Implements a functional corresponding to (the square of) an \(L^2\) norm of a scalar valued function. More...
#include <IP_L2NormFunctional.hh>
Inheritance diagram for pism::inverse::IP_L2NormFunctional2S:Public Member Functions | |
| IP_L2NormFunctional2S (std::shared_ptr< const Grid > grid) | |
| virtual | ~IP_L2NormFunctional2S () |
| virtual void | valueAt (array::Scalar &x, double *OUTPUT) |
| virtual void | dot (array::Scalar &a, array::Scalar &b, double *v) |
| Computes the inner product \(Q(a, b)\). | |
| virtual void | gradientAt (array::Scalar &x, array::Scalar &gradient) |
| Public Member Functions inherited from pism::inverse::IPInnerProductFunctional< array::Scalar > | |
| IPInnerProductFunctional (std::shared_ptr< const Grid > grid) | |
| virtual void | interior_product (array::Scalar &x, array::Scalar &y) |
| Computes the interior product of a vector with the IPInnerProductFunctional's underlying bilinear form. | |
| Public Member Functions inherited from pism::inverse::IPFunctional< IMVecType > | |
| IPFunctional (std::shared_ptr< const Grid > grid) | |
| virtual | ~IPFunctional () |
| virtual void | valueAt (IMVecType &x, double *OUTPUT)=0 |
| Computes the value of the functional at the vector x. | |
| virtual void | gradientAt (IMVecType &x, IMVecType &gradient)=0 |
| Computes the gradient of the functional at the vector x. | |
Private Member Functions | |
| IP_L2NormFunctional2S (IP_L2NormFunctional2S const &) | |
| IP_L2NormFunctional2S & | operator= (IP_L2NormFunctional2S const &) |
Additional Inherited Members | |
| Protected Attributes inherited from pism::inverse::IPFunctional< IMVecType > | |
| std::shared_ptr< const Grid > | m_grid |
| fem::ElementIterator | m_element_index |
| fem::Q1Element2 | m_element |
Detailed Description
Implements a functional corresponding to (the square of) an \(L^2\) norm of a scalar valued function.
The functional is, in continuous terms
\[ J(f) = \int_{\Omega} f^2 \; dA \]
where \(\Omega\) is the square domain. Numerically it is implemented using Q1 finite elements.
Definition at line 38 of file IP_L2NormFunctional.hh.
The documentation for this class was generated from the following files:
- src/inverse/functional/IP_L2NormFunctional.hh
- src/inverse/functional/IP_L2NormFunctional.cc
