A stencil scaling approach for accelerating matrix-free finite element implementations

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autor(en): Drzisga D, Bauer S, Mohr M, Rüde U, Waluga C, Wohlmuth BI
Zeitschrift: SIAM Journal on Scientific Computing
Verlag: Society for Industrial and Applied Mathematics
Jahr der Veröffentlichung: 2018
Band: 40
Heftnummer: 6
Seitenbereich: C748--C778
ISSN: 1064-8275


Abstract

We present a novel approach to fast on-the-fly low order finite element assembly for scalar elliptic partial differential equations of Darcy type with variable coefficients optimized for matrix-free implementations. Our approach introduces a new operator that is obtained by appropriately scaling the reference stiffness matrix from the constant coefficient case. Assuming sufficient regularity, an a priori analysis shows that solutions obtained by this approach are unique and have asymptotically optimal order convergence in the - and the -norms on hierarchical hybrid grids. For the preasymptotic regime, we present a local modification that guarantees uniform ellipticity of the operator. Cost considerations show that our novel approach requires roughly one-third of the floating-point operations compared to a classical finite element assembly scheme employing nodal integration. Our theoretical considerations are illustrated by …



FAU-Autoren / FAU-Herausgeber

Bauer, Simon
Lehrstuhl für Informatik 10 (Systemsimulation)
Rüde, Ulrich Prof. Dr.
Lehrstuhl für Informatik 10 (Systemsimulation)


Autor(en) der externen Einrichtung(en)
Technische Universität München (TUM)


Zitierweisen

APA:
Drzisga, D., Bauer, S., Mohr, M., Rüde, U., Waluga, C., & Wohlmuth, B.I. (2018). A stencil scaling approach for accelerating matrix-free finite element implementations. SIAM Journal on Scientific Computing, 40(6), C748--C778. https://dx.doi.org/10.1137/17M1148384

MLA:
Drzisga, Daniel, et al. "A stencil scaling approach for accelerating matrix-free finite element implementations." SIAM Journal on Scientific Computing 40.6 (2018): C748--C778.

BibTeX: 

Zuletzt aktualisiert 2019-02-04 um 11:10