Transverse demagnetizing factors of long rectangular bars. II. Numerical calculations for arbitrary susceptibility

For an infinitely long bar with rectangular cross section $\text{2a×2b}$ and constant susceptibility $\chi$ in a uniform transverse applied field $H_a$ along dimension a, the fluxmetric and magnetometric demagnetizing factors $N_{\mathrm{f,m}}$ as functions of $\mathrm{a/b}$ and $\chi$ are accurately computed using a finite-elements method. By comparison of the computed results with exact analytical results for $\text{χ=−1,0,∞}$ and with a set of conjugate relations derived in this work, the elements distributions have been optimized to give a minimum discretization error. This error is further greatly reduced in the final results of $N_{\mathrm{f,m}}$ by using an error correction approach previously proposed in a similar work for cylinders.