Analysis of high order fast interface tracking methods
type: Item
instance of: scholarly article
title: Analysis of high order fast interface tracking methods
zbMATH Open document ID: 1305.65176
author: Olof Runborg
published in: Numerische Mathematik
publication date: 2014-10-24T00:00:00Z
review text: The paper is devoted to the construction and analysis of fast high-order methods for tracking a front in a given velocity field. The methods begin with a high-order subdivision of the interface on which a multiresolution decomposition is based. Then it is shown that the associated wavelet vectors can be identified with the solutions to certain ordinary differential equations (ODEs). When numerically solving these ODEs, an important observation is that the step sizes of the solvers may be chosen in a way that depends on the wavelet scales. This allows to use computationally cheap methods for a large part of the work, and so the overall complexity is much smaller than in a straightforward approach. The author proves sufficient conditions on the stability properties of the ODE solver in order for the complete algorithm to be rapdily convergent. It turns out that, e.g., all explicit Runge-Kutta methods are admissible for properly chosen subdivision schemes.
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 6361285
zbMATH Keywords: interface tracking
zbMATH Keywords: velocity field
zbMATH Keywords: subdivision
zbMATH Keywords: wavelet
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: convergence
zbMATH Keywords: multiresolution
zbMATH Keywords: stability
zbMATH Keywords: algorithm
MaRDI profile type: Publication
full work available at URL: s00211-014-0613-5
OpenAlex ID: W2053777040
cites work: The Runge–Kutta Theory in a Nutshell
cites work: Coefficients for the study of Runge-Kutta integration processes
cites work: Fast geodesics computation with the phase flow method
cites work: Stationary subdivision
cites work: Two-Scale Difference Equations. I. Existence and Global Regularity of Solutions
cites work: Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
cites work: Normal multiresolution approximation of curves
cites work: Q3788458
cites work: A 4-point interpolatory subdivision scheme for curve design
cites work: Three-Dimensional Front Tracking
cites work: Front tracking for hyperbolic systems
cites work: A front-tracking method for viscous, incompressible multi-fluid flows
cites work: Normal multi-scale transforms for curves
cites work: Q5719651
cites work: Volume of fluid (VOF) method for the dynamics of free boundaries
cites work: A New Recurrence for Computing Runge–Kutta Truncation Error Coefficients
cites work: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
cites work: Smoothness of nonlinear median-interpolation subdivision
cites work: Normal Multi-scale Transforms for Surfaces
cites work: Fast interface tracking via a multiresolution representation of curves and surfaces
cites work: Convergence and \(C^1\) analysis of subdivision schemes on manifolds by proximity
cites work: Smoothness analysis of nonlinear subdivision schemes of homogeneous and affine invariant type
cites work: Q4010713
DOI: 10.1007/S00211-014-0613-5
description: scientific article; zbMATH DE number 6361285