Título:
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Defining an2-disparity measure to check and improve the geometric accuracy of noninterpolating curved high-order meshes
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Autor/a:
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Ruiz Gironés, Eloi; Sarrate Ramos, Josep; Roca Navarro, Francisco Javier
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Otros autores:
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Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
Abstract:
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We define an2-disparity measure between curved high-order meshes and parameterized manifolds in terms of an2norm. The main application of the proposed definition is to measure and improve the distance between a curved
high-order mesh and a target parameterized curve or surface. The approach allows considering meshes with the nodes on top of the curve or surface (interpolative), or floating freely in the physical space (non-interpolative). To compute the
disparity measure, the average of the squared point-wise differences is minimized in terms of the nodal coordinates of an auxiliary parametric high-order mesh. To improve the accuracy of approximating the target manifold with a noninterpolating
curved high-order mesh, we minimize the square of the disparity measure expressed both in terms of the nodal coordinates of the physical and parametric curved high-order meshes. The proposed objective functions are
continuously differentiable and thus, we are able to use minimization algorithms that require the first or the second derivatives of the objective function. Finally, we present several examples that show that the proposed methodology
generates high-order approximations of the target manifold with optimal convergence rates for the geometric accuracy even when non-uniform parameterizations of the manifolds are prescribed. Accordingly, we can generate coarse curved high-order meshes significantly more accurate than finer low-order meshes that feature the same resolution. |
Abstract:
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Peer Reviewed |
Materia(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional -Geometric programming -Geometry -Interpolation -Parameterization -Continuously differentiable -Convergence rates -Geometric accuracy -High-order -High-order approximation -Minimization algorithms -Non-interpolative mesh -Optimal convergence -Geometria computacional -Classificació AMS::51 Geometry::51L Geometric order structures |
Derechos:
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http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Tipo de documento:
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Artículo - Versión presentada Objeto de conferencia |
Editor:
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Elsevier
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