curl_curl_exact_solution.h

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2026 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
 
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
 
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
 
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 
#ifndef CURL_CURL_EXACT_SOLUTION_H
#define CURL_CURL_EXACT_SOLUTION_H
 
#include "libmesh/libmesh_common.h"
#include "libmesh/vector_value.h"
 
using namespace libMesh;
 
class CurlCurlExactSolution
{
public:
  CurlCurlExactSolution() = default;
  ~CurlCurlExactSolution() = default;
 
  RealGradient operator()(Real x, Real y, Real z)
  {
    const Real ux = (1.0 - y*y)*(1.0 - z*z);
    const Real uy = (1.0 - x*x)*(1.0 - z*z);
    const Real uz = (1.0 - x*x)*(1.0 - y*y);
 
    return RealGradient(ux, uy, uz);
  }
 
  RealTensor grad(Real x, Real y, Real z)
  {
    const Real dux_dx = 0.0;
    const Real dux_dy = (1.0 - z*z)*(-2.0*y);
    const Real dux_dz = (1.0 - y*y)*(-2.0*z);
 
    const Real duy_dx = (1.0 - z*z)*(-2.0*x);
    const Real duy_dy = 0.0;
    const Real duy_dz = (1.0 - x*x)*(-2.0*z);
 
    const Real duz_dx = (1.0 - y*y)*(-2.0*x);
    const Real duz_dy = (1.0 - x*x)*(-2.0*y);
    const Real duz_dz = 0.0;
 
    return RealTensor(dux_dx, dux_dy, dux_dz, duy_dx, duy_dy, duy_dz, duz_dx, duz_dy, duz_dz);
  }
 
  RealGradient curl(Real x, Real y, Real z)
  {
    const Real duz_dy = (1.0 - x*x)*(-2.0*y);
    const Real duy_dz = (1.0 - x*x)*(-2.0*z);
 
    const Real dux_dz = (1.0 - y*y)*(-2.0*z);
    const Real duz_dx = (1.0 - y*y)*(-2.0*x);
 
    const Real dux_dy = (1.0 - z*z)*(-2.0*y);
    const Real duy_dx = (1.0 - z*z)*(-2.0*x);
 
    return RealGradient(duz_dy - duy_dz, dux_dz - duz_dx, duy_dx - dux_dy);
  }
 
  RealGradient forcing(Real x, Real y, Real z)
  {
    const Real fx = 2.0*(1.0 - y*y) + 2.0*(1.0 - z*z) + (1.0 - y*y)*(1.0 - z*z);
    const Real fy = 2.0*(1.0 - x*x) + 2.0*(1.0 - z*z) + (1.0 - x*x)*(1.0 - z*z);
    const Real fz = 2.0*(1.0 - x*x) + 2.0*(1.0 - y*y) + (1.0 - x*x)*(1.0 - y*y);
 
    return RealGradient(fx, fy, fz);
  }
 
};
 
#endif // CURL_CURL_EXACT_SOLUTION_H