomin, Fabrizio Grandoni, Dieter Kratsch Algorithms - ESA 2008 . 2008

机译：多项式空间中的Steiner树计算更快
5. Computational uses of receptive field scatter: Sparse image representation, fast nonlinear diffusion, and image segmentation. [D] . Bomberger, Neil Alan. 2005

机译：感受野散射的计算用途：稀疏的图像表示，快速的非线性扩散和图像分割。
6. Representation of ... formula ...-Bernstein polynomials in terms of ... formula ...-Jacobi polynomials [O] . F Soleyman, I Area, M Masjed-Jamei, -1

机译：... ... ...-Bernstein多项式的表示形式... ... ... -Jacobi多项式
7. Fast computation of close-coupling exchange integrals using polynomials in a tree representation [O] . Wallerberger, M., Igenbergs, K., Schweinzer, J., 2011

机译：使用树表示中的多项式快速计算紧耦合交换积分

Fast computation of close-coupling exchange integrals using polynomials in a tree representation

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