Blending isogeometric analysis and local maximum entropy meshfree approximants
We present a method to blend local maximum entropy (LME) meshfree approximants and isogeometric analysis. The coupling strategy exploits the optimization program behind LME approximation, treats isogeometric and LME basis functions on an equal footing in the reproducibility constraints, but views th...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/116658 |
| Acceso en línea: | https://hdl.handle.net/2117/116658 https://dx.doi.org/10.1016/j.cma.2013.05.015 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometry, Algebraic Geometry High-fidelity geometry Isogeometric analysis Local refinement Max-ent approximants Volume discretization Geometria algebraica Geometria Classificació AMS::51 Geometry::51P05 Geometry and physics Classificació AMS::51 Geometry::51K Distance geometry Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional |
| Sumario: | We present a method to blend local maximum entropy (LME) meshfree approximants and isogeometric analysis. The coupling strategy exploits the optimization program behind LME approximation, treats isogeometric and LME basis functions on an equal footing in the reproducibility constraints, but views the former as data in the constrained minimization. The resulting scheme exploits the best features and overcomes the main drawbacks of each of these approximants. Indeed, it preserves the high fidelity boundary representation (exact CAD geometry) of isogeometric analysis, out of reach for bare meshfree methods, and easily handles volume discretization and unstructured grids with possibly local refinement, while maintaining the smoothness and non-negativity of the basis functions. We implement the method with B-Splines in two dimensions, but the procedure carries over to higher spatial dimensions or to other non-negative approximants such as NURBS or subdivision schemes. The performance of the method is illustrated with the heat equation, and linear and nonlinear elasticity. The ability of the proposed method to impose directly essential boundary conditions in non-convex domains, and to deal with unstructured grids and local refinement in domains of complex geometry and topology is highlighted by the numerical examples. |
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