Enhanced parametric shape descriptions in PGD-based space separated representations
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In this paper, a NURBS-based geometry representation is combined with a fully separated representation for allying efficiency and generality by addressing complex geometries, and some numerical examples are considered to prove the potential of the proposed methodology.Abstract:
Space separation within the Proper Generalized Decomposition—PGD—rationale allows solving high dimensional problems as a sequence of lower dimensional ones. In our former works, different geometrical transformations were proposed for addressing complex shapes and spatially non-separable domains. Efficient implementation of separated representations needs expressing the domain as a product of characteristic functions involving the different space coordinates. In the case of complex shapes, more sophisticated geometrical transformations are needed to map the complex physical domain into a regular one where computations are performed. This paper aims at proposing a very efficient route for accomplishing such space separation. A NURBS-based geometry representation, usual in computer aided design—CAD—, is retained and combined with a fully separated representation for allying efficiency (ensured by the fully separated representations) and generality (by addressing complex geometries). Some numerical examples are considered to prove the potential of the proposed methodology.read more
Citations
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Proper Generalized Decomposition for Parametric Study and Material Distribution Design of Multi-Directional Functionally Graded Plates Based on 3D Elasticity Solution.
TL;DR: In this paper, the Proper Generalized Decomposition (PGD) technique is adopted to solve the 3D elasticity problems in a high-dimensional parametric space, which is an a priori model order reduction technique that reduces the solution of 3D partial differential equations into a set of 1D ordinary differential equations.
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Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond
Ye Lu,Hengyang Li,Lei Zhang,Chanwook Park,Satyajit Mojumder,Stefan Knapik,Zhongsheng Sang,Shaoqiang Tang,Daniel W. Apley,Gregory J. Wagner,Wing Kam Liu +10 more
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Domain decomposition involving subdomain separable space representations for solving parametric problems in complex geometries
TL;DR: In this article , a domain decomposition technique combined with an enhanced geometry mapping based on the use of NURBS is considered for solving parametrized models in complex geometries (non simply connected) within the so-called proper generalized decomposition (PGD) framework, enabling the expression of the solution in each subdomain in a fully separated form, involving both the space and the model parameters.
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Parametric Analysis of Thick FGM Plates Based on 3D Thermo-Elasticity Theory: A Proper Generalized Decomposition Approach
TL;DR: In this paper , the general and well-known model reduction technique, PGD (Proper Generalized Decomposition), is used for parametric analysis of thermo-elasticity of FGMs (Functionally Graded Materials).
Journal ArticleDOI
Domain decomposition involving subdomain separable space representations for solving parametric problems in complex geometries
TL;DR: In this article , a domain decomposition technique combined with an enhanced geometry mapping based on the use of NURBS is considered for solving parametrized models in complex geometries (non simply connected) within the so-called proper generalized decomposition (PGD) framework, enabling the expression of the solution in each subdomain in a fully separated form, involving both the space and the model parameters.
References
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Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement
TL;DR: In this article, the concept of isogeometric analysis is proposed and the basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model.
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