
The parameteruniform convergence of a fitted operator method on nonuniform meshes for a singularly perturbed initial value problem
The parameteruniform convergence of a fitted operator method for a sing...
read it

Subdivision surfaces with isogeometric analysis adapted refinement weights
Subdivision surfaces provide an elegant isogeometric analysis framework ...
read it

Convergence Analysis of GradientBased Learning with NonUniform Learning Rates in NonCooperative MultiAgent Settings
Considering a class of gradientbased multiagent learning algorithms in...
read it

Convergence of the NonUniform Physarum Dynamics
Let c ∈Z^m_> 0, A ∈Z^n× m, and b ∈Z^n. We show under fairly general cond...
read it

NonUniform Stochastic Average Gradient Method for Training Conditional Random Fields
We apply stochastic average gradient (SAG) algorithms for training condi...
read it

Uniform Rates of Convergence of Some Representations of Extremes : a first approach
Uniform convergence rates are provided for asymptotic representations of...
read it

A locally mass conserving quadratic velocity, linear pressure element
By supplementing the pressure space for the TaylorHood element a triang...
read it
Tuned Hybrid NonUniform Subdivision Surfaces with Optimal Convergence Rates
This paper presents an enhanced version of our previous work, hybrid nonuniform subdivision surfaces [19], to achieve optimal convergence rates in isogeometric analysis. We introduce a parameter λ (1/4<λ<1) to control the rate of shrinkage of irregular regions, so the method is called tuned hybrid nonuniform subdivision (tHNUS). Our previous work corresponds to the case when λ=1/2. While introducing λ in hybrid subdivision significantly complicates the theoretical proof of G^1 continuity around extraordinary vertices, reducing λ can recover the optimal convergence rates when tuned hybrid subdivision functions are used as a basis in isogeometric analysis. From the geometric point of view, the tHNUS retains comparable shape quality as [19] under nonuniform parameterization. Its basis functions are refinable and the geometric mapping stays invariant during refinement. Moreover, we prove that a tuned hybrid subdivision surface is globally G^1continuous. From the analysis point of view, tHNUS basis functions form a nonnegative partition of unity, are globally linearly independent, and their spline spaces are nested. We numerically demonstrate that tHNUS basis functions can achieve optimal convergence rates for the Poisson's problem with nonuniform parameterization around extraordinary vertices.
READ FULL TEXT
Comments
There are no comments yet.