Approximation of fractional harmonic maps

04/20/2021
by   Harbir Antil, et al.
0

This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet energy on unit-length vector fields. We devise and analyze numerical methods for the approximation of various partial differential equations related to fractional harmonic maps. The compactness results imply the convergence of numerical approximations. Numerical examples on spin chain dynamics and point defects are presented to demonstrate the effectiveness of the proposed methods.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/11/2022

Higher order graded mesh scheme for time fractional differential equations

In this article, we propose a higher order approximation to Caputo fract...
research
09/27/2022

Benchmarking Numerical Algorithms for Harmonic Maps into the Sphere

We numerically benchmark methods for computing harmonic maps into the un...
research
08/17/2022

Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints

An error estimate for a canonical discretization of the harmonic map hea...
research
09/24/2022

Quasi-optimal error estimates for the approximation of stable harmonic maps

Based on a quantitative version of the inverse function theorem and an a...
research
01/27/2021

Consistent approximation of fractional order operators

Fractional order controllers become increasingly popular due to their ve...
research
09/23/2022

Rational approximation preconditioners for multiphysics problems

We consider a class of mathematical models describing multiphysics pheno...
research
05/24/2023

Harmonic Measures and Numerical Computation of Cauchy Problems for Laplace Equations

It is well known that Cauchy problem for Laplace equations is an ill-pos...

Please sign up or login with your details

Forgot password? Click here to reset