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

Drzisga D, Bauer S, Mohr M, Rüde U, Waluga C, Wohlmuth BI (2018)

Publication Type: Journal article

Publication year: 2018


Publisher: Society for Industrial and Applied Mathematics

Book Volume: 40

Pages Range: C748--C778

Journal Issue: 6

URI: https://epubs.siam.org/doi/pdf/10.1137/17M1148384

DOI: 10.1137/17M1148384


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 …

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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://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.

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