Parallel Adaptive Mesh Refinement Combined with Additive Multigrid for the Efficient Solution of the Poisson Equation

<table> Approximation of the gradient flux <svg height="14.3625" id="M83" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 15.275 14.3625" width="15.275" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝐹</tspan>
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<tspan style="font-size: 8.75px; " x="0" y="0">𝑒</tspan>
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</svg> using the value of <svg height="13.425" id="M84" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 10.2 13.425" width="10.2" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-61.26)">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝜙</tspan>
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</svg> at an auxiliary node <svg height="12.5625" id="M85" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 16.1 12.5625" width="16.1" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.5625)">
<g transform="translate(72,-61.95)">
<text transform="matrix(1,0,0,-1,-71.95,62)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑃</tspan>
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<tspan style="font-size: 8.75px; " x="0" y="0"></tspan>
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International Scholarly Research Notices

fig14

Figure 14

Figure 14: Parallel Adaptive Mesh Refinement Combined with Additive Multigrid for the Efficient Solution of the Poisson Equation 