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

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="246491.fig.004a" src="https://static.hindawi.com/articles/isrn/volume-2012/246491/figures/246491.fig.004a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>The third level of Morton SFC</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="246491.fig.004b" src="https://static.hindawi.com/articles/isrn/volume-2012/246491/figures/246491.fig.004b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Computing the location of point <svg height="9.875" id="M20" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.7624998 9.875" width="7.7624998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑝</tspan>
</text>
</g>
</g>
</svg> on the line.</td></tr></table></td></tr></table>

<table>Mapping a point <svg height="9.875" id="M18" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.7624998 9.875" width="7.7624998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑝</tspan>
</text>
</g>
</g>
</svg> with integer coordinates <svg height="13.575" id="M19" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 32.674999 13.575" width="32.674999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.575)">
<g transform="translate(72,-61.14)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="15.616247" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="21.867746" y="0">)</tspan>
</text>
</g>
</g>
</svg> in a two-dimensional Cartesian mesh to an associated point on a Morton curve.</table>

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fig4

Figure 4

Figure 4: Parallel Adaptive Mesh Refinement Combined with Additive Multigrid for the Efficient Solution of the Poisson Equation 