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

<table>Conventional and adjoint gradient of
all cost terms separately as a function of the height of the passive shield for <svg height="14.6" id="M153" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 41.112499 14.6" width="41.112499" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝜇</tspan>
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<text transform="matrix(1,0,0,-1,-64.34,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">r</tspan>
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<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">1</tspan>
</text>
</g>
</g>
</svg> and <svg height="14.4625" id="M154" 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>
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</svg> S/m (no active
shield).</table>

Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: Adjoint Variable Method for the Study of Combined Active and Passive Magnetic Shielding 