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

<table>Total
conventional and adjoint gradients as a function of the height of the passive
shield for several <svg height="10.725" id="M159" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 13.9125 10.725" width="13.9125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.725)">
<g transform="translate(72,-63.42)">
<text transform="matrix(1,0,0,-1,-71.95,66.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜇</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.34,63.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">r</tspan>
</text>
</g>
</g>
</svg> and <svg height="14.4625" id="M160" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 86.887497 14.4625" width="86.887497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.4625)">
<g transform="translate(72,-60.43)">
<text transform="matrix(1,0,0,-1,-71.95,60.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜎</tspan>
<tspan style="font-size: 12.50px; " x="10.802592" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.842981" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="29.094481" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="32.22023" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="41.247398" y="0">×</tspan>
<tspan style="font-size: 12.50px; " x="52.024982" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="58.276482" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-7.41,65.96)">
<tspan style="font-size: 8.75px; " x="0" y="0">6</tspan>
</text>
</g>
</g>
</svg> S/m (no active
shield).</table>

Mathematical Problems in Engineering

fig6

Figure 6

Figure 6: Adjoint Variable Method for the Study of Combined Active and Passive Magnetic Shielding 