Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="142923.fig.0012a" src="https://static.hindawi.com/articles/jam/volume-2011/142923/figures/142923.fig.0012a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Order 2</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="142923.fig.0012b" src="https://static.hindawi.com/articles/jam/volume-2011/142923/figures/142923.fig.0012b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Order 4</td></tr></table></td></tr></table>

<table>Error difference, <svg height="12.4375" id="M213" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 9.5625 12.4375" width="9.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M530 686q-79 -330 -126 -595q-5 -24 4 -24q22 0 77 53l16 -24q-42 -49 -88 -78.5t-72 -29.5q-37 0 -19 83l21 99h-2q-62 -83 -153 -141q-65 -41 -97 -41q-28 0 -48 31.5t-20 91.5q0 71 32.5 144t88.5 118q36 30 94 52.5t94 22.5q38 0 68 -13l29 158q7 40 2 47.5t-38 7.5
h-35l1 26q39 4 76 13.5t58.5 17t27.5 7.5q16 0 9 -26zM387 375q-11 11 -38.5 20t-51.5 9q-45 0 -79 -23q-46 -32 -77.5 -107.5t-31.5 -143.5q0 -40 9.5 -58.5t23.5 -18.5q40 0 113.5 70t99.5 118z" id="x1D451"></path></g>
</svg>, for second- and fourth-order synthetic fields.</table>

Journal of Applied Mathematics

fig12

Figure 12

Figure 12: Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators 