CSV kind format, (semicolon ; separator, first row as header)
Decimal separator: "."

numerical_comparison_case1.csv
The theoretical magnetic field produced by a box-shapped lattice of magnetic particles centered at (0,0,0), along the central x-axis. The lattice is an orthogonal regular grid of 10*21*21 cubic particles (4410 particles). Size of particles 100 nm side length, distance between particles centers 200 nm. Particles Magnetization M 130000 A/m (direction x).
Comparison of results by different methods (FEA, bulk magnet analytical equations using an Average Magnetization, numerical iterative method simulating an increasing number of particles until results convergence)
Given the relatively low number of particles, the iterative method was finally used to calculate the whole 4410 group of particles with magnetization M (Superposition Principle).
The average magnetization used in the method of the same name was calculated as Mave 17950 A/m, the equivalent bulk magnet used the average magnetization method had dimensions 1.94.14.1 micrometers.

experimental_comparison.csv
Theoretical and experimental values of the magnetic field produced by a box-shapped part made of a composite material with high density of magnetic quasi-spherical particles (Fe3O4), for different amount of particles. Average size of particles 140 nm (size distribution already published in previous papers, referenced in related paper), density of Fe3O4 assumed 5000 kg/m^3 for calculations. Magnetic orientation of particles -X, remanence Mr of the material powder 44350 A/m, saturation magnetization Ms of the powder 381950 A/m (measured by VSM, see paper). The part always has dimensions 12x12xh mm, where h varies depending on the total amount (weigth) of the embedded particles (from 1 to 15 milligrams total). For details on the measurement method and the geometry of the part, see the paper.
Experimental field H is given (what that field is, is discussed in the papers, we assume it is related to the mean value of the Hx component along the sensor wire).
Calculated values are given, for the mean value of the calculated Hx along many points of the sensor wire positions (Hx_ave). These calculations are done by two methods, numeric (iterative) method, and the Analytical (Maverage) method.
The calculations are done twice for each method, first assuming that working point of the particles lays near remanence (Mr), secondly assuming they reorient and reach saturation (Ms).

