Implements a functional corresponding to (the square of) an \(L^2\) norm of a vector valued function. More...

Inheritance diagram for pism::inverse::IP_L2NormFunctional2V:

Public Member Functions
	IP_L2NormFunctional2V (std::shared_ptr< const Grid > grid)

virtual	~IP_L2NormFunctional2V ()

virtual void	valueAt (array::Vector &x, double *v)

virtual void	dot (array::Vector &a, array::Vector &b, double *v)
	Computes the inner product \(Q(a, b)\).

virtual void	gradientAt (array::Vector &x, array::Vector &gradient)

Public Member Functions inherited from pism::inverse::IPInnerProductFunctional< array::Vector >
	IPInnerProductFunctional (std::shared_ptr< const Grid > grid)

virtual void	interior_product (array::Vector &x, array::Vector &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_L2NormFunctional2V (IP_L2NormFunctional2V const &)

IP_L2NormFunctional2V &	operator= (IP_L2NormFunctional2V 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 vector 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 60 of file IP_L2NormFunctional.hh.

The documentation for this class was generated from the following files:

Public Member Functions