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Book chapter(2021)
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Harald van Brummelen, Cornelis Vuik, Matthias Möller, Clemens Verhoosel, Bernd Simeon, Bert Jüttler
With 66 participants from 14 countries, the 3rd Conference on Isogeometric Analysis and Applications 2018 was a successful continuation of the IGAA conference series that was started in 2012 in Linz, Austria and had its second edition in 2014 in Annweiler am Trifels, Germany. IGAA 2018 has brought together senior experts from academia and industry as well as young scientists standing at the beginning of their career to discuss the current state of the art in IGA and its potential for commercial application in industry. This book contains a selection of 12 papers addressing various aspects of IGA ranging from the mathematical analysis of approximation properties over the generation of analysis-suitable parametrizations and the efficient solution of linear systems of equations, to its use in practical applications. A conference like IGAA cannot be organized without external support. The organizers would like to thank the 4TU Applied Mathematics Institute (4TU.AMI), the TU Delft Institute for Computational Science and Engineering (DCSE), the J.M. Burgerscentrum, and the NWO Cluster Nonlinear Dynamics of Natural Systems (NDNS+) for generous financial support. Financial support from the European Commission through project MOTOR (GA no. 678727) is also greatly acknowledged. We finally would like to express our gratitude to Mrs. Deborah Dongor and her colleagues for taking care of the local organization of this event.
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With 66 participants from 14 countries, the 3rd Conference on Isogeometric Analysis and Applications 2018 was a successful continuation of the IGAA conference series that was started in 2012 in Linz, Austria and had its second edition in 2014 in Annweiler am Trifels, Germany. IGAA 2018 has brought together senior experts from academia and industry as well as young scientists standing at the beginning of their career to discuss the current state of the art in IGA and its potential for commercial application in industry. This book contains a selection of 12 papers addressing various aspects of IGA ranging from the mathematical analysis of approximation properties over the generation of analysis-suitable parametrizations and the efficient solution of linear systems of equations, to its use in practical applications. A conference like IGAA cannot be organized without external support. The organizers would like to thank the 4TU Applied Mathematics Institute (4TU.AMI), the TU Delft Institute for Computational Science and Engineering (DCSE), the J.M. Burgerscentrum, and the NWO Cluster Nonlinear Dynamics of Natural Systems (NDNS+) for generous financial support. Financial support from the European Commission through project MOTOR (GA no. 678727) is also greatly acknowledged. We finally would like to express our gratitude to Mrs. Deborah Dongor and her colleagues for taking care of the local organization of this event.
Journal article(2020)
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Alexander Shamanskiy, Michael Helmut Gfrerer, Jochen Hinz, Bernd Simeon
The construction of volumetric parametrizations for computational domains is a key step in the pipeline of isogeometric analysis. Here, we investigate a solution to this problem based on the mesh deformation approach. The desired domain is modeled as a deformed configuration of an initial simple geometry. Assuming that the parametrization of the initial domain is bijective and that it is possible to find a locally invertible displacement field, the method yields a bijective parametrization of the target domain. We compute the displacement field by solving the equations of nonlinear elasticity with the neo-Hookean material law, and we show an efficient variation of the incremental loading algorithm tuned specifically to this application. In order to construct the initial domain, we simplify the target domain's boundary by means of an L2-projection onto a coarse basis and then apply the Coons patch approach. The proposed methodology is not restricted to a single patch scenario but can be utilized to construct multi-patch parametrizations with naturally looking boundaries between neighboring patches. We illustrate its performance and compare the result to other established parametrization approaches on a range of two-dimensional and three-dimensional examples.
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The construction of volumetric parametrizations for computational domains is a key step in the pipeline of isogeometric analysis. Here, we investigate a solution to this problem based on the mesh deformation approach. The desired domain is modeled as a deformed configuration of an initial simple geometry. Assuming that the parametrization of the initial domain is bijective and that it is possible to find a locally invertible displacement field, the method yields a bijective parametrization of the target domain. We compute the displacement field by solving the equations of nonlinear elasticity with the neo-Hookean material law, and we show an efficient variation of the incremental loading algorithm tuned specifically to this application. In order to construct the initial domain, we simplify the target domain's boundary by means of an L2-projection onto a coarse basis and then apply the Coons patch approach. The proposed methodology is not restricted to a single patch scenario but can be utilized to construct multi-patch parametrizations with naturally looking boundaries between neighboring patches. We illustrate its performance and compare the result to other established parametrization approaches on a range of two-dimensional and three-dimensional examples.
