Finite Element Methods

Collaboration diagram for Finite Element Methods:

Classes
struct	dg::InverseTriDiagonal< value_type >
	DEPRECATED/UNTESTED Fast inverse tridiagonal sparse matrix. More...
struct	dg::KroneckerTriDiagonal2d< Container >
	Fast tridiagonal sparse matrix in 2d \( T_y\otimes T_x\). More...
struct	dg::InverseKroneckerTriDiagonal2d< Container >
	Fast inverse tridiagonal sparse matrix in 2d \( T_y^{-1}\otimes T_x^{-1}\). More...

Functions
template<class real_type >
dg::TriDiagonal< dg::HVec_t< real_type > >	dg::create::fem_mass (const RealGrid1d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int v_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::TriDiagonal< dg::HVec_t< real_type > >	dg::create::fem_linear2const (const RealGrid1d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int c_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > >	dg::create::fem_mass (const aRealTopology2d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int v_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > >	dg::create::inv_fem_mass (const aRealTopology2d< real_type > &g)
	Inverse finite element mass matrix \( S^{-1} \).
template<class real_type >
dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > >	dg::create::fem_linear2const (const aRealTopology2d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int c_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > >	dg::create::inv_fem_linear2const (const aRealTopology2d< real_type > &g)
	Inverse finite element mass matrix \( S^{-1} \).
template<class real_type >
dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > >	dg::create::fem_mass2d (const aRealTopology3d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int v_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > >	dg::create::inv_fem_mass2d (const aRealTopology3d< real_type > &g)
	Inverse finite element mass matrix \( S^{-1} \).
template<class real_type >
dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > >	dg::create::fem_linear2const2d (const aRealTopology3d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int c_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > >	dg::create::inv_fem_linear2const2d (const aRealTopology3d< real_type > &g)
	Inverse finite element mass matrix \( S^{-1} \).
template<class real_type >
thrust::host_vector< real_type >	dg::create::fem_weights (const RealGrid1d< real_type > &g)
	finite element weight coefficients
template<class real_type >
thrust::host_vector< real_type >	dg::create::fem_inv_weights (const RealGrid1d< real_type > &g)
	inverse finite element weight coefficients
template<class real_type >
thrust::host_vector< real_type >	dg::create::fem_weights (const aRealTopology2d< real_type > &g)
	finite element weight coefficients
template<class real_type >
thrust::host_vector< real_type >	dg::create::fem_inv_weights (const aRealTopology2d< real_type > &g)
	inverse finite element weight coefficients
template<class real_type >
thrust::host_vector< real_type >	dg::create::fem_weights (const aRealTopology3d< real_type > &g)
	finite element weight coefficients
template<class real_type >
thrust::host_vector< real_type >	dg::create::fem_inv_weights (const aRealTopology3d< real_type > &g)
	inverse finite element weight coefficients

Detailed Description

Function Documentation

fem_inv_weights() [1/3]

template<class real_type >

thrust::host_vector< real_type > dg::create::fem_inv_weights

(

const aRealTopology2d< real_type > &

g

)

inverse finite element weight coefficients

Parameters

g

The grid

Returns

Host Vector

See also

Introduction to dg methods

fem_inv_weights() [2/3]

template<class real_type >

thrust::host_vector< real_type > dg::create::fem_inv_weights

(

const aRealTopology3d< real_type > &

g

)

inverse finite element weight coefficients

Parameters

g

The grid

Returns

Host Vector

See also

Introduction to dg methods

fem_inv_weights() [3/3]

template<class real_type >

thrust::host_vector< real_type > dg::create::fem_inv_weights

(

const RealGrid1d< real_type > &

g

)

inverse finite element weight coefficients

Parameters

g

The grid

Returns

Host Vector

See also

Introduction to dg methods

fem_linear2const() [1/2]

template<class real_type >

dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > > dg::create::fem_linear2const

(

const aRealTopology2d< real_type > &

g

)

\( S_{ij} = \frac{1}{w_i}\int c_i(x) v_j(x) \) finite element projection matrix

where \( c_i\) are the constant finite elements and \( v_j\) are triangles

Template Parameters

real_type

The value type

Parameters

g

The grid

Returns

Host Matrix

See also

Introduction to dg methods

Attention

No periodic boundary conditions

fem_linear2const() [2/2]

template<class real_type >

dg::TriDiagonal< dg::HVec_t< real_type > > dg::create::fem_linear2const

(

const RealGrid1d< real_type > &

g

)

