Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

<div class="floats-full-page floats-full-page-other"><h2>Table 5</h2><div class="floats-full-page-caption">Comparison of the micro-model to the macro-model as in Example <a href="../../938727/#ex3.6">3.6</a>. </div><div class="floats-full-page-content"><table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr /></td></tr><tr class="thead"><td align="left"><span style="width: 22.725px;"><svg height="19.0375" id="M514" style="vertical-align:-3.97134pt" version="1.1" viewbox="0 0 22.725 19.0375" width="22.725" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.0375)">
<g transform="translate(72,-56.77)">
<text transform="matrix(1,0,0,-1,-71.95,60.78)">
<tspan style="font-size: 12.50px; " x="0" y="0">ℎ</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.74,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="9.21">1</tspan>
<tspan style="font-size: 8.75px; " x="0" y="0">−</tspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 55.700001px;"><svg height="20.1625" id="M515" style="vertical-align:-5.32956pt" version="1.1" viewbox="0 0 55.700001 20.1625" width="55.700001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,20.1625)">
<g transform="translate(72,-55.87)">
<text transform="matrix(1,0,0,-1,-71.95,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">‖</tspan>
<tspan style="font-size: 12.50px; " x="6.5390692" y="0">𝑒</tspan>
</text>
<text transform="matrix(1,0,0,-1,-59.85,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑁</tspan>
<tspan style="font-size: 8.75px; " x="0" y="8.1300001">𝜀</tspan>
</text>
<text transform="matrix(1,0,0,-1,-51.11,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">‖</tspan>
</text>
<text transform="matrix(1,0,0,-1,-44.57,58.11)">
<tspan style="font-size: 8.75px; " x="0" y="0">∗</tspan>
<tspan style="font-size: 8.75px; " x="4.5772958" y="0">,</tspan>
<tspan style="font-size: 8.75px; " x="6.765296" y="0">𝐿</tspan>
</text>
<text transform="matrix(1,0,0,-1,-31.61,55.92)">
<tspan style="font-size: 6.25px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 55.700001px;"><svg height="20.1625" id="M516" style="vertical-align:-5.32956pt" version="1.1" viewbox="0 0 55.700001 20.1625" width="55.700001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,20.1625)">
<g transform="translate(72,-55.87)">
<text transform="matrix(1,0,0,-1,-71.95,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">‖</tspan>
<tspan style="font-size: 12.50px; " x="6.5390692" y="0">𝑒</tspan>
</text>
<text transform="matrix(1,0,0,-1,-59.85,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑁</tspan>
<tspan style="font-size: 8.75px; " x="0" y="8.1300001">𝜀</tspan>
</text>
<text transform="matrix(1,0,0,-1,-51.11,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">‖</tspan>
</text>
<text transform="matrix(1,0,0,-1,-44.57,58.11)">
<tspan style="font-size: 8.75px; " x="0" y="0">∗</tspan>
<tspan style="font-size: 8.75px; " x="4.5772958" y="0">,</tspan>
<tspan style="font-size: 8.75px; " x="6.765296" y="0">𝐿</tspan>
</text>
<text transform="matrix(1,0,0,-1,-31.61,55.92)">
<tspan style="font-size: 6.25px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"> run time(s)</td></tr><tr><td class="thead-hr" colspan="4"><hr /></td></tr><tr><td align="left"> 100</td><td align="center"><span style="width: 89.262497px;"><svg height="14.375" id="M517" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 89.262497 14.375" width="89.262497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.375)">
<g transform="translate(72,-60.5)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="37.158916" y="0">×</tspan>
<tspan style="font-size: 12.50px; " x="47.936501" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="54.188004" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-11.5,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">−</tspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">3</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 89.262497px;"><svg height="14.375" id="M518" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 89.262497 14.375" width="89.262497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.375)">
<g transform="translate(72,-60.5)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="37.158916" y="0">×</tspan>
<tspan style="font-size: 12.50px; " x="47.936501" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="54.188004" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-11.5,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">−</tspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"> 511</td></tr><tr><td align="left">50</td><td align="center"><span style="width: 89.262497px;"><svg height="14.375" id="M519" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 89.262497 14.375" width="89.262497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.375)">
<g transform="translate(72,-60.5)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="37.158916" y="0">×</tspan>
<tspan style="font-size: 12.50px; " x="47.936501" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="54.188004" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-11.5,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">−</tspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">3</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 89.262497px;"><svg height="14.375" id="M520" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 89.262497 14.375" width="89.262497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.375)">
<g transform="translate(72,-60.5)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="37.158916" y="0">×</tspan>
<tspan style="font-size: 12.50px; " x="47.936501" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="54.188004" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-11.5,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">−</tspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"> 56</td></tr><tr><td align="left">10</td><td align="center"><span style="width: 89.262497px;"><svg height="14.375" id="M521" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 89.262497 14.375" width="89.262497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.375)">
<g transform="translate(72,-60.5)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="37.158916" y="0">×</tspan>
<tspan style="font-size: 12.50px; " x="47.936501" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="54.188004" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-11.5,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">−</tspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">3</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 89.262497px;"><svg height="14.375" id="M522" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 89.262497 14.375" width="89.262497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.375)">
<g transform="translate(72,-60.5)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="37.158916" y="0">×</tspan>
<tspan style="font-size: 12.50px; " x="47.936501" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="54.188004" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-11.5,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">−</tspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"> 3</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr" /></td></tr></table></td></tr></table></div></div>

Table 5 | Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

title

Table 5: Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

description

Table 5

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