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| 1 | // This file is part of Bembel, the higher order C++ boundary element library. | ||
| 2 | // | ||
| 3 | // Copyright (C) 2022 see <http://www.bembel.eu> | ||
| 4 | // | ||
| 5 | // It was written as part of a cooperation of J. Doelz, H. Harbrecht, S. Kurz, | ||
| 6 | // M. Multerer, S. Schoeps, and F. Wolf at Technische Universitaet Darmstadt, | ||
| 7 | // Universitaet Basel, and Universita della Svizzera italiana, Lugano. This | ||
| 8 | // source code is subject to the GNU General Public License version 3 and | ||
| 9 | // provided WITHOUT ANY WARRANTY, see <http://www.bembel.eu> for further | ||
| 10 | // information. | ||
| 11 | #ifndef BEMBEL_SRC_HELMHOLTZ_SINGLELAYERPOTENTIAL_HPP_ | ||
| 12 | #define BEMBEL_SRC_HELMHOLTZ_SINGLELAYERPOTENTIAL_HPP_ | ||
| 13 | |||
| 14 | namespace Bembel { | ||
| 15 | // forward declaration of class HelmholtzSingleLayerPotential in order to define | ||
| 16 | // traits | ||
| 17 | template <typename LinOp> | ||
| 18 | class HelmholtzSingleLayerPotential; | ||
| 19 | |||
| 20 | /** | ||
| 21 | * \brief Specification of the PotentialTraits for the Helmholtz. | ||
| 22 | */ | ||
| 23 | template <typename LinOp> | ||
| 24 | struct PotentialTraits<HelmholtzSingleLayerPotential<LinOp>> { | ||
| 25 | typedef Eigen::VectorXcd::Scalar Scalar; | ||
| 26 | static constexpr int OutputSpaceDimension = 1; | ||
| 27 | }; | ||
| 28 | |||
| 29 | /** | ||
| 30 | * \ingroup Helmholtz | ||
| 31 | * \brief This class implements the specification of the integration for the | ||
| 32 | * single layer potential for Helmholtz. | ||
| 33 | */ | ||
| 34 | template <typename LinOp> | ||
| 35 | class HelmholtzSingleLayerPotential | ||
| 36 | : public PotentialBase<HelmholtzSingleLayerPotential<LinOp>, LinOp> { | ||
| 37 | // implementation of the kernel evaluation, which may be based on the | ||
| 38 | // information available from the superSpace | ||
| 39 | public: | ||
| 40 | 2 | HelmholtzSingleLayerPotential() {} | |
| 41 | Eigen::Matrix<typename PotentialReturnScalar< | ||
| 42 | typename LinearOperatorTraits<LinOp>::Scalar, | ||
| 43 | std::complex<double>>::Scalar, | ||
| 44 | 1, 1> | ||
| 45 | 38401 | evaluateIntegrand_impl(const FunctionEvaluator<LinOp> &fun_ev, | |
| 46 | const ElementTreeNode &element, | ||
| 47 | const Eigen::Vector3d &point, | ||
| 48 | const SurfacePoint &p) const { | ||
| 49 | // get evaluation points on unit square | ||
| 50 |
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38401 | auto s = p.segment<2>(0); |
| 51 | |||
| 52 | // get quadrature weights | ||
| 53 |
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38401 | auto ws = p(2); |
| 54 | |||
| 55 | // get points on geometry and tangential derivatives | ||
| 56 |
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38401 | auto x_f = p.segment<3>(3); |
| 57 |
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38401 | auto x_f_dx = p.segment<3>(6); |
| 58 |
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38401 | auto x_f_dy = p.segment<3>(9); |
| 59 | |||
| 60 | // compute surface measures from tangential derivatives | ||
| 61 |
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38401 | auto x_kappa = x_f_dx.cross(x_f_dy).norm(); |
| 62 | |||
| 63 | // evaluate kernel | ||
| 64 |
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38401 | auto kernel = evaluateKernel(point, x_f); |
| 65 | |||
| 66 | // assemble Galerkin solution | ||
| 67 |
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38401 | auto cauchy_value = fun_ev.evaluate(element, p); |
| 68 | |||
| 69 | // integrand without basis functions | ||
| 70 |
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38401 | auto integrand = kernel * cauchy_value * x_kappa * ws; |
| 71 | |||
| 72 |
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76802 | return integrand; |
| 73 | } | ||
| 74 | |||
| 75 | /** | ||
| 76 | * \brief Fundamental solution of Laplace problem | ||
| 77 | */ | ||
| 78 | 38401 | std::complex<double> evaluateKernel(const Eigen::Vector3d &x, | |
| 79 | const Eigen::Vector3d &y) const { | ||
| 80 |
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38401 | auto r = (x - y).norm(); |
| 81 |
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38401 | return std::exp(-std::complex<double>(0., 1.) * wavenumber_ * r) / 4. / |
| 82 | 76802 | BEMBEL_PI / r; | |
| 83 | } | ||
| 84 | ////////////////////////////////////////////////////////////////////////////// | ||
| 85 | // setters | ||
| 86 | ////////////////////////////////////////////////////////////////////////////// | ||
| 87 | 2 | void set_wavenumber(std::complex<double> wavenumber) { | |
| 88 | 2 | wavenumber_ = wavenumber; | |
| 89 | 2 | } | |
| 90 | ////////////////////////////////////////////////////////////////////////////// | ||
| 91 | // getters | ||
| 92 | ////////////////////////////////////////////////////////////////////////////// | ||
| 93 | std::complex<double> get_wavenumber() { return wavenumber_; } | ||
| 94 | |||
| 95 | private: | ||
| 96 | std::complex<double> wavenumber_; | ||
| 97 | }; | ||
| 98 | |||
| 99 | } // namespace Bembel | ||
| 100 | #endif // BEMBEL_SRC_HELMHOLTZ_SINGLELAYERPOTENTIAL_HPP_ | ||
| 101 |