IGS: An IsoGeometric approach for smoothing on surfaces

IGS: an IsoGeometric approach for Smoothing on surfaces

On Isogeometric Subdivision Methods for PDEs on Surfaces

Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an isogeometric discretization approach to partial differential equations on surfaces using subdivision methodology. Elliptic equations with the Laplace-Beltra...

Spline Smoothing on Surfaces

We present a method for estimating functions on topologically and/or geometrically complex surfaces from possibly noisy observations. Our approach is an extension of spline smoothing, using a Þnite element method. The paper has a substantial tutorial component: we start by reviewing smoothness measures for functions deÞned on surfaces, simplicial surfaces and differentiable structures on such s...

Isogeometric Analysis of Electrophysiological Models on Surfaces

In this project we numerically simulate electrophysiological models for cardiac applications by means of Isogeometric Analysis. Specifically, we aim at understanding the advantages of using high order continuous NURBS (Non-Uniform Rational B-Splines) basis functions in the approximation of the traveling waves of the action potential. As application, we consider the numerical simulations on the ...

Isogeometric analysis for second order partial differential equations on surfaces

We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitates the encapsulation of the exact geometrical description of the manifold in the analysis when this is represented by B–splines or NURBS. Our ...