Mathematical Problems in Engineering

Research Article

Adjoint Variable Method for the Study of Combined Active and Passive Magnetic Shielding

Table 1

Comparison of optimization techniques concerning calculation time (CPU) and optimal cost value 𝐹 m i n for several shielding problems.
Optimized parametersGeneticGradient conv.Gradient adjoint
Pas.Act.CPU 𝐹 m i n CPU 𝐹 m i n CPU 𝐹 m i n
1a ℎ p ( 𝜇 r = 1 )—1h 24' 29”4.39243' 15”4.39248' 10”4.3939
1b ℎ p ( 𝜇 r = 3 7 2 )—1h 00' 39”2.95626' 28”2.95629' 24”3.1376
2— 𝐼 r 1 , 𝐼 i 1 , 𝑟 1 2h 19' 33”2.90239' 31”2.916611' 20”2.9194
3a ℎ p ( 𝜇 r = 3 7 2 ) 𝐼 r 1 , 𝐼 i 1 , 𝑟 1 2h 19' 45”2.90778' 40”2.928511' 59”3.0154
3b8' 13”2.91008' 15”2.9681
4— 𝐼 r 𝑖 , 𝐼 i 𝑖 , 𝑟 𝑖 , 𝑖 = 1 ⋯ 3 2h 48' 01”2.86351h 16' 54”3.052316' 13”2.9832