Lines Matching refs:bm

10 …ordinates for this problem are $\bm{x}=(x,y,z)\in \mathbb{R}^3$, while the coordinates of the refe…
23 …noted by $\bar{\bm{x}}=(\bar{x},\bar{y},\bar{z})$, and physical coordinates on the discrete surfac…
26 …tial \bm{x}}{\partial \bm{X}}_{(2\times2)} = \frac{\partial {\bm{x}}}{\partial \bar{\bm{x}}}_{(2\t…
32 …left(\frac{\partial \bar{\bm{x}}}{\partial \bm{X}}\right)\right\| \left\|col_2 \left(\frac{\partia…
35 …rix ${\partial\bar{\bm{x}}}/{\partial \bm{X}}_{(3\times2)}$ is provided by the library, while ${\p…
38 …bm{x}}}{\partial \bm{X}}\right) / \left\| col_1\left(\frac{\partial\bar{\bm{x}}}{\partial \bm{X}}\…
60 …bm{x}}=(\overset{\circ}{x},\overset{\circ}{y},\overset{\circ}{z})$, and physical coordinates on th…
63 …c}{\bm{x}}}{\partial \bm{X}}_{(3\times2)} = \frac{\partial \overset{\circ}{\bm{x}}}{\partial \bm{x…
69 …partial \overset{\circ}{\bm{x}}}{\partial \bm{X}}\right) \times col_2 \left(\frac{\partial \overse…
77 …oted by $\bm x(\bm X)$, are mapped to their corresponding radial projections on the circle, which …
80 …rix ${\partial\bm{x}}/{\partial \bm{X}}_{(3\times2)}$ 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 …overset{\circ}{\bm{x}}}{\partial \bm{x}} = \frac{1}{\lVert \bm x \rVert} \bm I_{(3\times 3)} - \fr…
105 …acobian-sphere`, the pseudo-inverse of $\partial \overset{\circ}{\bm{x}} / \partial \bm{X}$ is use…
109 …bm{X}}{\partial \overset{\circ}{\bm{x}}}_{(2\times 3)} \equiv \left(\frac{\partial \overset{\circ}…
112 This enables computation of gradients of an arbitrary function $u(\overset{\circ}{\bm x})$ in the e…
115 …overset{\circ}{\bm x}}_{(1\times 3)} = \frac{\partial u}{\partial \bm X}_{(1\times 2)} \frac{\part…
121 …ega} \frac{\partial v}{\partial \overset\circ{\bm x}} \left( \frac{\partial u}{\partial \overset\c…
122 …bm X} \underbrace{\frac{\partial \bm X}{\partial \overset\circ{\bm x}} \left( \frac{\partial \bm X…
125 …have identified the $2\times 2$ contravariant metric tensor $\bm g$ (sometimes written $\bm g^{ij}…
129 …bm g = \left(\frac{\partial \overset{\circ}{\bm{x}}}{\partial \bm{X}}^T \frac{\partial\overset{\ci…
136 …bm x}} \left( \frac{\partial u}{\partial \overset\circ{\bm x}} \right)^T \, dS     = \int_{\Omega}…
153 …sis operations, $\bm{B}$, and $\bm{B}^T$, respectively, act on the different grid levels with corr…