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Isogeometric Analysis (IGA)

Isogeometric Analysis (IGA)

The main idea behind Isogeoemtric Analysis (IGA) is to improve the interoperability between design, i.e., Computer Aided Design (CAD) and analysis, i.e., Finite Element Method (FEM). To achieve this IGA use CAD mathematical primitives, i.e., splines and NURBS, to represent both the finite element (FE) geometry as well as the Partial Differential Equation (PDE) unknowns (e.g. the displacements in structural mechanics). In this manner one may represent the geometry in the FE-analysis exactly similar to the designed geometry. Furthermore, the smoothness of splines is useful in improving the accuracy per degree of freedom and solving higher order PDEs via direct approximations.

IGA activity at SINTEF

SINTEF have made innovative contributions to IGA and together with NTNU (Department of Mathematical Sciences and Department Structural Mechanics) and UiO (Department of Mathmatics) represent the Norwegian IGA Node (NIGAN) that is among the worlds leading groups of IGA education, research and software development. In particular, we have pioneered the Local Refined B-Splines (LR B-splines) both as a computational geometry tool (Dokken et al. 2013) and as an adaptive analysis tool (Johannessen et al. 2014; Kumar et al. 2015; Kumar et al. 2017).  In (Stahl et al. 2017) we show how we may enable interoperability (similar mathematical representation of geometry and physical unknowns) throughout the design, analysis and visualization process.

Tor Dokken, Tom Lyche, Kjell Fredrik Pettersen (2013): "Polynomial splines over locally refined box-partitions", Computer Aided Geometric Design, 30:331-356, 2013.

Kjetil André Johannessen, Trond Kvamsdal, Tor Dokken (2014): "Isogeometric analysis using LR B-splines", Computer Methods in Applied Mechanics and Engineering, 269: 471-514, 2014.

Mukesh Kumar, Trond Kvamsdal and Kjetil A. Johannessen (2015): "Simple a posteriori error estimators in adaptive isogeometric analysis", Computers and Mathematics with Applications, 70: 1555-1582, 2015.

Mukesh Kumar, Trond Kvamsdal and Kjetil A. Johannessen (2017): "Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis", Computer Methods in Applied Mechanics and Engineering, 316: 1086-1156, 2017.

 

Annette Stahl, Trond Kvamsdal, Christian Schellewald (2017): "Post-processing and visualization techniques for isogeometric analysis results",  Computer Methods in Applied Mechanics and Engineering,  316:880-943, 2017.

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Senior Research Scientist