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/petsc/src/ts/tests/
H A Dex15.c83 const PetscScalar *u, *cdot; in IFunction_TransientVar() local
88 PetscCall(VecGetArrayRead(Cdot, &cdot)); in IFunction_TransientVar()
91 f[0] = cdot[0] + PetscExpScalar(u[0]); in IFunction_TransientVar()
92 f[1] = cdot[1] - PetscExpScalar(u[0]); in IFunction_TransientVar()
95 PetscCall(VecRestoreArrayRead(Cdot, &cdot)); in IFunction_TransientVar()
/petsc/doc/tutorials/
H A Dguide_to_examples_by_physics.md37 -\nabla\cdot \bm \sigma = \bm f
43 -\nabla\cdot \left( \lambda I \operatorname{trace}(\bm\varepsilon) + 2\mu \bm\varepsilon \right) = …
116 \frac{\partial u}{\partial t} + u\cdot\nabla u - \nabla \cdot \left(\mu \left(\nabla u + \nabla u^T…
117 \nabla\cdot u &= 0 \end{aligned}
/petsc/doc/manual/
H A Dsnes.md206 - \nabla\cdot(\kappa(u) \nabla u) = 0
212 A(u) v \simeq -\nabla\cdot(\kappa(u) \nabla v).
420 if set, and `SNESLINESEARCHCP`, which minimizes $F(x) \cdot Y$ where
432 `SNESLINESEARCHCP`, it seeks to find the root of $F(x) \cdot Y$.
435 It works as follows (with $f(\lambda)=F(x-\lambda Y) \cdot Y / ||Y||$ for brevity):
446 - relative tolerance $f(\lambda_j) < \mathtt{rtol} \cdot f(\lambda_0)$
566 b &= 2\delta\mathbf x^Q\cdot (\Delta\mathbf x + \delta s\delta\mathbf x^F) + 2\psi^2 \Delta\lambda,…
583 \text{sign}(\delta\lambda) = \text{sign}\big(\delta\mathbf x^Q \cdot (\Delta\mathbf x)_{i-1} + \psi…
605 \delta \lambda = -\frac{\Delta \mathbf x \cdot \delta \mathbf x^F}{\Delta\mathbf x \cdot \delta\mat…
994 $\| \cdot \|$ denotes an arbitrary norm in $\Re^n$ .
[all …]
H A Dts.md335 …mpressible Navier-Stokes equations, since the continuity equation $\nabla\cdot u = 0$ does not inv…
/petsc/doc/tutorials/physics/
H A Dguide_to_stokes.md13 -\nabla \cdot \left(\mu \left(\nabla u + \nabla u^T \right)\right) + \nabla p + f &= 0 \\
14 \nabla\cdot u &= 0 \end{aligned}
24 \nabla \cdot \sigma + f = 0,
30 \nabla \cdot (\rho u) = 0,
37 \nabla \cdot \mu \left( \nabla u + \nabla u^T \right) - \nabla p + f &= 0 \\
38 \nabla \cdot u &= 0
42 …he pressure, $\mu$ is the dynamic shear viscosity, with units $N\cdot s/m^2$ or $Pa\cdot s$. If we…
48 …left< v, \frac{\partial\sigma}{\partial n} \right>_\Gamma - \left< \nabla\cdot v, p \right> - \lef…
49 \left< q, -\nabla \cdot u \right> &= 0 & \text{for all} \ q \in Q