Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 361, Issue -, Pages -Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2019.112776
Keywords
Assembly; Surrogate numerical methods; Isogeometric analysis; A priori error analysis
Funding
- European Union [800898]
- German Research Foundation, Germany through the Priority Programme 1648 Software for Exascale Computing (SPPEXA) [WO671/11-1]
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A new methodology in isogeometric analysis (IGA) is presented. This methodology delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed from element-scale quadrature formulas. To generate surrogate matrices, quadrature must only be performed on certain elements in the computational domain. This, in turn, determines only a subset of the entries in the final matrix. The remaining matrix entries are computed by a simple B-spline interpolation procedure. Poisson's equation, membrane vibration, plate bending, and Stokes' flow problems are studied. In these problems, the use of surrogate matrices has a negligible impact on solution accuracy. Because only a small fraction of the original quadrature must be performed, we are able to report beyond a fifty-fold reduction in overall assembly time in the same software. The capacity for even further speed-ups is clearly demonstrated. The implementation used here was achieved by a small number of modifications to the open-source IGA software library GeoPDEs Similar modifications could be made to other present-day software libraries. (C) 2019 Elsevier B.Y. All rights reserved.
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