From 244af449fc4713be1f1e836e14153dab8097acf0 Mon Sep 17 00:00:00 2001
From: kanschat <kanschat@0785d39b-7218-0410-832d-ea1e28bc413d>
Date: Fri, 19 Aug 2011 13:45:18 +0000
Subject: [PATCH] add trace operators

git-svn-id: https://svn.dealii.org/trunk@24117 0785d39b-7218-0410-832d-ea1e28bc413d
---
 deal.II/include/deal.II/integrators/maxwell.h | 221 +++++++++++++++++-
 1 file changed, 214 insertions(+), 7 deletions(-)

diff --git a/deal.II/include/deal.II/integrators/maxwell.h b/deal.II/include/deal.II/integrators/maxwell.h
index 54a3f16999..b7a6c334ba 100644
--- a/deal.II/include/deal.II/integrators/maxwell.h
+++ b/deal.II/include/deal.II/integrators/maxwell.h
@@ -37,7 +37,7 @@ namespace LocalIntegrators
  *   \partial_3 u_2 - \partial_2 u_3 \\
  *   \partial_1 u_3 - \partial_3 u_1 \\
  *   \partial_2 u_1 - \partial_1 u_2
- * \end{pmatrix}
+ * \end{pmatrix}.
  * @f]
  *
  * In two space dimensions, the curl is obtained by extending a vector
@@ -46,7 +46,7 @@ namespace LocalIntegrators
  * curl of a vector function and the vector curl of a scalar
  * function. The current implementation exchanges the sign and we have:
  * @f[
- *  \nabla \times \mathbf u = \partial_1 u_2 - \partial 2 u_1
+ *  \nabla \times \mathbf u = \partial_1 u_2 - \partial 2 u_1,
  *  \qquad
  *  \nabla \times p = \begin{pmatrix}
  *    \partial_2 p \\ -\partial_1 p
@@ -156,8 +156,8 @@ namespace LocalIntegrators
  * \int_Z \nabla\!\times\! u \cdot
  * \nabla\!\times\! v \,dx
  * @f]
+ * in weak form.
  *
- * @ingroup Integrators
  * @author Guido Kanschat
  * @date 2011
  */
@@ -203,14 +203,15 @@ namespace LocalIntegrators
     }
     
 /**
- * The curl operator
+ * The matrix for the curl operator
  * @f[
  * \int_Z \nabla\!\times\! u \cdot v \,dx.
  * @f]
  *
- * This is the standard curl operator in 3D and the scalar curl in 2D.
-  *
- * @ingroup Integrators
+ * This is the standard curl operator in 3D and the scalar curl in
+ * 2D. The vector curl operator can be obtained by exchanging test and
+ * trial functions.
+ *
  * @author Guido Kanschat
  * @date 2011
 */
@@ -247,6 +248,212 @@ namespace LocalIntegrators
 		}
 	}
     }
+
+				     /**
+				      * The matrix for weak boundary
+				      * condition of Nitsche type for
+				      * the tangential component in
+				      * Maxwell systems.
+				      *
+				      * @f[
+				      * \int_F \biggl( 2\gamma
+				      * (u\times n) (v\times n) -
+				      * (u\times n)(\nu \nabla\times
+				      * v) - (v\times
+				      * n)(\nu \nabla\times u)
+				      * \biggr)
+				      * @f]
+				      *
+				      * @author Guido Kanschat
+				      * @date 2011
+				      */
+      template <int dim>
+      void nitsche_curl_matrix (
+	FullMatrix<double>& M,
+	const FEValuesBase<dim>& fe,
+	double penalty,
+	double factor = 1.)
