Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis

Cohen, Elaine; Martín, Tobías; Kirby, Robert M.; Lyche, Tom; Riesenfeld, Richard F.

doi:10.1016/j.cma.2009.09.010

Cited by 177 publications

(95 citation statements)

References 21 publications

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“…It is evident from the previous work, that most of the techniques used for surface construction method are based on optimization [5,16,17]. Optimization methods for surface construction deal with bigger number of variables like control points, knot vector and order of the B-spline surface and are also subjected to many nonlinear constraints.…”

Section: Surface Fittingmentioning

confidence: 99%

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

Gondegaon¹,

Voruganti²

2017

Journal of Theoretical and Applied Mechanics

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Isogeometric Analysis (IGA) involves unification of modelling and analysis by adopting the same basis functions (splines), for both. Hence, spline based parametric model is the starting step for IGA. Representing a complex domain, using parametric geometric model is a challenging task. Parameterization problem can be defined as, finding an optimal set of control points of a B-spline model for exact domain modelling. Also, the quality of parameterization, too has significant effect on IGA. Finding the B-spline control points for any given domain, which gives accurate results is still an open issue. In this paper, a new planar B-spline parameterization technique, based on domain mapping method is proposed. First step of the methodology is to map an input (non-convex) domain onto a unit circle (convex) with the use of harmonic functions. The unique properties of harmonic functions: global minima and mean value property, ensures the mapping is bi-jective and with no selfintersections. Next step is to map the unit circle to unit square to make it apt for B-spline modelling. Square domain is re-parameterized by using conventional centripetal method. Once the domain is properly parameterized, the required control points are computed by solving the B-spline tensor product equation. The proposed methodology is validated by applying the developed B-spline model for a static structural analysis of a plate, using isogeometric analysis. Different domains are modelled to show effectiveness of the given technique. It is observed that the proposed method is versatile and computationally efficient.

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Section: Surface Fittingmentioning

confidence: 99%

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

Gondegaon¹,

Voruganti²

2017

Journal of Theoretical and Applied Mechanics

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“…The equivalent challenge is now to specify the interior control points given the boundary control points [34,2,11]. This problem is sketched in Fig.…”

Section: The Challenge: Parametrize the Interiormentioning

confidence: 99%

“…This accuracy needs to be estimated, which can be done by comparing the solutions from several analyses or by evaluating the residual. In any case, when using methods in this class we aim at analysis-aware parametrizations [34,2]. The quality measure for these methods depends not only on the parametrization, but also on the solution to the PDE at hand (the Poisson problem (1) in our case).…”

Section: Analysis-oriented Measuresmentioning

confidence: 99%

“…A key ingredient of isogeometric analysis is the parametrization of the physical domain over which the PDE is posed, in many ways analogous to mesh generation in standard finite element analysis. Just as mesh quality affects the accuracy of a finite element approximation, the quality of the parametrization affects the accuracy of isogeometric analysis, see [21,2,34,35].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Planar Parametrization in Isogeometric Analysis

Gravesen

Evgrafov

Nguyen

et al. 2014

Mathematical Methods for Curves and Surfaces

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Abstract. Before isogeometric analysis can be applied to solving a partial differential equation posed over some physical domain, one needs to construct a valid parametrization of the geometry. The accuracy of the analysis is affected by the quality of the parametrization. The challenge of computing and maintaining a valid geometry parametrization is particularly relevant in applications of isogemetric analysis to shape optimization, where the geometry varies from one optimization iteration to another. We propose a general framework for handling the geometry parametrization in isogeometric analysis and shape optimization. It utilizes an expensive non-linear method for constructing/updating a high quality reference parametrization, and an inexpensive linear method for maintaining the parametrization in the vicinity of the reference one. We describe several linear and non-linear parametrization methods, which are suitable for our framework. The non-linear methods we consider are based on solving a constrained optimization problem numerically, and are divided into two classes, geometry-oriented methods and analysisoriented methods. Their performance is illustrated through a few numerical examples.

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“…As a result, exact geometry is introduced into the analysis. The smooth basis can then be leveraged in analysis [5,6,7] and lead to innovative approaches to model design [8,9,10], analysis [11,12,13,14], optimization [15], and adaptivity [16,17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Robust Poisson Surface Reconstruction

Estellers

Scott

Tew

et al. 2015

Lecture Notes in Computer Science

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Abstract. We propose a method to reconstruct surfaces from oriented point clouds with non-uniform sampling and noise by formulating the problem as a convex minimization that reconstructs the indicator function of the surface's interior. Compared to previous models, our reconstruction is robust to noise and outliers because it substitutes the leastsquares fidelity term by a robust Huber penalty; this allows to recover sharp corners and avoids the shrinking bias of least squares. We choose an implicit parametrization to reconstruct surfaces of unknown topology and close large gaps in the point cloud. For an efficient representation, we approximate the implicit function by a hierarchy of locally supported basis elements adapted to the geometry of the surface. Unlike ad-hoc bases over an octree, our hierarchical B-splines from isogeometric analysis locally adapt the mesh and degree of the splines during reconstruction. The hierarchical structure of the basis speeds-up the minimization and efficiently represents clustered data. We also advocate for convex optimization, instead isogeometric finite-element techniques, to efficiently solve the minimization and allow for non-differentiable functionals. Experiments show state-of-the-art performance within a more flexible framework.

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Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis

Cited by 177 publications

References 21 publications

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

Planar Parametrization in Isogeometric Analysis

Robust Poisson Surface Reconstruction

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