\( S_{ij} = \frac{1}{w_i}\int c_i(x) v_j(x) \) finite element projection matrix

where \( c_i\) are the constant finite elements and \( v_j\) are triangles

Template Parameters

real_type

The value type

Parameters

g

The grid

Returns

Host Matrix

See also

Introduction to dg methods

Attention

No periodic boundary conditions

fem_linear2const2d()

template<class real_type >

dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > > dg::create::fem_linear2const2d

(

const aRealTopology3d< real_type > &

g

)

\( S_{ij} = \frac{1}{w_i}\int c_i(x) v_j(x) \) finite element projection matrix

where \( c_i\) are the constant finite elements and \( v_j\) are triangles

Template Parameters

real_type

The value type

Parameters

g

The grid

Returns

Host Matrix

See also

Introduction to dg methods

Attention

No periodic boundary conditions

fem_mass() [1/2]

template<class real_type >

dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > > dg::create::fem_mass

(

const aRealTopology2d< real_type > &

g

)

\( S_{ij} = \frac{1}{w_i}\int v_i(x) v_j(x) \) finite element projection matrix

where \( v_j\) are triangle finite elements

Template Parameters

real_type

The value type

Parameters

g

The grid

Returns

Host Matrix

See also

Introduction to dg methods

Attention

No periodic boundary conditions

fem_mass() [2/2]

template<class real_type >

dg::TriDiagonal< dg::HVec_t< real_type > > dg::create::fem_mass

(

const RealGrid1d< real_type > &

g

)

\( S_{ij} = \frac{1}{w_i}\int v_i(x) v_j(x) \) finite element projection matrix

where \( v_j\) are triangle finite elements

Template Parameters

real_type

The value type

Parameters

g

The grid

Returns

Host Matrix

See also

Introduction to dg methods

Attention

No periodic boundary conditions

fem_mass2d()

template<class real_type >

dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > > dg::create::fem_mass2d

(

const aRealTopology3d< real_type > &

g

)

\( S_{ij} = \frac{1}{w_i}\int v_i(x) v_j(x) \) finite element projection matrix

where \( v_j\) are triangle finite elements

Template Parameters

real_type

The value type

Parameters

g

The grid

Returns

Host Matrix

See also

Introduction to dg methods

Attention

No periodic boundary conditions

fem_weights() [1/3]

template<class real_type >

thrust::host_vector< real_type > dg::create::fem_weights

(

const aRealTopology2d< real_type > &

g

)

finite element weight coefficients

These will emulate the trapezoidal rule for integration

Parameters

g

The grid

Returns

Host Vector

See also

Introduction to dg methods

fem_weights() [2/3]

template<class real_type >

thrust::host_vector< real_type > dg::create::fem_weights

(

const aRealTopology3d< real_type > &

g

)

finite element weight coefficients

These will emulate the trapezoidal rule for integration

Parameters

g

The grid

Returns

Host Vector

See also

Introduction to dg methods

fem_weights() [3/3]

template<class real_type >

thrust::host_vector< real_type > dg::create::fem_weights

(

const RealGrid1d< real_type > &

g

)

finite element weight coefficients

These will emulate the trapezoidal rule for integration

Parameters

g

The grid

Returns

Host Vector

See also

Introduction to dg methods

inv_fem_linear2const()

template<class real_type >

dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > > dg::create::inv_fem_linear2const

(

const aRealTopology2d< real_type > &

g

)

Inverse finite element mass matrix \( S^{-1} \).

Template Parameters

real_type

The value type

Parameters

g

The grid

Returns

Host Matrix

See also

Introduction to dg methods

Attention

No periodic boundary conditions

inv_fem_linear2const2d()

template<class real_type >

dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > > dg::create::inv_fem_linear2const2d

(

const aRealTopology3d< real_type > &

g

)

Inverse finite element mass matrix \( S^{-1} \).

Template Parameters

real_type

The value type

Parameters

g

The grid

Returns

Host Matrix

See also

Introduction to dg methods

Attention

No periodic boundary conditions

inv_fem_mass()

template<class real_type >

dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > > dg::create::inv_fem_mass

(

const aRealTopology2d< real_type > &

g

)

Inverse finite element mass matrix \( S^{-1} \).

Template Parameters

real_type

The value type

Parameters

g

The grid

Returns

Host Matrix

See also

Introduction to dg methods

Attention

No periodic boundary conditions

inv_fem_mass2d()

template<class real_type >

dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > > dg::create::inv_fem_mass2d

(

const aRealTopology3d< real_type > &

g

)

Inverse finite element mass matrix \( S^{-1} \).

Template Parameters

real_type

The value type

Parameters

g

The grid

Returns

Host Matrix

See also

Introduction to dg methods

Attention

No periodic boundary conditions