A distortion measure to validate and generate curved high-order meshes on CAD surfaces with independence of parameterization

This is the accepted version of the following article: [Gargallo-Peiró, A., Roca, X., Peraire, J., and Sarrate, J. (2016) A distortion measure to validate and generate curved high-order meshes on CAD surfaces with independence of parameterization. Int. J. Numer. Meth. Engng, 106: 1100–1130. doi: 10.1002/nme.5162], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5162/abstractA framework to validate and generate curved nodal high-order meshes on Computer-Aided Design (CAD) surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin-shell and 3D finite element analysis with unstructured high-order methods. First, we define a distortion (quality) measure for high-order meshes on parameterized surfaces that we prove to be independent of the surface parameterization. Second, we derive a smoothing and untangling procedure based on the minimization of a regularization of the proposed distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes to enforce that the nodes slide on the surfaces. Moreover, the proposed algorithm repairs invalid curved meshes (untangling), deals with arbitrary polynomial degrees (high-order), and handles with low-quality CAD parameterizations (independence of parameterization). Third, we use the optimization procedure to generate curved nodal high-order surface meshes by means of an a posteriori approach. Given a linear mesh, we increase the polynomial degree of the elements, curve them to match the geometry, and optimize the location of the nodes to ensure mesh validity. Finally, we present several examples to demonstrate the features of the optimization procedure, and to illustrate the surface mesh generation process.Peer ReviewedPostprint (author's final draft

Subsidies in an R&D growth model with elastic labor

This paper compares different subsidies in an R&D growth model with competitive suppliers of a final good and monopolistic suppliers of intermediate goods. Unlike existing studies with lump-sum taxes and fixed labor, we assume distortionary taxes and elastic labor, finding some new insights. First, subsidizing R&D investment is more effective than subsidizing final output or subsidizing the purchase of intermediate goods in terms of promoting growth. Second, in terms of raising welfare, the R&D subsidy may also be more effective than the other subsidies and all of them are dominated by their mix, but none can achieve the social optimum.

On the exchange of momentum over the open ocean

Author Posting. © American Meteorological Society, 2013. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 43 (2013): 1589–1610, doi:10.1175/JPO-D-12-0173.1.This study investigates the exchange of momentum between the atmosphere and ocean using data collected from four oceanic field experiments. Direct covariance estimates of momentum fluxes were collected in all four experiments and wind profiles were collected during three of them. The objective of the investigation is to improve parameterizations of the surface roughness and drag coefficient used to estimate the surface stress from bulk formulas. Specifically, the Coupled Ocean–Atmosphere Response Experiment (COARE) 3.0 bulk flux algorithm is refined to create COARE 3.5. Oversea measurements of dimensionless shear are used to investigate the stability function under stable and convective conditions. The behavior of surface roughness is then investigated over a wider range of wind speeds (up to 25 m s−1) and wave conditions than have been available from previous oversea field studies. The wind speed dependence of the Charnock coefficient α in the COARE algorithm is modified to , where m = 0.017 m−1 s and b = −0.005. When combined with a parameterization for smooth flow, this formulation gives better agreement with the stress estimates from all of the field programs at all winds speeds with significant improvement for wind speeds over 13 m s−1. Wave age– and wave slope–dependent parameterizations of the surface roughness are also investigated, but the COARE 3.5 wind speed–dependent formulation matches the observations well without any wave information. The available data provide a simple reason for why wind speed–, wave age–, and wave slope–dependent formulations give similar results—the inverse wave age varies nearly linearly with wind speed in long-fetch conditions for wind speeds up to 25 m s−1.This work was funded by the National Science Foundation Grant OCE04-24536 as part of the CLIVAR Mode Water Dynamics Experiment (CLIMODE) and the Office of Naval Research Grant N00014-05-1-0139 as part of the CBLAST-LOW program.2014-02-0

Constrained Texture Mapping And Foldover-free Condition

Texture mapping has been widely used in image processing and graphics to enhance the realism of CG scenes. However to perfectly match the feature points of a 3D model with the corresponding pixels in texture images, the parameterisation which maps a 3D mesh to the texture space must satisfy the positional constraints. Despite numerous research efforts, the construction of a mathematically robust foldover-free parameterisation subject to internal constraints is still a remaining issue. In this paper, we address this challenge by developing a two-step parameterisation method. First, we produce an initial parameterisation with a method traditionally used to solve structural engineering problems, called the bar-network. We then derive a mathematical foldover-free condition, which is incorporated into a Radial Basis Function based scheme. This method is therefore able to guarantee that the resulting parameterization meets the hard constraints without foldovers

Almost Isometric Mesh Parameterization through Abstract Domains

In this paper, we propose a robust, automatic technique to build a global hi-quality parameterization of a two-manifold triangular mesh. An adaptively chosen 2D domain of the parameterization is built as part of the process. The produced parameterization exhibits very low isometric distortion, because it is globally optimized to preserve both areas and angles. The domain is a collection of equilateral triangular 2D regions enriched with explicit adjacency relationships (it is abstract in the sense that no 3D embedding is necessary). It is tailored to minimize isometric distortion, resulting in excellent parameterization qualities, even when meshes with complex shape and topology are mapped into domains composed of a small number of large continuous regions. Moreover, this domain is, in turn, remapped into a collection of 2D square regions, unlocking many advantages found in quad-based domains (e. g., ease of packing). The technique is tested on a variety of cases, including challenging ones, and compares very favorably with known approaches. An open-source implementation is made available

Multilevel Solvers for Unstructured Surface Meshes

Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner