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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_LAPLACE_SINGLELAYERPOTENTIAL_HPP_ | ||
| 12 | #define BEMBEL_SRC_LAPLACE_SINGLELAYERPOTENTIAL_HPP_ | ||
| 13 | |||
| 14 | namespace Bembel { | ||
| 15 | // forward declaration of class LaplaceSingleLayerPotential in order to define | ||
| 16 | // traits | ||
| 17 | template <typename LinOp> | ||
| 18 | class LaplaceSingleLayerPotential; | ||
| 19 | /** | ||
| 20 | * \brief Specification of the PotentialTraits for Laplace. | ||
| 21 | */ | ||
| 22 | template <typename LinOp> | ||
| 23 | struct PotentialTraits<LaplaceSingleLayerPotential<LinOp>> { | ||
| 24 | typedef Eigen::VectorXd::Scalar Scalar; | ||
| 25 | static constexpr int OutputSpaceDimension = 1; | ||
| 26 | }; | ||
| 27 | |||
| 28 | /** | ||
| 29 | * \ingroup Laplace | ||
| 30 | * \brief This class implements the specification of the integration for the | ||
| 31 | * single layer potential for Laplace. | ||
| 32 | */ | ||
| 33 | template <typename LinOp> | ||
| 34 | class LaplaceSingleLayerPotential | ||
| 35 | : public PotentialBase<LaplaceSingleLayerPotential<LinOp>, LinOp> { | ||
| 36 | // implementation of the kernel evaluation, which may be based on the | ||
| 37 | // information available from the superSpace | ||
| 38 | public: | ||
| 39 | 2 | LaplaceSingleLayerPotential() {} | |
| 40 | Eigen::Matrix< | ||
| 41 | typename PotentialReturnScalar< | ||
| 42 | typename LinearOperatorTraits<LinOp>::Scalar, double>::Scalar, | ||
| 43 | 1, 1> | ||
| 44 | 384001 | evaluateIntegrand_impl(const FunctionEvaluator<LinOp> &fun_ev, | |
| 45 | const ElementTreeNode &element, | ||
| 46 | const Eigen::Vector3d &point, | ||
| 47 | const SurfacePoint &p) const { | ||
| 48 | // get evaluation points on unit square | ||
| 49 |
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384001 | auto s = p.segment<2>(0); |
| 50 | |||
| 51 | // get quadrature weights | ||
| 52 |
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384001 | auto ws = p(2); |
| 53 | |||
| 54 | // get points on geometry and tangential derivatives | ||
| 55 |
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384001 | auto x_f = p.segment<3>(3); |
| 56 |
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384001 | auto x_f_dx = p.segment<3>(6); |
| 57 |
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384001 | auto x_f_dy = p.segment<3>(9); |
| 58 | |||
| 59 | // compute surface measures from tangential derivatives | ||
| 60 |
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384001 | auto x_kappa = x_f_dx.cross(x_f_dy).norm(); |
| 61 | |||
| 62 | // evaluate kernel | ||
| 63 |
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384001 | auto kernel = evaluateKernel(point, x_f); |
| 64 | |||
| 65 | // assemble Galerkin solution | ||
| 66 |
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384001 | auto cauchy_value = fun_ev.evaluate(element, p); |
| 67 | |||
| 68 | // integrand without basis functions | ||
| 69 |
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384001 | auto integrand = kernel * cauchy_value * x_kappa * ws; |
| 70 | |||
| 71 |
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768002 | return integrand; |
| 72 | } | ||
| 73 | |||
| 74 | /** | ||
| 75 | * \brief Fundamental solution of Laplace problem | ||
| 76 | */ | ||
| 77 | 384001 | double evaluateKernel(const Eigen::Vector3d &x, | |
| 78 | const Eigen::Vector3d &y) const { | ||
| 79 |
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384001 | return 1. / 4. / BEMBEL_PI / (x - y).norm(); |
| 80 | } | ||
| 81 | }; | ||
| 82 | |||
| 83 | } // namespace Bembel | ||
| 84 | #endif // BEMBEL_SRC_LAPLACE_SINGLELAYERPOTENTIAL_HPP_ | ||
| 85 |