+      {
+	const unsigned int n_dofs = fe.dofs_per_cell;
+	
+	AssertDimension(fe.get_fe().n_components(), dim);
+	AssertDimension(M.m(), n_dofs);
+	AssertDimension(M.n(), n_dofs);
+	
+					 // Depending on the
+					 // dimension, the cross
+					 // product is either a scalar
+					 // (2d) or a vector
+					 // (3d). Accordingly, in the
+					 // latter case we have to sum
+					 // up three bilinear forms,
+					 // but in 2d, we don't. Thus,
+					 // we need to adapt the loop
+					 // over all dimensions
+	const unsigned int d_max = (dim==2) ? 1 : dim;
+	
+	for (unsigned k=0;k<fe.n_quadrature_points;++k)
+	  {
+	    const double dx = factor * fe.JxW(k);
+	    const Point<dim>& n = fe.normal_vector(k);
+	    for (unsigned i=0;i<n_dofs;++i)
+	      for (unsigned j=0;j<n_dofs;++j)
+		for (unsigned int d=0;d<d_max;++d)
+		  {
+		    const unsigned int d1 = (d+1)%dim;
+		    const unsigned int d2 = (d+2)%dim;
+		    
+		    const double cv = fe.shape_grad_component(i,k,d1)[d2] - fe.shape_grad_component(i,k,d2)[d1];
+		    const double cu = fe.shape_grad_component(j,k,d1)[d2] - fe.shape_grad_component(j,k,d2)[d1];
+		    const double v= fe.shape_value_component(i,k,d1)*n(d2) - fe.shape_value_component(i,k,d2)*n(d1);
+		    const double u= fe.shape_value_component(j,k,d1)*n(d2) - fe.shape_value_component(j,k,d2)*n(d1);
+		    
+		    M(i,j) += dx*(2.*penalty*u*v - cv*u - cu*v);
+		  }
+	  }
+      }
+				     /**
+				      * The product of two tangential
+				      * traces,
+				      * @f[
+				      * \int_F (u\times n)(v\times n)
+				      * \, ds.
+				      * @f]
+				      *
+				      * @author Guido Kanschat
+				      * @date 2011
+				      */
+      template <int dim>
+      void tangential_trace_matrix (
+	FullMatrix<double>& M,
+	const FEValuesBase<dim>& fe,
+	double factor = 1.)
+      {
+	const unsigned int n_dofs = fe.dofs_per_cell;
+	
+	AssertDimension(fe.get_fe().n_components(), dim);
+	AssertDimension(M.m(), n_dofs);
+	AssertDimension(M.n(), n_dofs);
+	
+					 // Depending on the
+					 // dimension, the cross
+					 // product is either a scalar
+					 // (2d) or a vector
+					 // (3d). Accordingly, in the
+					 // latter case we have to sum
+					 // up three bilinear forms,
+					 // but in 2d, we don't. Thus,
+					 // we need to adapt the loop
+					 // over all dimensions
+	const unsigned int d_max = (dim==2) ? 1 : dim;
+	
+	for (unsigned k=0;k<fe.n_quadrature_points;++k)
+	  {
+	    const double dx = factor * fe.JxW(k);
+	    const Point<dim>& n = fe.normal_vector(k);
+	    for (unsigned i=0;i<n_dofs;++i)
+	      for (unsigned j=0;j<n_dofs;++j)
+		for (unsigned int d=0;d<d_max;++d)
+		  {
+		    const unsigned int d1 = (d+1)%dim;
+		    const unsigned int d2 = (d+2)%dim;
+		    
+		    const double v= fe.shape_value_component(i,k,d1)*n(d2) - fe.shape_value_component(i,k,d2)*n(d1);
+		    const double u= fe.shape_value_component(j,k,d1)*n(d2) - fe.shape_value_component(j,k,d2)*n(d1);
+		    
+		    M(i,j) += dx*u*v;
+		  }
+	  }
+      }
+
+      				       /**
+					* The interior penalty fluxes
+					* for Maxwell systems.
