Complexity Analysis of a Fast Directional Matrix-Vector Multiplication

Günther Of; Raphael Watschinger

doi:10.1007/978-3-030-67077-1_3

Complexity Analysis of a Fast Directional Matrix-Vector Multiplication

Günther Of^*, Raphael Watschinger

^*Corresponding author for this work

Institute of Applied Mathematics (5040)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Abstract

We consider a fast, data-sparse directional method to realize matrix-vector products related to point evaluations of the Helmholtz kernel. The method is based on a hierarchical partitioning of the point sets and the matrix. The considered directional multi-level approximation of the Helmholtz kernel can be applied even on high-frequency levels efficiently. We provide a detailed analysis of the almost linear asymptotic complexity of the presented method. Our numerical experiments are in good agreement with the provided theory.

Original language	English
Title of host publication	High Performance Computing in Science and Engineering - 4th International Conference, HPCSE 2019, Revised Selected Papers
Subtitle of host publication	4th International Conference, HPCSE 2019, Karolinka, Czech Republic, May 20–23, 2019, Revised Selected Papers
Editors	Tomáš Kozubek, Peter Arbenz, Jiří Jaroš, Lubomír Říha, Jakub Šístek, Petr Tichý
Publisher	Springer, Cham
Pages	39-59
Number of pages	21
ISBN (Electronic)	978-3-030-67077-1
ISBN (Print)	978-3-030-67076-4
DOIs	https://doi.org/10.1007/978-3-030-67077-1_3
Publication status	Published - 2021
Event	HPCSE 2019: High Performance Computing in Science and Engineering - Karolinka, Czech Republic Duration: 20 May 2019 → 23 May 2019 http://hpcse.it4i.cz/HPCSE19/

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	12456
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	HPCSE 2019
Country/Territory	Czech Republic
City	Karolinka
Period	20/05/19 → 23/05/19
Internet address	http://hpcse.it4i.cz/HPCSE19/

Keywords

Helmholtz
Fast multipole method
Hierarchical matrix

ASJC Scopus subject areas

Numerical Analysis

Fields of Expertise

Information, Communication & Computing

Access to Document

10.1007/978-3-030-67077-1_3

https://www.applied.math.tugraz.at/berichte/Bericht0720.pdf

Cite this

Of, G., & Watschinger, R. (2021). Complexity Analysis of a Fast Directional Matrix-Vector Multiplication. In T. Kozubek, P. Arbenz, J. Jaroš, L. Říha, J. Šístek, & P. Tichý (Eds.), High Performance Computing in Science and Engineering - 4th International Conference, HPCSE 2019, Revised Selected Papers: 4th International Conference, HPCSE 2019, Karolinka, Czech Republic, May 20–23, 2019, Revised Selected Papers (pp. 39-59). (Lecture Notes in Computer Science; Vol. 12456). Springer, Cham. https://doi.org/10.1007/978-3-030-67077-1_3

Complexity Analysis of a Fast Directional Matrix-Vector Multiplication. / Of, Günther; Watschinger, Raphael.
High Performance Computing in Science and Engineering - 4th International Conference, HPCSE 2019, Revised Selected Papers: 4th International Conference, HPCSE 2019, Karolinka, Czech Republic, May 20–23, 2019, Revised Selected Papers. ed. / Tomáš Kozubek; Peter Arbenz; Jiří Jaroš; Lubomír Říha; Jakub Šístek; Petr Tichý. Springer, Cham, 2021. p. 39-59 (Lecture Notes in Computer Science; Vol. 12456).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Of, G & Watschinger, R 2021, Complexity Analysis of a Fast Directional Matrix-Vector Multiplication. in T Kozubek, P Arbenz, J Jaroš, L Říha, J Šístek & P Tichý (eds), High Performance Computing in Science and Engineering - 4th International Conference, HPCSE 2019, Revised Selected Papers: 4th International Conference, HPCSE 2019, Karolinka, Czech Republic, May 20–23, 2019, Revised Selected Papers. Lecture Notes in Computer Science, vol. 12456, Springer, Cham, pp. 39-59, HPCSE 2019, Karolinka, Czech Republic, 20/05/19. https://doi.org/10.1007/978-3-030-67077-1_3

Of G, Watschinger R. Complexity Analysis of a Fast Directional Matrix-Vector Multiplication. In Kozubek T, Arbenz P, Jaroš J, Říha L, Šístek J, Tichý P, editors, High Performance Computing in Science and Engineering - 4th International Conference, HPCSE 2019, Revised Selected Papers: 4th International Conference, HPCSE 2019, Karolinka, Czech Republic, May 20–23, 2019, Revised Selected Papers. Springer, Cham. 2021. p. 39-59. (Lecture Notes in Computer Science). doi: 10.1007/978-3-030-67077-1_3

Of, Günther ; Watschinger, Raphael. / Complexity Analysis of a Fast Directional Matrix-Vector Multiplication. High Performance Computing in Science and Engineering - 4th International Conference, HPCSE 2019, Revised Selected Papers: 4th International Conference, HPCSE 2019, Karolinka, Czech Republic, May 20–23, 2019, Revised Selected Papers. editor / Tomáš Kozubek ; Peter Arbenz ; Jiří Jaroš ; Lubomír Říha ; Jakub Šístek ; Petr Tichý. Springer, Cham, 2021. pp. 39-59 (Lecture Notes in Computer Science).

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Complexity Analysis of a Fast Directional Matrix-Vector Multiplication

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

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