Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4964240 | Computer Methods in Applied Mechanics and Engineering | 2017 | 59 Pages |
Abstract
We develop a multi-degree polar spline framework with applications to both geometric modeling and isogeometric analysis. First, multi-degree splines are introduced as piecewise non-uniform rational B-splines (NURBS) of non-uniform or variable polynomial degree, and a simple algorithm for their construction is presented. Then, an extension to two-dimensional polar configurations is provided by means of a tensor-product construction with a collapsed edge. Suitable combinations of these basis functions, encoded in a so-called isogeometric analysis suitable extraction operator, yield Ck smooth polar splines for any kâ¥0. We show that it is always possible to construct a set of smooth polar spline basis functions that form a convex partition of unity and possess locality. Explicit constructions for kâ{0,1,2} are presented. Optimal approximation behavior is observed numerically, and examples of applications to free-form design, smooth hole-filling, and high-order partial differential equations demonstrate the applicability of the developed framework.
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Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Deepesh Toshniwal, Hendrik Speleers, René R. Hiemstra, Thomas J.R. Hughes,