Cosmin Anitescu
Bauhaus University, Weimar
AlgorithmNumerical integrationMathematical analysisFinite element methodArtificial intelligenceResidualImage registrationBoundary value problemEstimatorExtended finite element methodContext (language use)Isogeometric analysisApplied mathematicsShape optimizationMathematicsComputer scienceFracture (geology)Artificial neural networkSpline (mathematics)Basis functionBoundary (topology)Boundary element methodDiscretizationPartial differential equation
52Publications
15H-index
1,427Citations
Publications 53
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Abstract null null null The capability of boundary element methods (BEM) for solving three-dimensional time harmonic Helmholtz acoustic scattering problems is presented in the framework of the isogeometric analysis (IGA). Both the CAD geometry and the physical boundary variables are approximated using Non-uniform Rational B-splines basis functions (NURBS) in an isogeometric setting. A detailed comparison between two null BEM null methods: the conventional boundary integral equation ( null null n...
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#1Rijul Singla (Oceaneering International)
#2Cosmin Anitescu (Bauhaus University, Weimar)H-Index: 15
Last. Xiaoying Zhuang (Leibniz University of Hanover)H-Index: 55
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#1Huilong Ren (Bauhaus University, Weimar)H-Index: 11
#2Xiaoying Zhuang (Leibniz University of Hanover)H-Index: 55
Last. Timon Rabczuk (Ton Duc Thang University)H-Index: 101
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Abstract Boundary conditions are critical to the partial differential equations (PDEs) as they constrain the PDEs ensuring a unique and well defined solution. Based on combinatorial and surgery theory of manifolds, we develop multi-element boundary conditions as the generalization of the traditional boundary conditions in classical mechanics: Dirichlet boundary conditions, Neumann boundary conditions and Robin boundary conditions. The multi-element boundary/domain conditions glue the physical qu...
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#1Jorge López (Bauhaus University, Weimar)H-Index: 2
#2Cosmin Anitescu (Bauhaus University, Weimar)H-Index: 15
Last. Timon Rabczuk (Ton Duc Thang University)H-Index: 101
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Abstract A method for isogeometric structural shape optimization using a multilevel approach and automated sensitivity analysis is presented in this work. The analysis mesh is obtained after carrying out successive refinements using the knot insertion and/or degree elevation algorithms, while retaining the coarse geometry for the domain design. Even though analytical sensitivities can be derived and implemented, they are prone to implementation errors and time consuming to derive. To circumvent ...
2 CitationsSource
#1Ahmed Mostafa Shaaban (Bauhaus University, Weimar)H-Index: 2
#2Cosmin Anitescu (Bauhaus University, Weimar)H-Index: 15
Last. Timon Rabczuk (Ton Duc Thang University)H-Index: 101
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Abstract The boundary element method (BEM) has been widely used for approximating the solution of the Helmholtz acoustic equation due to its superiority for handling unbounded domains by modeling only the inner boundaries and avoiding the truncation error, present in the finite element method (FEM). Non-uniform rational B-splines basis functions (NURBS) are used in an isogeometric setting to describe both the CAD geometries and the physical fields. Isogeometric analysis (IGA) is coupled with BEM...
4 CitationsSource
#1Jorge López (Bauhaus University, Weimar)H-Index: 2
#2Cosmin Anitescu (Bauhaus University, Weimar)H-Index: 15
Last. Naif Alajlan (KSU: King Saud University)H-Index: 28
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A method for shape optimization using Bezier triangles is introduced. The proposed procedure takes as input a CAD-compatible boundary representation of the domain and outputs an optimal design while maintaining an exact geometry representation at each iteration. The use of a triangular discretization allows the modeling of complex geometric domains, including voids, using a single patch. Some topology changes, such as those resulting from merging boundaries, can also be easily considered. An aut...
2 CitationsSource
#1Jorge López (Bauhaus University, Weimar)H-Index: 2
#2Cosmin Anitescu (Bauhaus University, Weimar)H-Index: 15
Last. Timon Rabczuk (Ton Duc Thang University)H-Index: 101
view all 3 authors...
Abstract This paper presents the development of a complete CAD-compatible framework for structural shape optimization in 3D. The boundaries of the domain are described using NURBS while the interior is discretized with Bezier tetrahedra. The tetrahedral mesh is obtained from the mesh generator software Gmsh. A methodology to reconstruct the NURBS surfaces from the triangular faces of the boundary mesh is presented. The description of the boundary is used for the computation of the analytical sen...
3 CitationsSource
#1Tomás Ayala (University of Chile)H-Index: 1
#2Javier Videla (UNSW: University of New South Wales)H-Index: 5
Last. Elena Atroshchenko (UNSW: University of New South Wales)H-Index: 11
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Abstract In this work, the isogeometric collocation (IGA-C) is paired with two types of enrichment: Plane Wave (PW-) and Generalized Harmonic Polynomial (GHP-) functions, to solve 2D-problems for the Helmholtz equation. A parametric study is conducted, and a detailed assessment of the performance of the method in a number of benchmark problems is provided. Three different collocation methods are tested for the non-enriched formulation, namely Greville abscissae (GA), Approximated Cauchy–Galerkin...
1 CitationsSource