bm (reference) in projects: libCEED - OpenGrok search results

Searched refs:bm (Results 1 – 11 of 11) sorted by relevance

/libCEED/examples/solids/
H A D	index.md	16 …am below, where $\bm \sigma$ and $\bm \epsilon$ are stress and strain, respectively, in the small … 20 {\overbrace{\bm S(\bm E)}^{\text{Finite Strain Hyperelastic}}} 22 {\overbrace{\bm S = \mathsf C \bm E}^{\text{St. Venant-Kirchoff}}} \\ 23 …@V{\text{geometric}}V{\begin{smallmatrix}\bm E \to \bm \epsilon \\ \bm S \to \bm \sigma \end{small… 24 …@V{\begin{smallmatrix}\bm E \to \bm \epsilon \\ \bm S \to \bm \sigma \end{smallmatrix}}V{\text{geo… 25 {\underbrace{\bm \sigma(\bm \epsilon)}_\text{Small Strain Hyperelastic}} 27 {\underbrace{\bm \sigma = \mathsf C \bm \epsilon}_\text{Linear Elastic}} 47 \nabla \cdot \bm{\sigma} + \bm{g} = \bm{0} 50 where $\bm{\sigma}$ and $\bm{g}$ are stress and forcing functions, respectively. 51 …}`lin-elas` by a test function $\bm v$ and integrate the divergence term by parts to arrive at the… [all …]
H A D	README.md	209 * - Displacement, $\bm u$ 215 * - Body force (gravity) on volume, $\int \rho \bm g$ 219 …eter 100` to measure displacement in centimeters), but $E$ and $\int \rho \bm g$ have the same dep… 225 …ment in the $z$ direction, pressure, $\operatorname{trace} \bm{E}$, $\operatorname{trace} \bm{E}^2… 237 - $\lambda \operatorname{trace} \bm{\epsilon}$ 238 - $\lambda \log \operatorname{trace} \bm{\epsilon}$ 242 - $\operatorname{trace} \bm{\epsilon}$ 243 - $\operatorname{trace} \bm{\epsilon}$ 244 - $\operatorname{trace} \bm{E}$ 246 * - $\operatorname{trace} \bm{E}^2$ [all …]
/libCEED/examples/petsc/
H A D	index.md	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 … [all …]
/libCEED/examples/fluids/
H A D	index.md	21 \frac{\partial \rho}{\partial t} + \nabla \cdot \bm{U} &= 0 \\ 22 \frac{\partial \bm{U}}{\partial t} + \nabla \cdot \left( \frac{\bm{U} \otimes \bm{U}}{\rho} + P \bm… 23 … \nabla \cdot \left( \frac{(E + P)\bm{U}}{\rho} -\bm{u} \cdot \bm{\sigma} - k \nabla T \right) - \… 27 where $\bm{\sigma} = \mu(\nabla \bm{u} + (\nabla \bm{u})^T + \lambda (\nabla \cdot \bm{u})\bm{I}_3)… 28 …bm{U}=\rho \bm{u}$, where $\bm{u}$ is the vector velocity field), $E$ the total energy density (de… 31 P = \left( {c_p}/{c_v} -1\right) \left( E - {\bm{U}\cdot\bm{U}}/{(2 \rho)} \right) \, , 39 \frac{\partial \bm{q}}{\partial t} + \nabla \cdot \bm{F}(\bm{q}) -S(\bm{q}) = 0 \, , 45 \bm{q} = \begin{pmatrix} \rho \\ \bm{U} \equiv \rho \bm{ u }\\ … 52 \bm{F}(\bm{q}) &= 54 \bm{U}\\ [all …]
H A D	README.md	302 …for pure advection, which holds density $\rho$ and momentum density $\rho \bm u$ constant while ad… 613 …\rho \bm{u}, \rho e$), `primitive` ($P, \bm{u}, T$), or `entropy` ($\frac{\gamma - s}{\gamma - 1} …
/libCEED/doc/sphinx/source/
