Abstract
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 H-1 - and the L-2-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 numerical tests that confirm the expectations with respect to accuracy and run-time. A large scale application with more than a hundred billion (1.6 . 10(11)) degrees of freedom executed on 14 310 compute cores demonstrates the efficiency of the new scaling approach.
Item Type: | Journal article |
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Faculties: | Geosciences > Department of Earth and Environmental Sciences |
Subjects: | 500 Science > 550 Earth sciences and geology |
ISSN: | 1064-8275 |
Language: | English |
Item ID: | 67873 |
Date Deposited: | 19. Jul 2019, 12:23 |
Last Modified: | 04. Nov 2020, 13:50 |