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Efficient implementation of the fast multipole method
KTH, School of Biotechnology (BIO), Theoretical Chemistry.
KTH, School of Biotechnology (BIO), Theoretical Chemistry.
2006 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 125, no 8, 084106- p.Article in journal (Refereed) Published
Abstract [en]

A number of computational techniques are described that reduce the effort related to the continuous fast multipole method, used for the evaluation of Coulomb matrix elements as needed in Hartree-Fock and density functional theories. A new extent definition for Gaussian charge distributions is proposed, as well as a new way of dividing distributions into branches. Also, a new approach for estimating the error caused by truncation of multipole expansions is presented. It is found that the use of dynamically truncated multipole expansions gives a speedup of a factor of 10 in the work required for multipole interactions, compared to the case when all interactions are computed using a fixed multipole expansion order. Results of benchmark calculations on three-dimensional systems are reported, demonstrating the usefulness of our present implementation of the fast multipole method.

Place, publisher, year, edition, pages
2006. Vol. 125, no 8, 084106- p.
Keyword [en]
Electric charge; Error detection; Matrix algebra; Numerical methods; Probability density function; Coulomb matrix elements; Fast multipole method; Gaussian charge distributions; Computational methods
National Category
Theoretical Chemistry
Identifiers
URN: urn:nbn:se:kth:diva-6666DOI: 10.1063/1.2244565ISI: 000240237000010Scopus ID: 2-s2.0-33748258300OAI: oai:DiVA.org:kth-6666DiVA: diva2:11439
Note
QC 20100817Available from: 2006-12-19 Created: 2006-12-19 Last updated: 2010-08-17Bibliographically approved
In thesis
1. Fock Matrix Construction for Large Systems
Open this publication in new window or tab >>Fock Matrix Construction for Large Systems
2006 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

This licentiate thesis deals with quantum chemistry methods for large systems. In particular, the thesis focuses on the efficient construction of the Coulomb and exchange matrices which are important parts of the Fock matrix in Hartree--Fock calculations.The methods described are also applicable in Kohn--Sham Density FunctionalTheory calculations, where the Coulomb and exchange matrices areparts of the Kohn--Sham matrix. Screening techniques for reducing the computational complexity of bot Coulomb and exchange computations are discussed, as well as the fast multipole method, used for efficient computation of the Coulomb matrix.

The thesis also discusses how sparsity in the matrices occurring in Hartree--Fock and Kohn--Sham Density Functional Theory calculations can be used to achieve more efficient storage of matrices as well as more efficient operations on them.

As an example of a possible type of application, the thesis includes a theoretical study of Heisenberg exchange constants, using unrestricted Kohn--Sham Density Functional Theory calculations.

Place, publisher, year, edition, pages
Stockholm: KTH, 2006. viii, 28 p.
Keyword
quantum chemistry
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-4247 (URN)978-91-7178-535-0 (ISBN)
Presentation
2006-12-15, FD41, Albanova, Roslagstullsbacken 21, Stockholm, 11:15
Opponent
Supervisors
Note
QC 20101123Available from: 2006-12-19 Created: 2006-12-19 Last updated: 2010-11-23Bibliographically approved
2. Quantum Chemistry for Large Systems
Open this publication in new window or tab >>Quantum Chemistry for Large Systems
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis deals with quantum chemistry methods for large systems. In particular, the thesis focuses on the efficient construction of the Coulomb and exchange matrices which are important parts of the Fock matrix in Hartree-Fock calculations. Density matrix purification, which is a method used to construct the density matrix for a given Fock matrix, is also discussed.

The methods described are not only applicable in the Hartree-Fock case, but also in Kohn-Sham Density Functional Theory calculations, where the Coulomb and exchange matrices are parts of the Kohn-Sham matrix. Screening techniques for reducing the computational complexity of both Coulomb and exchange computations are discussed, including the fast multipole method, used for efficient computation of the Coulomb matrix.

The thesis also discusses how sparsity in the matrices occurring in Hartree-Fock and Kohn-Sham Density Functional Theory calculations can be used to achieve more efficient storage of matrices as well as more efficient operations on them.

Place, publisher, year, edition, pages
Stockholm: KTH, 2007. xi, 56 p.
Series
Trita-BIO-Report, ISSN 1654-2312 ; 2007:13
Keyword
quantum chemistry, fast multipole method, density matrix purification, sparse matrices
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-4561 (URN)978-91-7178-797-2 (ISBN)
Public defence
2007-12-12, FA32, Albanova, Roslagstullsbacken 21, 106 91 Stockholm, 13:00
Opponent
Supervisors
Note
QC 20100817Available from: 2007-12-04 Created: 2007-12-04 Last updated: 2010-08-17Bibliographically approved

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