Lines Matching refs:x

10 …ith the exception that the physical coordinates for this problem are $\bm{x}=(x,y,z)\in \mathbb{R}…
23 …e, denoted by $\bar{\bm{x}}=(\bar{x},\bar{y},\bar{z})$, and physical coordinates on the discrete s…
26 …c{\partial \bm{x}}{\partial \bm{X}}_{(2\times2)} = \frac{\partial {\bm{x}}}{\partial \bar{\bm{x}}}…
32 …|col_1\left(\frac{\partial \bar{\bm{x}}}{\partial \bm{X}}\right)\right\| \left\|col_2 \left(\frac{…
35 … ${\partial\bar{\bm{x}}}/{\partial \bm{X}}_{(3\times2)}$ is provided by the library, while ${\part…
38 …x}}}{\partial \bm{X}}\right) / \left\| col_1\left(\frac{\partial\bar{\bm{x}}}{\partial \bm{X}}\rig…
60 …c}{\bm{x}}=(\overset{\circ}{x},\overset{\circ}{y},\overset{\circ}{z})$, and physical coordinates o…
63 …t{\circ}{\bm{x}}}{\partial \bm{X}}_{(3\times2)} = \frac{\partial \overset{\circ}{\bm{x}}}{\partial…
69 …frac{\partial \overset{\circ}{\bm{x}}}{\partial \bm{X}}\right) \times col_2 \left(\frac{\partial \…
77 …d by $\bm x(\bm X)$, are mapped to their corresponding radial projections on the circle, which hav…
80 …x ${\partial\bm{x}}/{\partial \bm{X}}_{(3\times2)}$ is provided by the library, while ${\partial \…
84 \overset{\circ}{\bm x}(\bm x) = \frac{1}{\lVert \bm x \rVert} \bm x_{(3\times 1)}
90 …rset{\circ}{\bm{x}}}{\partial \bm{x}} = \frac{1}{\lVert \bm x \rVert} \bm I_{(3\times 3)} - \frac{…
105 …q}`eq-jacobian-sphere`, the pseudo-inverse of $\partial \overset{\circ}{\bm{x}} / \partial \bm{X}$…
109 …x}}}_{(2\times 3)} \equiv \left(\frac{\partial \overset{\circ}{\bm{x}}}{\partial \bm{X}}\right)_{(…
112 This enables computation of gradients of an arbitrary function $u(\overset{\circ}{\bm x})$ in the e…
115 …rset{\circ}{\bm x}}_{(1\times 3)} = \frac{\partial u}{\partial \bm X}_{(1\times 2)} \frac{\partial…
121 …a} \frac{\partial v}{\partial \overset\circ{\bm x}} \left( \frac{\partial u}{\partial \overset\cir…
122 …ac{\partial \bm X}{\partial \overset\circ{\bm x}} \left( \frac{\partial \bm X}{\partial \overset\c…
129 …x}}}{\partial \bm{X}}^T \frac{\partial\overset{\circ}{\bm{x}}}{\partial \bm{X}} \right)^{-1}_{(2\t…
136 …x}} \left( \frac{\partial u}{\partial \overset\circ{\bm x}} \right)^T \, dS     = \int_{\Omega} \f…
150 -\nabla\cdot \left( \kappa \left( x \right) \nabla x \right) = g \left( x \right)