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dc.contributor.authorRuiz-Gironés, Eloi
dc.contributor.authorSarrate, Jose
dc.contributor.authorRoca, Xevi
dc.contributor.otherBarcelona Supercomputing Center
dc.identifier.citationRuiz-Gironés, Eloi; Sarrate, Jose; Roca, Xevi. Defining an L2-disparity Measure to Check and Improve the Geometric Accuracy of Non-interpolating Curved High-order Meshes. "Procedia Engineering", 2015, vol. 124, p. 122-134.
dc.description.abstractWe define an Full-size image L2-disparity measure between curved high-order meshes and parameterized manifolds in terms of an Full-size image L2 norm. 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 non-interpolating 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.
dc.description.sponsorshipThis research was partially supported by CONACYT-SENER ("Fondo Sectorial CONACYT SENER HIDROCARBUROS", gran contract 163723). The work of the corresponding author was partially supported by the Boeing CO. & US Air Force Office of Scientific Research & European Comission through the Boeing-MIT Alliance & Computational Math Program & Marie Sklodowska-Curie Actions (HiPerMeGaFlows project), respectively.
dc.format.extent13 p.
dc.rightsAttribution-NonCommercial-NoDerivs 4.0 International License
dc.subjectÀrees temàtiques de la UPC::Enginyeria electrònica
dc.subject.lcshGeometric analysis
dc.subject.otherHigh-order mesh
dc.subject.otherNon-interpolative mesh
dc.subject.otherDisparity between manifolds
dc.subject.otherGeometric accuracy
dc.subject.otherConvergence rate
dc.titleDefining an L2-disparity Measure to Check and Improve the Geometric Accuracy of Non-interpolating Curved High-order Meshes
dc.subject.lemacModels geomètrics
dc.description.peerreviewedPeer Reviewed
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/658853/EU/High-Performance Curved Meshing and Unstructured High-Order Galerkin Solvers for High-Fidelity Flow Simulation/HiPerMeGaFlowS
local.citation.publicationNameProcedia Engineering

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