کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4626122 1340511 2016 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
C1 finite elements on non-tensor-product 2d and 3d manifolds
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
C1 finite elements on non-tensor-product 2d and 3d manifolds
چکیده انگلیسی

Geometrically continuous (Gk) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are Ck also for non-tensor-product layout. This paper describes and analyzes one such concrete C1 geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed G1 surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Remarkably, for Poisson’s equation on the disk using interior vertices of valence 3 and symmetric layout, we observe O(h3) convergence in the L∞ norm for this family of elements. Numerical experiments confirm the elements to be effective for solving the trivariate Poisson equation on the solid cylinder, deformations thereof (a turbine blade), modeling and computing geodesics on smooth free-form surfaces via the heat equation, for solving the biharmonic equation on the disk and for Koiter-type thin-shell analysis.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 272, Part 1, 1 January 2016, Pages 148–158
نویسندگان
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