Code for solving harmonic map heat flow (HMHF) into 2-spheres

Installation

matlab (at least R2022b) and ngsolve (latest version) are needed to run the code.

Usage

• RSHMHF_FD: BDF1/BDF2 + Finite difference discretizations with matlab for radially symmetric HMHF (RSHMHF)
  • "Discretization error analysis for a radially symmetric harmonic map heat flow problem" - Nguyen, Reusken (2025) arXiv
• RSHMHF_FE: BDF1/BDF2 + P1/P2 Finite element discretizations with ngsolve for RSHMHF
  • convex_lin: "Error analysis for a finite element discretization of a radially symmetric harmonic map heat flow problem" - Nguyen, Reusken (2025)
  • max_lin: "A comparative study of finite element methods for a class of harmonic map heat flow problems" - Nguyen, Reusken (2025)
• HMHF_FE: BDF1/BDF2 + P1/P2 Finite element discretizations wtih ngsolve for HMHF
  • Dim2d:
    • PPFEM: p.139 of "Computational Micromagnetism" - Andreas Prohl (2001) DOI
    • TFEM: "Higher-order linearly implicit full discretization of the Landau-Lifshitz-Gilbert equation" - Akrivis, Feischl, Kovács, Lubich (2021) DOI
    • CPFEM: "Constraint preserving implicit finite element discretization of harmonic map flow into spheres" - Bartels, Prohl (2007) DOI

Tests

Run the following in command line to test mesh size and time step convergence for P1 and BDF1 of RSHMHF FE

foo@bar:~$ python3 -m Tests.conv_RSHMHF_FE

Run the following in command line to test mesh size and time step convergence for P1 and BDF1 of PPFEM and TFEM of HMHF FE on unit disk in dimension 2

foo@bar:~$ python3 -m Tests.conv_HMHF2D_FE