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Reference documentation for deal.II version 9.6.0
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Local integrators related to curl operators and their traces. More...
Functions | |
template<int dim> | |
Tensor< 1, dim > | curl_curl (const Tensor< 2, dim > &h0, const Tensor< 2, dim > &h1, const Tensor< 2, dim > &h2) |
template<int dim> | |
Tensor< 1, dim > | tangential_curl (const Tensor< 1, dim > &g0, const Tensor< 1, dim > &g1, const Tensor< 1, dim > &g2, const Tensor< 1, dim > &normal) |
template<int dim> | |
void | curl_curl_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const double factor=1.) |
template<int dim> | |
void | curl_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, double factor=1.) |
template<int dim> | |
void | nitsche_curl_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const unsigned int face_no, double penalty, double factor=1.) |
template<int dim> | |
void | tangential_trace_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, double factor=1.) |
template<int dim> | |
void | ip_curl_matrix (FullMatrix< double > &M11, FullMatrix< double > &M12, FullMatrix< double > &M21, FullMatrix< double > &M22, const FEValuesBase< dim > &fe1, const FEValuesBase< dim > &fe2, const double pen, const double factor1=1., const double factor2=-1.) |
Local integrators related to curl operators and their traces.
We use the following conventions for curl operators. First, in three space dimensions
\[ \nabla\times \mathbf u = \begin{pmatrix} \partial_2 u_3 - \partial_3 u_2 \\ \partial_3 u_1 - \partial_1 u_3 \\ \partial_1 u_2 - \partial_2 u_1 \end{pmatrix}. \]
In two space dimensions, the curl is obtained by extending a vector u to \((u_1, u_2, 0)^T\) and a scalar p to \((0,0,p)^T\). Computing the nonzero components, we obtain the scalar curl of a vector function and the vector curl of a scalar function. The current implementation exchanges the sign and we have:
\[ \nabla \times \mathbf u = \partial_1 u_2 - \partial_2 u_1, \qquad \nabla \times p = \begin{pmatrix} \partial_2 p \\ -\partial_1 p \end{pmatrix} \]
Tensor< 1, dim > LocalIntegrators::Maxwell::curl_curl | ( | const Tensor< 2, dim > & | h0, |
const Tensor< 2, dim > & | h1, | ||
const Tensor< 2, dim > & | h2 ) |
Auxiliary function. Given the tensors of dim
second derivatives, compute the curl of the curl of a vector function. The result in two and three dimensions is:
\[ \nabla\times\nabla\times \mathbf u = \begin{pmatrix} \partial_1\partial_2 u_2 - \partial_2^2 u_1 \\ \partial_1\partial_2 u_1 - \partial_1^2 u_2 \end{pmatrix} \]
and
\[ \nabla\times\nabla\times \mathbf u = \begin{pmatrix} \partial_1\partial_2 u_2 + \partial_1\partial_3 u_3 - (\partial_2^2+\partial_3^2) u_1 \\ \partial_2\partial_3 u_3 + \partial_2\partial_1 u_1 - (\partial_3^2+\partial_1^2) u_2 \\ \partial_3\partial_1 u_1 + \partial_3\partial_2 u_2 - (\partial_1^2+\partial_2^2) u_3 \end{pmatrix}. \]
Tensor< 1, dim > LocalIntegrators::Maxwell::tangential_curl | ( | const Tensor< 1, dim > & | g0, |
const Tensor< 1, dim > & | g1, | ||
const Tensor< 1, dim > & | g2, | ||
const Tensor< 1, dim > & | normal ) |
Auxiliary function. Given dim
tensors of first derivatives and a normal vector, compute the tangential curl
\[ \mathbf n \times \nabla \times u. \]
void LocalIntegrators::Maxwell::curl_curl_matrix | ( | FullMatrix< double > & | M, |
const FEValuesBase< dim > & | fe, | ||
const double | factor = 1. ) |
void LocalIntegrators::Maxwell::curl_matrix | ( | FullMatrix< double > & | M, |
const FEValuesBase< dim > & | fe, | ||
const FEValuesBase< dim > & | fetest, | ||
double | factor = 1. ) |
void LocalIntegrators::Maxwell::nitsche_curl_matrix | ( | FullMatrix< double > & | M, |
const FEValuesBase< dim > & | fe, | ||
const unsigned int | face_no, | ||
double | penalty, | ||
double | factor = 1. ) |
void LocalIntegrators::Maxwell::tangential_trace_matrix | ( | FullMatrix< double > & | M, |
const FEValuesBase< dim > & | fe, | ||
double | factor = 1. ) |
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inline |