Tensor Numerical Methods in Quantum Chemistry
159,95 €
inkl. 7% MwSt. und
ggf. zzgl. Versand
<p>The conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality", that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multivariate functions and operators discretized on Cartesian grids thus reducing solution of the multidimensional integral-differential equations to 1D calculations. We explain basic tensor formats and algorithms and show how the orthogonal Tucker tensor decomposition originating from chemometrics made a revolution in numerical analysis, relying on rigorous results from approximation theory. Benefits of tensor approach are demonstrated in ab-initio electronic structure calculations. </p> <ul> <li>Computation of the 3D convolution integrals for functions with multiple singularities is replaced by a sequence of 1D operations, thus enabling accurate MATLAB calculations on a laptop using 3D uniform tensor grids of the size up to 10<sup>15</sup>. </li> <li>Fast tensor-based Hartree-Fock solver, incorporating the grid-based low-rank factorization of the two-electron integrals, serves as a prerequisite for economical calculation of the excitation energies of molecules. </li> <li>Tensor approach suggests efficient grid-based numerical treatment of the long-range electrostatic potentials on large 3D finite lattices with defects.The novel range-separated tensor format applies to interaction potentials of multi-particle systems of general type opening the new prospects for tensor methods in scientific computing. </li></ul> <p>This research monograph presenting the modern tensor techniques applied to problems in quantum chemistry may be interesting for a wide audience of students and scientists working in computational chemistry, material science and scientific computing. </p>
![Tensor Numerical Methods in Quantum Chemistry Tensor Numerical Methods in Quantum Chemistry](https://cos.richshop.de/servlet/images/9783110391374.jpg?w=300)
- Autor: Venera Khoromskaia / Boris N. Khoromskij
- Seitenzahl: 297
- Format: EPUB
- DRM: hard-drm (mit Kopierschutz)
- Erscheinungsdatum: 11.06.2018
- Herausgeber: DE GRUYTER