Lines Matching refs:X

10 …in \mathbb{R}^3$, while the coordinates of the reference element are $\bm{X}=(X,Y) \equiv (X_0,X_1…
23 …coordinates on the discrete surface, denoted by $\bm{{x}}=(x,y)$, to $\bm{X}=(X,Y) \in \textrm{I}$…
26 …}{\partial \bm{X}}_{(2\times2)} = \frac{\partial {\bm{x}}}{\partial \bar{\bm{x}}}_{(2\times3)} \fr…
32 …\partial \bar{\bm{x}}}{\partial \bm{X}}\right)\right\| \left\|col_2 \left(\frac{\partial \bar{\bm{…
35 …cube`, the right-most Jacobian matrix ${\partial\bar{\bm{x}}}/{\partial \bm{X}}_{(3\times2)}$ is p…
38 …X}}\right) / \left\| col_1\left(\frac{\partial\bar{\bm{x}}}{\partial \bm{X}}\right)\right\| , col_…
60 …cle and 1D linear element in figure {numref}`fig-sphere-coords`), to $\bm{X}=(X,Y) \in \textrm{I}$…
63 …{\partial \bm{X}}_{(3\times2)} = \frac{\partial \overset{\circ}{\bm{x}}}{\partial \bm{x}}_{(3\time…
69 …rset{\circ}{\bm{x}}}{\partial \bm{X}}\right) \times col_2 \left(\frac{\partial \overset{\circ}{\bm…
77 …$q_1$, marked by blue dots, with physical coordinates denoted by $\bm x(\bm X)$, are mapped to the…
80 …rms-sphere`, the right-most Jacobian matrix ${\partial\bm{x}}/{\partial \bm{X}}_{(3\times2)}$ is p…
105 …re`, the pseudo-inverse of $\partial \overset{\circ}{\bm{x}} / \partial \bm{X}$ is used to derive …
109 …X}}{\partial \overset{\circ}{\bm{x}}}_{(2\times 3)} \equiv \left(\frac{\partial \overset{\circ}{\b…
115 …c}{\bm x}}_{(1\times 3)} = \frac{\partial u}{\partial \bm X}_{(1\times 2)} \frac{\partial \bm X}{\…
122 …X} \underbrace{\frac{\partial \bm X}{\partial \overset\circ{\bm x}} \left( \frac{\partial \bm X}{\…
129 …X}}^T \frac{\partial\overset{\circ}{\bm{x}}}{\partial \bm{X}} \right)^{-1}_{(2\times 2)} \frac{\pa…
136 …X} \underbrace{\left(\frac{\partial \overset{\circ}{\bm{x}}}{\partial \bm{X}}^T \frac{\partial\ove…