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


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)


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

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.


Zuletzt aktualisiert 2019-02-04 um 11:10