An Adaptive Domain Partitioning Technique for Meshfree-Type Methods

<table>The domain <svg height="10.6875" id="M50" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">Ω</tspan>
</text>
</g>
</g>
</svg> has been split into two overlapping subdomains <svg height="14.6" id="M51" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.85 14.6" width="17.85" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">Ω</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.65,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg> and <svg height="14.6" id="M52" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.85 14.6" width="17.85" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">Ω</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.65,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg> with interior boundaries <svg height="14.375" id="M53" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 15.3875 14.375" width="15.3875" 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,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">Γ</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.61,60.55)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg> and <svg height="14.375" id="M54" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 15.3875 14.375" width="15.3875" 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,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">Γ</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.61,60.55)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg>.</table>

Journal of Applied Mathematics

An Adaptive Domain Partitioning Technique for Meshfree-Type Methods

Figure 2