The point wise contribution to the Poisson balance equation. Note that these contributions are just the point-wise potential values. You can get to this by going through the weak form derivation. The derivative is just one since the residual is just the variable. More...
#include <mixed_gravity.hpp>
Public Types | |
| using | Operands = utils::types::TypeList<Operand<Potential>> |
| This equation only depends on the potential field. | |
 Public Types inherited from serif::equations::Contribution< Operand< Gradient, Divergence > > | |
| using | Test |
| The test type of the contribution. | |
| using | TestOperand |
| The operand type of the contribution (associating a test function and a term) | |
| using | Support |
| The domain support of the contribution (which then boils down to the dofs which are supported by the term on that test function) | |
Static Public Member Functions | |
| static PointLinearization< Operands > | evaluate (const EquationPoint< Operands > &point) |
| Evaluate the Poisson balance equation at a given point. Fundamentally all this this is doing is returning the gravitational potential since to satisfy the Poisson balance equation that should be zero. The derivative of the residual with respect to the potential is then just one. | |
| static int | additional_order (Operand< Potential >, int) |
| Return the additional order of the Poisson balance equation with respect to the potential operand. The contribution is linear in potential so the additional order is always 0. | |
Detailed Description
The point wise contribution to the Poisson balance equation. Note that these contributions are just the point-wise potential values. You can get to this by going through the weak form derivation. The derivative is just one since the residual is just the variable.
| Equation Contributions |
|---|
|
Member Typedef Documentation
◆ Operands
| using serif::equations::gravity_contributions::PotentialValue::Operands = utils::types::TypeList<Operand<Potential>> |
This equation only depends on the potential field.
Member Function Documentation
◆ additional_order()
|
inlinestatic |
Return the additional order of the Poisson balance equation with respect to the potential operand. The contribution is linear in potential so the additional order is always 0.
- Parameters
-
operand-type The type of the operand being evaluated, which must be the potential operand. position-order The order of the position being evaluated, which is not used in this implementation.
- Returns
- The additional order of the Poisson balance equation with respect to the potential operand, which is always 0.
◆ evaluate()
|
inlinestatic |
Evaluate the Poisson balance equation at a given point. Fundamentally all this this is doing is returning the gravitational potential since to satisfy the Poisson balance equation that should be zero. The derivative of the residual with respect to the potential is then just one.
When you go through the weak form derivation and the integration by parts you find that the point wise contribution to the gravity gradient row of the system is the divergence of the test function times the potential. \( \left(\nabla \cdot v\right) \phi \). The derivative is then trivially one.
- Parameters
-
point The point at which to evaluate the Poisson balance equation.
- Returns
- A PointLinearization object containing the residual and field derivatives for the Poisson balance equation at the given point.
The documentation for this class was generated from the following file:
- src/include/serif/equations/mixed_gravity.hpp
