Isogeometrische Kollokationsverfahren für komplexe Modelle
Zusammenfassung der Projektergebnisse
In this project, several research tasks have been carried out with respect to isogeometric collocation. Firstly, a method based on isogeometric collocation at Gauss points has been developed. This method allows adaptive hierarchical refinement based on PHT-splines and has good efficiency (in terms of accuracy vs computational cost) when compared to standard Galerkin approaches. The proposed approach was tested on several benchmark problems from 2D linear elasticity. Next, several methods have been developed to take advantage of isogeometric (splinebased) discretizations particularly from the geometric parameterization point of view. A dynamic method was developed for modeling bas-relief geometries starting from a binary image, based on the solution of a time-dependent equation. This allows the creation of CAD-compatible shapes since the solution field can be directly used as the spline representation of the height for the bas-relief object. Moreover, an investigation on using the extended Loop subdivision in the context of isgeometric analysis was conducted. The proposed method showed good accuracy for solving PDEs on surfaces, particularly when high-order PDEs were considered, such as the biharmonic and triharmonic equation. Finally, we have applied isogeometric collocation methods to the study of the timeharmonic Helmholtz equation for acoustic problems. Two approaches have been considered, one based on enriched approximation spaces, and the other based on a boundary element method. The enrichment approach can significantly increase the accuracy of the solution, however, the matrix can become very ill-conditioned for fine meshes or a large number of enrichment functions. The plane wave entrenchments seem to be more effective than those based on generalized harmonic polynomials. Boundary element methods have also been used for the study of acoustic problems, where they are particularly advantageous on unbounded domains and have been applied to shape optimization problems.
Projektbezogene Publikationen (Auswahl)
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An adaptive isogeometric analysis collocation method with a recovery-based error estimator. Computer Methods in Applied Mechanics and Engineering, 345, 52-74.
Jia, Yue; Anitescu, Cosmin; Zhang, Yongjie Jessica & Rabczuk, Timon
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Isogeometric analysis for surface PDEs with extended Loop subdivision. Journal of Computational Physics, 398, 108892.
Pan, Qing; Rabczuk, Timon; Xu, Gang & Chen, Chong
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Dynamic spline bas-relief modeling with isogeometric collocation method. Computer Aided Geometric Design, 81, 101913.
Xu, Jinlan; Ling, Chengnan; Xu, Gang; Ji, Zhongping; Wu, Xiangyang & Rabczuk, Timon
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Enriched Isogeometric Collocation for two-dimensional time-harmonic acoustics. Computer Methods in Applied Mechanics and Engineering, 365, 113033.
Ayala, Tomás; Videla, Javier; Anitescu, Cosmin & Atroshchenko, Elena
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3D isogeometric boundary element analysis and structural shape optimization for Helmholtz acoustic scattering problems. Computer Methods in Applied Mechanics and Engineering, 384, 113950.
Shaaban, Ahmed Mostafa; Anitescu, Cosmin; Atroshchenko, Elena & Rabczuk, Timon
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An isogeometric Burton-Miller method for the transmission loss optimization with application to mufflers with internal extended tubes. Applied Acoustics, 185, 108410.
Shaaban, Ahmed Mostafa; Anitescu, Cosmin; Atroshchenko, Elena & Rabczuk, Timon
