PMC

Stress relaxation data for an idealized generalized Maxwell material with M=3 time constants, fit with M=1 ((a) and (e)), M=2 ((b) and (f)), M=3 ((c) and (g)), and M=4 ((d) and (h)) time constants.

Stress relaxation data for an idealized generalized Maxwell material with M=3 time constants, fit using the discrete spectral approach with 1000 time constants distributed equidistantly in log space over the interval 10^{− 1}s ≤ τ ≤ 10³s.

Simulation results of the multiscale solver compared with an LLG-only calculation. Both algorithms are applied to the same model with 14,512 elements. A permeability of is used for the material of the shields within the Maxwell solver. In order to get matching results at high fields one needs to use a saturated material law.

a Decaying wave for the Maxwell material model. Solid lines are the pressure along the pipe, for increasing times (every 0.15 s). The dashed line is (). Values: = 2 s, c = 5 m/s, T = 0.2 s and L = 10 m. b Decaying wave for the Maxwell material model. Solid lines are the pressure along the pipe, for increasing times (every 0.15 s). The dashed line is (). Values: = 0.2 s, c = 5 m/s, T = 0.2 s and L = 10 m. c Decaying wave for the Zener material model. Solid lines are the pressure along the pipe, for increasing times (every 0.15 s). Dashed lines are the exponential decaying for and for calculated with () and (), respectively. Values: = 2 s, = 4 m/s, =3 m/s, T = 0.2 s and L = 10 m. d Decaying wave for the Zener material model: Solid lines are the pressure along the pipe, for increasing times (every 0.15 s). Dashed lines are the exponential decaying for and calculated with () and for calculated with (). Values: = 0.2 s, = 4 m/s, =3 m/s, T = 0.2 s and L = 10 m. e Decaying wave for the Zener material model: Solid lines are the pressure along the pipe, for increasing times (every 0.15 s). Dashed lines are the exponential decaying for , and calculated with () and for calculated with (). Values: = 0.05 s, = 4 m/s, =3 m/s, T = 0.2 s and L = 10 m