Differential Operrators

## Functions

acl::VectorOfElements | asl::laplas (const TemplateVE &a)
| differential operator \( \Delta a \) More...
acl::VectorOfElements | asl::gradient (const TemplateVE &a)
| differential operator \( \vec\nabla a \) More...
acl::VectorOfElements | asl::dx (const TemplateVE &a)
| differential operator \( \partial_x a \) More...
acl::VectorOfElements | asl::dy (const TemplateVE &a)
| differential operator \( \partial_y a \) More...
acl::VectorOfElements | asl::dz (const TemplateVE &a)
| differential operator \( \partial_z a \) More...
acl::VectorOfElements | asl::dxi (const TemplateVE &a, unsigned int i)
| differential operator \( \partial_{i} a \) More...
acl::VectorOfElements | asl::divAgradB (const TemplateVE &a, const TemplateVE &b)
| differential operator \( \nabla(a \nabla b) \) More...
acl::VectorOfElements | asl::div (const vector< TemplateVE > &a)
| differential operator \( \nabla \cdot \vec a \) More...
acl::VectorOfElements | asl::divProduct (const vector< TemplateVE > &a, const TemplateVE &c)
| differential operator \( \nabla \cdot (\vec a c) \) More...
acl::VectorOfElements | asl::div (const TemplateVE &ax, const TemplateVE &ay)
| differential operator \( \nabla \cdot \vec a \) More...
acl::VectorOfElements | asl::div (const TemplateVE &ax, const TemplateVE &ay, const TemplateVE &az)
| differential operator \( \nabla \cdot \vec a \) More...
acl::VectorOfElements | asl::dIdJ (unsigned int i, unsigned int j, const TemplateVE &a)
| differential operator \( \nabla_i \nabla_j a \) More...
acl::VectorOfElements | asl::cellValues (const TemplateVE &a, unsigned int iEl)
| returns VectorOfElements containing values in cell corners More...
acl::VectorOfElements | asl::gradient (const TemplateVE &a, unsigned int iEl)
| differential operator \( \vec\nabla a \) within a cell More...
vector< acl::Element > | asl::gcGradientAllCells (const TemplateVE &a, vector< acl::VectorOfElements > &values)
| differential operator \( \vec\nabla a \) within all cells More...

## Detailed Description

## Function Documentation

## cellValues()

acl::VectorOfElements asl::cellValues | ( | const TemplateVE & | a,
|  | unsigned int | iEl
| ) |  |

returns VectorOfElements containing values in cell corners

## dIdJ()

acl::VectorOfElements asl::dIdJ | ( | unsigned int | i,
|  | unsigned int | j,
|  | const TemplateVE & | a
| ) |  |

differential operator \( \nabla_i \nabla_j a \)

## div() [1/3]

acl::VectorOfElements asl::div | ( | const TemplateVE & | ax,
|  | const TemplateVE & | ay
| ) |  |

differential operator \( \nabla \cdot \vec a \)

## div() [2/3]

acl::VectorOfElements asl::div | ( | const TemplateVE & | ax,
|  | const TemplateVE & | ay,
|  | const TemplateVE & | az
| ) |  |

differential operator \( \nabla \cdot \vec a \)

## div() [3/3]

acl::VectorOfElements asl::div | ( | const vector< TemplateVE > & | a | ) |

differential operator \( \nabla \cdot \vec a \)

## divAgradB()

acl::VectorOfElements asl::divAgradB | ( | const TemplateVE & | a,
|  | const TemplateVE & | b
| ) |  |

differential operator \( \nabla(a \nabla b) \)

## divProduct()

acl::VectorOfElements asl::divProduct | ( | const vector< TemplateVE > & | a,
|  | const TemplateVE & | c
| ) |  |

differential operator \( \nabla \cdot (\vec a c) \)

This is a discret approximation discribef by the following expression:

\[ \nabla_\alpha (v_\alpha c) = \frac{1}{2}\sum_i w_i a_{i\alpha} (v_{0\alpha}+v_{i\alpha})(c_0+c_i) ) \]

where \( w_i \) are coefficients corresponding to a gradient ones

## dx()

acl::VectorOfElements asl::dx | ( | const TemplateVE & | a | ) |

differential operator \( \partial_x a \)

Examples
  acousticWaves.cc, bus_wind.cc, compressor.cc, cubeGravity.cc, cubeIncompressibleGravity.cc, cubePoroelasticGravity.cc, flow.cc, flow2.cc, flow3.cc, flowKDPGrowth.cc, flowRotatingCylinders.cc, jumpingBox.cc, levelSetBasic.cc, levelSetFacetedGrowth.cc, levelSetNormalGrowth.cc, locomotive.cc, locomotive_laminar.cc, locomotive_stability.cc, multicomponent_flow.cc, multiphase_flow.cc, pitot_tube_ice.cc, poroelastic.cc, surfaceFlux.cc, testDistanceFunction.cc, testSMDiff.cc, testSMDiff3C.cc, testSMPhi.cc, and testSMPhiBV.cc.

## dxi()

acl::VectorOfElements asl::dxi | ( | const TemplateVE & | a,
|  | unsigned int | i
| ) |  |

differential operator \( \partial_{i} a \)

## dy()

acl::VectorOfElements asl::dy | ( | const TemplateVE & | a | ) |

differential operator \( \partial_y a \)

## dz()

acl::VectorOfElements asl::dz | ( | const TemplateVE & | a | ) |

differential operator \( \partial_z a \)

## gcGradientAllCells()

vector<acl::Element> asl::gcGradientAllCells | ( | const TemplateVE & | a,
|  | vector< acl::VectorOfElements > & | values
| ) |  |

differential operator \( \vec\nabla a \) within all cells

The function generates code that computes the gradient values in each cell. The gradient values are written in `values` which are private variables. The corresponding amount of variables are automaticaly generated.

## gradient() [1/2]

acl::VectorOfElements asl::gradient | ( | const TemplateVE & | a | ) |

differential operator \( \vec\nabla a \)

## gradient() [2/2]

acl::VectorOfElements asl::gradient | ( | const TemplateVE & | a,
|  | unsigned int | iEl
| ) |  |

differential operator \( \vec\nabla a \) within a cell

## laplas()

acl::VectorOfElements asl::laplas | ( | const TemplateVE & | a | ) |

differential operator \( \Delta a \)