DOI: 10.11583/dtu.16558014.v1
title: Data set for "Direct Exchange Calculation for Unstructured Micromagnetic Meshes"

description: This is the data set for the paper [Poulsen, E. B., Insinga, A. R. and Bjørk, R., Direct exchange calculation for unstructured micromagnetic meshes, Journal of Magnetism and Magnetic Materials, 551, 169093, 2022]. The DOI for the publication is 10.1016/j.jmmm.2022.169093 .These data are located on the repository at data.dtu.dk, with DOI:10.11583/DTU.16558014 and URL: https://doi.org/10.11583/DTU.16558014 .The corresponding model used to run the experiments can be found on MagTense.org, DOI: 10.11583/DTU.16558014.<br>Analytical_function_results.txt:A series of second order partial derivative methods, Green-Gauss (GG), least squares (LSQR), Direct Laplacian (DL) and Second order finite differences were employed to calculate the exchange energy of a magnetic configuration according to three different magnetizations: Flower, Vortex and SinCos. The finite difference method was employed only on a Cartesian mesh, but the remaining methods were tested both on a Cartesian and a tetrahedral mesh. The file contains the relative error of the exchange energy as a function of mesh resolution for all of the weights.<br>Standard_problem_3_E_cross_finite_difference.txt:This file contains the cross-over energy in units of exchange length for the mumag standard problem 3 for a uniform square grid with the exchange energy calculated using a finite difference approach.<br>Standard_problem_3_E_cross_Cartesian_prisms_weights.txt:This file contains the cross-over energy in units of exchange length for the mumag standard problem 3 for a prism grid with prisms of uniform size. The number of tiles (N_tiles) are NxNxN, where N is the number of prisms in each dimension. The results for different weights in the exchange operators are given in different columns.<br>Standard_problem_3_E_cross_tetrahedral_weights.txt:This file contains the cross-over energy in units of exchange length for the mumag standard problem 3 for a tetrahedral grid (of similar-sized "N_grids" tetrahedrons). The results for different weights in the exchange operators are given in different columns.<br>Standard_problem_3_E_cross_unstructured_Cartesian_prisms_n_9_weight_8.txt:This file contains the cross-over energy in units of exchange length for the mumag standard problem 3 for a unstructured Cartesian grid. A weight factor of 8 has been used for the calculations. The grid consists of 9 grains with 2 refinement levels.<br>Standard_problem_3_E_cross_unstructured_tetrahedral_n_4_weight_8.txt:The cross-over energy in units of exchange length for the mumag standard problem 3 for a unstructured tetrahedral grid. A weight factor of 8 has been used for the calculations. The grid consists of 4 grains.<br>Standard_problem_4_abs_diff_finite_difference.txt:This file contains the sum of the absolute difference between calculated magnetization components and a mean of previously published solutions on the mumag webpage, integrated over the first 100 ns of the time evolution. The Cartesian grid is uniform and the exchange energy is calculated using a standard finite difference approach.<br>Standard_problem_4_abs_diff_Cartesiance_n_4_ref_1.txt:The sum of the absolute difference between calculated magnetization components and a mean of previously published solutions on the mumag webpage, integrated over the first 100 ns of the time evolution. The Cartesian grid consists of 4 grains with 1 refinement level.<br>Standard_problem_4_abs_diff_Cartesiance_n_4_ref_2.txt:The sum of the absolute difference between calculated magnetization components and a mean of previously published solutions on the mumag webpage, integrated over the first 100 ns of the time evolution. The Cartesian grid consists of 4 grains with 2 refinement levels.<br>Standard_problem_4_abs_diff_Cartesiance_n_9_ref_1.txt:The sum of the absolute difference between calculated magnetization components and a mean of previously published solutions on the mumag webpage, integrated over the first 100 ns of the time evolution. The Cartesian grid consists of 9 grains with 1 refinement level.<br>Standard_problem_4_abs_diff_Cartesiance_n_9_ref_2.txt:The sum of the absolute difference between calculated magnetization components and a mean of previously published solutions on the mumag webpage, integrated over the first 100 ns of the time evolution. The Cartesian grid consists of 9 grains with 2 refinement levels.