Quadrature rules on the interval . I guess I’ll talk about this at the end of the week.</p>
<div class="code-embed-wrapper"> <pre class="language-python code-embed-pre line-numbers" data-start="1" data-line-offset="0"><code class="language-python code-embed-code">from scipy.special import roots_jacobi as rj<br/>def quadtriangle(f, w00, w10, x00, x10):<br/> total = 0<br/> for i in range(len(w00)):<br/> subsum = 0<br/> for j in range(len(w10)):<br/> subsum += w10[j] / 2 * f([(1 + x00[i]) * (1 - x10[j]) / 2 - 1, x10[j]])<br/> total += w00[i] * subsum<br/> return total<br/>def f(x):<br/> return x[0]**2 + x[1]**2<br/>p = 4<br/>x00, w00 = rj(p + 1, 0, 0)<br/>x10, w10 = rj(p + 1, 1, 0)<br/>print(quadtriangle(f, w00, w10, x00, x10))</code></pre> <div class="code-embed-infos"> <span class="code-embed-name">Quadrature rules</span> </div> </div>
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Quadrature Rules on Triangles
![](https://s0.wp.com/latex.php?latex
<ol>
<li>Tensor products + transformations</li>
<li>“Symmetric quadrature rules”</li>
</ol>
<p>The latter offers better convergence with smaller points, and has better spread-out points than the tensor product version, but offers less technical support through software packages; we refer the reader to the following <a href="http://onlinelibrary.wiley.com/doi/10.1002/nme.1620210612/full">paper</a>. We will discuss the first, and exposit a little more; I will be borrowing heavily from Karniadakis and Sherwin’s fluid dynamics textbook.</p>
<p>Suppose our triangle at (-1, -1), (1, -1), and (-1, 1) (so called reference triangle) uses <img src=)
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Take 4 at a stable blog
Take 4 at a stable blog
Quadrature rules on the interval
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