SingleLayerPotential.hpp

// This file is part of Bembel, the higher order C++ boundary element library.
//
// Copyright (C) 2022 see <http://www.bembel.eu>
//
// It was written as part of a cooperation of J. Doelz, H. Harbrecht, S. Kurz,
// M. Multerer, S. Schoeps, and F. Wolf at Technische Universitaet Darmstadt,
// Universitaet Basel, and Universita della Svizzera italiana, Lugano. This
// source code is subject to the GNU General Public License version 3 and
// provided WITHOUT ANY WARRANTY, see <http://www.bembel.eu> for further
// information.
#ifndef BEMBEL_SRC_LAPLACE_SINGLELAYERPOTENTIAL_HPP_
#define BEMBEL_SRC_LAPLACE_SINGLELAYERPOTENTIAL_HPP_
 
namespace Bembel {
// forward declaration of class LaplaceSingleLayerPotential in order to define
// traits
template <typename LinOp>
class LaplaceSingleLayerPotential;
template <typename LinOp>
struct PotentialTraits<LaplaceSingleLayerPotential<LinOp>> {
  typedef Eigen::VectorXd::Scalar Scalar;
  static constexpr int OutputSpaceDimension = 1;
};
 
template <typename LinOp>
class LaplaceSingleLayerPotential
    : public PotentialBase<LaplaceSingleLayerPotential<LinOp>, LinOp> {
  // implementation of the kernel evaluation, which may be based on the
  // information available from the superSpace
 public:
  LaplaceSingleLayerPotential() {}
  Eigen::Matrix<
      typename PotentialReturnScalar<
          typename LinearOperatorTraits<LinOp>::Scalar, double>::Scalar,
      1, 1>
  evaluateIntegrand_impl(const FunctionEvaluator<LinOp> &fun_ev,
                         const ElementTreeNode &element,
                         const Eigen::Vector3d &point,
                         const SurfacePoint &p) const {
    // get evaluation points on unit square
    auto s = p.segment<2>(0);
 
    // get quadrature weights
    auto ws = p(2);
 
    // get points on geometry and tangential derivatives
    auto x_f = p.segment<3>(3);
    auto x_f_dx = p.segment<3>(6);
    auto x_f_dy = p.segment<3>(9);
 
    // compute surface measures from tangential derivatives
    auto x_kappa = x_f_dx.cross(x_f_dy).norm();
 
    // evaluate kernel
    auto kernel = evaluateKernel(point, x_f);
 
    // assemble Galerkin solution
    auto cauchy_value = fun_ev.evaluate(element, p);
 
    // integrand without basis functions
    auto integrand = kernel * cauchy_value * x_kappa * ws;
 
    return integrand;
  }
 
  double evaluateKernel(const Eigen::Vector3d &x,
                        const Eigen::Vector3d &y) const {
    return 1. / 4. / BEMBEL_PI / (x - y).norm();
  }
};
 
}  // namespace Bembel
#endif  // BEMBEL_SRC_LAPLACE_SINGLELAYERPOTENTIAL_HPP_