Reduced basis approximation and a posteriori error estimation: applications to elasticity problems in several parametric settings Article Swipe
D.B.P. Huynh
,
Federico Pichi
,
Gianluigi Rozza
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1801.06553
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1801.06553
In this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinley parametrized geometries. The essential ingredients of the methodology are: a Galerkin projection onto a low-dimensional space associated with a smooth "parametric manifold" - dimension reduction, an efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations - rapid convergence, an a posteriori error estimation procedures - rigorous and sharp bounds for the functional outputs related with the underlying solution or related quantities of interest, like stress intensity factor, and Offline-Online computational decomposition strategies - minimum marginal cost for high performance in the real-time and many-query (e.g., design and optimization) contexts. We present several illustrative results for linear elasticity problem in parametrized geometries representing 2D Cartesian or 3D axisymmetric configurations like an arc-cantilever beam, a center crack problem, a composite unit cell or a woven composite beam, a multi-material plate, and a closed vessel. We consider different parametrization for the systems: either physical quantities - to model the materials and loads - and geometrical parameters - to model different geometrical configurations - with isotropic and orthotropic materials working in plane stress and plane strain approximation. We would like to underline the versatility of the methodology in very different problems. As last example we provide a nonlinear setting with increased complexity.
Related Topics
Concepts
Mathematical optimization
Linear elasticity
Mathematics
Applied mathematics
Parametric statistics
Galerkin method
Elasticity (physics)
A priori and a posteriori
Orthotropic material
Basis function
Mathematical analysis
Finite element method
Structural engineering
Statistics
Materials science
Philosophy
Composite material
Epistemology
Engineering
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1801.06553
- https://arxiv.org/pdf/1801.06553
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4302420722
All OpenAlex metadata
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https://openalex.org/W4302420722Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1801.06553Digital Object Identifier
- Title
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Reduced basis approximation and a posteriori error estimation: applications to elasticity problems in several parametric settingsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
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2018Year of publication
- Publication date
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2018-01-19Full publication date if available
- Authors
-
D.B.P. Huynh, Federico Pichi, Gianluigi RozzaList of authors in order
- Landing page
-
https://arxiv.org/abs/1801.06553Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1801.06553Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/1801.06553Direct OA link when available
- Concepts
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Mathematical optimization, Linear elasticity, Mathematics, Applied mathematics, Parametric statistics, Galerkin method, Elasticity (physics), A priori and a posteriori, Orthotropic material, Basis function, Mathematical analysis, Finite element method, Structural engineering, Statistics, Materials science, Philosophy, Composite material, Epistemology, EngineeringTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.Lagrange) | 6 |
| abstract_inverted_index.composite | 142, 148 |
| abstract_inverted_index.contexts. | 113 |
| abstract_inverted_index.different | 159, 181, 210 |
| abstract_inverted_index.dimension | 43 |
| abstract_inverted_index.effective | 48 |
| abstract_inverted_index.efficient | 46 |
| abstract_inverted_index.essential | 23 |
| abstract_inverted_index.increased | 221 |
| abstract_inverted_index.intensity | 90 |
| abstract_inverted_index.interest, | 87 |
| abstract_inverted_index.isotropic | 186 |
| abstract_inverted_index.manifold" | 41 |
| abstract_inverted_index.materials | 171, 189 |
| abstract_inverted_index.nonlinear | 218 |
| abstract_inverted_index.problems. | 211 |
| abstract_inverted_index.real-time | 106 |
| abstract_inverted_index.underline | 202 |
| abstract_inverted_index.associated | 36 |
| abstract_inverted_index.elasticity | 16, 121 |
| abstract_inverted_index.estimation | 14, 67 |
| abstract_inverted_index.functional | 76 |
| abstract_inverted_index.geometries | 125 |
| abstract_inverted_index.many-query | 108 |
| abstract_inverted_index.parameters | 177 |
| abstract_inverted_index.posteriori | 12, 65 |
| abstract_inverted_index.procedures | 68 |
| abstract_inverted_index.projection | 31 |
| abstract_inverted_index.quantities | 85, 166 |
| abstract_inverted_index.reduction, | 44 |
| abstract_inverted_index.strategies | 96 |
| abstract_inverted_index.underlying | 81 |
| abstract_inverted_index."parametric | 40 |
| abstract_inverted_index.complexity. | 222 |
| abstract_inverted_index.geometrical | 176, 182 |
| abstract_inverted_index.geometries. | 21 |
| abstract_inverted_index.ingredients | 24 |
| abstract_inverted_index.methodology | 27, 207 |
| abstract_inverted_index.numerically | 57 |
| abstract_inverted_index.orthotropic | 188 |
| abstract_inverted_index.performance | 103 |
| abstract_inverted_index.versatility | 204 |
| abstract_inverted_index.axisymmetric | 131 |
| abstract_inverted_index.convergence, | 62 |
| abstract_inverted_index.illustrative | 117 |
| abstract_inverted_index.parametrized | 20, 124 |
| abstract_inverted_index.representing | 126 |
| abstract_inverted_index.approximation | 9 |
| abstract_inverted_index.computational | 94 |
| abstract_inverted_index.decomposition | 95 |
| abstract_inverted_index.optimization) | 112 |
| abstract_inverted_index.(hierarchical, | 5 |
| abstract_inverted_index.Offline-Online | 93 |
| abstract_inverted_index.approximation. | 197 |
| abstract_inverted_index.approximations | 59 |
| abstract_inverted_index.arc-cantilever | 135 |
| abstract_inverted_index.configurations | 132, 183 |
| abstract_inverted_index.identification | 53 |
| abstract_inverted_index.multi-material | 151 |
| abstract_inverted_index.low-dimensional | 34 |
| abstract_inverted_index.parametrization | 160 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |