Isogeometric Analysis of geometric Partial Differential Equations

被引:11
作者
Bartezzaghi, Andrea [1 ]
Dede, Luca [1 ]
Quarteroni, Alfio [1 ]
机构
[1] Ecole Polytech Fed Lausanne, MATHICSE Math Inst Computat Sci & Engn, CMCS Chair Modeling & Sci Comp, Stn 8, CH-1015 Lausanne, Switzerland
基金
瑞士国家科学基金会;
关键词
Geometric Partial Differential Equation; Surface; High order; Isogeometric Analysis; Mean curvature flow; Willmore flow; NAVIER-STOKES EQUATIONS; FINITE-ELEMENT-METHOD; MEAN-CURVATURE FLOW; WILLMORE FLOW; EVOLUTION-EQUATIONS; BOUNDARY-CONDITIONS; WAVE-PROPAGATION; SURFACES; DYNAMICS; FLUID;
D O I
10.1016/j.cma.2016.08.014
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We consider the numerical approximation of geometric Partial Differential Equations (PDEs) defined on surfaces in the 3D space. In particular, we focus on the geometric PDEs deriving from the minimization of an energy functional by L2-gradient flow. We analyze two energy functionals: the area, which leads to the mean curvature flow, a nonlinear second order PDE, and the Willmore energy, leading to the Willmore flow, a nonlinear fourth order POE. We consider surfaces represented by single patch tensor product NURBS and discretize the PDEs by means of NURBS-based Isogeometric Analysis in the framework of the Galerkin method. To approximate the high order geometric PDEs we use high order continuous NURBS basis functions. For the time discretization of the nonlinear geometric PDEs, we use Backward Differentiation Formulas (BDF) with extrapolation of the geometric quantities involved in the weak formulation of the problem; in this manner, we solve a linear problem at each time step. We report numerical results concerning the mean curvature and Willmore flows on different geometries of interest and we show the accuracy and efficiency of the proposed approximation scheme. (C) 2016 Elsevier B.V. All rights reserved.
引用
收藏
页码:625 / 647
页数:23
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