H A D	libCEEDapi.md	18 \langle v, u \rangle = \int_\Omega v u d \bm{x}, 21 where $\bm{x} \in \mathbb{R}^d \supset \Omega$. 26 \langle \bm v, \bm f(u) \rangle = \int_\Omega \bm v \cdot \bm f_0 (u, \nabla u) + \nabla \bm v … 29 for all $\bm v$ in the corresponding homogeneous space $V_0$, where $\bm f_0$ and $\bm f_1$ contain… 30 …bm f_0$ represents all terms in {eq}`residual` which multiply the (possibly vector-valued) test fu… 31 For an n-component problems in $d$ dimensions, $\bm f_0 \in \mathbb{R}^n$ and $\bm f_1 \in \mathbb{… 34 …bm v \!:\! \bm f_1$ represents contraction over both fields and spatial dimensions while a single … 39 …tory), we store the term $\bm f_0$ directly into `v`, and the term $\bm f_1$ directly into `dv` (w… 40 If equation {eq}`residual` only presents a term of the type $\bm f_0$, the {ref}`CeedQFunction` wil… 41 If equation {eq}`residual` also presents a term of the type $\bm f_1$, then the {ref}`CeedQFunction… [all …]
/libCEED/examples/
H A D	bps.md	`30 u(\bm x) &= \sum_{j=1}^n u_j \, \phi_j(\bm x) ,\\ 31 v(\bm x) &= \sum_{i=1}^n v_i \, \phi_i(\bm x) . 39 \langle v,u \rangle = \bm v^T M \bm u , \qquad \langle v,f\rangle = \bm v^T \bm b \,. 42 Here, we have introduced the mass matrix, $M$, and the right-hand side, $\bm b$, 69 a(v,u) = \bm v^T K \bm u ,`
H A D	notation.md	`10 …inates are denoted by $\bm{x}=(x,y,z) \equiv (x_0,x_1,x_2) \in\Omega_e$, while the reference coord…`
/libCEED/examples/ceed/
H A D	index.md	27 with $v(x) \in \mathcal{V}_p = \{ v \in H^{1}(\Omega_e) \,\|\, v \in P_p(\bm{I}), e=1,\ldots,N_e \}$… 43 In particular, we select $u(\bm x) = x_0 + x_1 + x_2$, for which $\nabla u = [1, 1, 1]^T$, and thus… 48 \nabla \cdot \nabla u = 0, \textrm{ for } \bm{x} \in \Omega , 54 \int_\Omega \nabla v \cdot \nabla u \, dV - \int_{\partial \Omega} v \nabla u \cdot \hat{\bm n}\, d… 57 Since we have chosen $u$ such that $\nabla u \cdot \hat{\bm n} = 1$, the boundary integrand is $v 1… 84 with $v(x) \in \mathcal{V}_p = \{ v \in H^{1}(\Omega_e) \,\|\, v \in P_p(\bm{I}), e=1,\ldots,N_e \}$…
/libCEED/python/tests/
H A D	test-3-basis.py	`15 import buildmats as bm namespace 212 interp, grad = bm.buildmats(qref, qweight, libceed.scalar_types[ 236 interp, grad = bm.buildmats(qref, qweight, libceed.scalar_types[ 280 interp, grad = bm.buildmats(qref, qweight, libceed.scalar_types[ 319 interp, div = bm.buildmatshdiv(qref, qweight, libceed.scalar_types[ 352 interp, curl = bm.buildmatshcurl(qref, qweight, libceed.scalar_types[`
H A D	test-5-operator.py	`15 import buildmats as bm namespace 637 interp, grad = bm.buildmats(qref, qweight, libceed.scalar_types[ 744 interp, grad = bm.buildmats(qref, qweight, libceed.scalar_types[ 858 interp, grad = bm.buildmats(qref, qweight, libceed.scalar_types[ 1034 interp, grad = bm.buildmats(qref, qweight, libceed.scalar_types[ 1201 interp, grad = bm.buildmats(qref, qweight, libceed.scalar_types[ 1383 interp, grad = bm.buildmats(qref, qweight, libceed.scalar_types[`

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