+					*
+					* @f[
+					* \int_F \biggl( \gamma
+					* \{u\times n\}\{v\times n\} -
+					* \{u\times n\}\{\nu \nabla\times
+					* v\}- \{v\times
+					* n\}\{\nu \nabla\times u\}
+					* \biggr)\;dx
+					* @f]
+				      *
+				      * @author Guido Kanschat
+				      * @date 2011
+					*/
+      template <int dim>
+      inline 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.)
+      {
+	const unsigned int n_dofs = fe1.dofs_per_cell;
+	
+	AssertDimension(fe1.get_fe().n_components(), dim);
+	AssertDimension(fe2.get_fe().n_components(), dim);
+	AssertDimension(M11.m(), n_dofs);
+	AssertDimension(M11.n(), n_dofs);
+	AssertDimension(M12.m(), n_dofs);
+	AssertDimension(M12.n(), n_dofs);
+	AssertDimension(M21.m(), n_dofs);
+	AssertDimension(M21.n(), n_dofs);
+	AssertDimension(M22.m(), n_dofs);
+	AssertDimension(M22.n(), n_dofs);
+	
+	const double nu1 = factor1;
+	const double nu2 = (factor2 < 0) ? factor1 : factor2;
+	const double penalty = .5 * pen * (nu1 + nu2);
+
+					 // Depending on the
+					 // dimension, the cross
+					 // product is either a scalar
+					 // (2d) or a vector
+					 // (3d). Accordingly, in the
+					 // latter case we have to sum
+					 // up three bilinear forms,
+					 // but in 2d, we don't. Thus,
+					 // we need to adapt the loop
+					 // over all dimensions
+	const unsigned int d_max = (dim==2) ? 1 : dim;
+	
+	for (unsigned k=0;k<fe1.n_quadrature_points;++k)
+	  {
+	    const double dx = fe1.JxW(k);
+	    const Point<dim>& n = fe1.normal_vector(k);
+	    for (unsigned i=0;i<n_dofs;++i)
+	      for (unsigned j=0;j<n_dofs;++j)
+		for (unsigned d=0;d<d_max;++d)
+		  {
+		    const unsigned int d1 = (d+1)%dim;
+		    const unsigned int d2 = (d+2)%dim;
+						     // curl u, curl v
+		    const double cv1 = nu1*fe1.shape_grad_component(i,k,d1)[d2] - fe1.shape_grad_component(i,k,d2)[d1];
+		    const double cv2 = nu2*fe2.shape_grad_component(i,k,d1)[d2] - fe2.shape_grad_component(i,k,d2)[d1];
+		    const double cu1 = nu1*fe1.shape_grad_component(j,k,d1)[d2] - fe1.shape_grad_component(j,k,d2)[d1];
+		    const double cu2 = nu2*fe2.shape_grad_component(j,k,d1)[d2] - fe2.shape_grad_component(j,k,d2)[d1];
+		    
+						     // u x n, v x n
+		    const double u1= fe1.shape_value_component(j,k,d1)*n(d2) - fe1.shape_value_component(j,k,d2)*n(d1);
+		    const double u2=-fe2.shape_value_component(j,k,d1)*n(d2) + fe2.shape_value_component(j,k,d2)*n(d1);
+		    const double v1= fe1.shape_value_component(i,k,d1)*n(d2) - fe1.shape_value_component(i,k,d2)*n(d1);
+		    const double v2=-fe2.shape_value_component(i,k,d1)*n(d2) + fe2.shape_value_component(i,k,d2)*n(d1);
+		    
+		    M11(i,j) += .5*dx*(2.*penalty*u1*v1 - cv1*u1 - cu1*v1);
+		    M12(i,j) += .5*dx*(2.*penalty*v1*u2 - cv1*u2 - cu2*v1);
+		    M21(i,j) += .5*dx*(2.*penalty*u1*v2 - cv2*u1 - cu1*v2);
+		    M22(i,j) += .5*dx*(2.*penalty*u2*v2 - cv2*u2 - cu2*v2);
+		  }
+	  }
+      }
+      
+
   }
 }
 
-- 
2.39.5