DeepAI AI Chat
Log In Sign Up

Data-based Adaptive Refinement of Finite Element Thin Plate Spline

by   L. Fang, et al.
Huaqiao University
Australian National University

The thin plate spline, as introduced by Duchon, interpolates a smooth surface through scattered data. It is computationally expensive when there is a large number of data points. The finite element thin plate spline (TPSFEM) possesses similar smoothing properties and is efficient for large data sets. Its efficiency is further improved by adaptive refinement that adapts the precision of the finite element grid. Adaptive refinement processes and error indicators developed for partial differential equations (PDEs) may not apply to the TPSFEM that incorporates information about the scattered data. This additional information results in features not evident in PDEs. An iterative adaptive refinement process and four error indicators were adapted for the TPSFEM. We give comprehensive depictions of the process in this article and evaluate the error indicators through a numerical experiment with two bathymetric surveys in square and L-shaped domains.


page 13

page 14

page 16


Smooth digital terrain modelling in irregular domain using adaptive finite element thin plate spline smoother

Digital terrain models of geological information occasionally require sm...

Subdivision surfaces with isogeometric analysis adapted refinement weights

Subdivision surfaces provide an elegant isogeometric analysis framework ...

IFISS3D: A computational laboratory for investigating finite element approximation in three dimensions

IFISS is an established MATLAB finite element software package for study...

An MP-DWR method for h-adaptive finite element methods

In a dual weighted residual based adaptive finite element method for sol...

Tensor B-Spline Numerical Methods for PDEs: a High-Performance Alternative to FEM

Tensor B-spline methods are a high-performance alternative to solve part...

An adaptive finite element/finite difference domain decomposition method for applications in microwave imaging

A new domain decomposition method for Maxwell's equations in conductive ...

Scalable adaptive PDE solvers in arbitrary domains

Efficiently and accurately simulating partial differential equations (PD...