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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 | |||
| 12 | #ifndef BEMBEL_SRC_HOMOGENISEDLAPLACE_SINGLELAYERPOTENTIAL_HPP_ | ||
| 13 | #define BEMBEL_SRC_HOMOGENISEDLAPLACE_SINGLELAYERPOTENTIAL_HPP_ | ||
| 14 | |||
| 15 | namespace Bembel { | ||
| 16 | // forward declaration of class HomogenisedLaplaceSingleLayerPotential | ||
| 17 | // in order to define traits | ||
| 18 | template<typename LinOp> | ||
| 19 | class HomogenisedLaplaceSingleLayerPotential; | ||
| 20 | |||
| 21 | /** | ||
| 22 | * \brief Specification of the PotentialTraits for the Homogenised Laplace. | ||
| 23 | */ | ||
| 24 | template<typename LinOp> | ||
| 25 | struct PotentialTraits<HomogenisedLaplaceSingleLayerPotential<LinOp>> { | ||
| 26 | typedef Eigen::VectorXd::Scalar Scalar; | ||
| 27 | static constexpr int OutputSpaceDimension = 1; | ||
| 28 | }; | ||
| 29 | |||
| 30 | /** | ||
| 31 | * \ingroup HomogenisedLaplace | ||
| 32 | * \brief This class implements the specification of the integration for the | ||
| 33 | * single layer potential for the homogenised Laplace. | ||
| 34 | */ | ||
| 35 | template<typename LinOp> | ||
| 36 | class HomogenisedLaplaceSingleLayerPotential : public PotentialBase< | ||
| 37 | HomogenisedLaplaceSingleLayerPotential<LinOp>, LinOp> { | ||
| 38 | // implementation of the kernel evaluation, which may be based on the | ||
| 39 | // information available from the superSpace | ||
| 40 | |||
| 41 | public: | ||
| 42 | /** | ||
| 43 | * \brief Constructs an object initialising the coefficients and the degree | ||
| 44 | * via the static variable HomogenisedLaplaceSingleLayerOperator::precision. | ||
| 45 | */ | ||
| 46 | 2 | HomogenisedLaplaceSingleLayerPotential() { | |
| 47 | 2 | this->deg = getDegree( | |
| 48 | HomogenisedLaplaceSingleLayerOperator::getPrecision()); | ||
| 49 |
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2 | this->cs = getCoefficients( |
| 50 | HomogenisedLaplaceSingleLayerOperator::getPrecision()); | ||
| 51 | 2 | } | |
| 52 | Eigen::Matrix< | ||
| 53 | typename PotentialReturnScalar< | ||
| 54 | typename LinearOperatorTraits<LinOp>::Scalar, | ||
| 55 | 480000 | double>::Scalar, 1, 1> evaluateIntegrand_impl( | |
| 56 | const FunctionEvaluator<LinOp> &fun_ev, const ElementTreeNode &element, | ||
| 57 | const Eigen::Vector3d &point, const SurfacePoint &p) const { | ||
| 58 | // get evaluation points on unit square | ||
| 59 |
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480000 | auto s = p.segment < 2 > (0); |
| 60 | |||
| 61 | // get quadrature weights | ||
| 62 |
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480000 | auto ws = p(2); |
| 63 | |||
| 64 | // get points on geometry and tangential derivatives | ||
| 65 |
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480000 | auto x_f = p.segment < 3 > (3); |
| 66 |
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480000 | auto x_f_dx = p.segment < 3 > (6); |
| 67 |
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480000 | auto x_f_dy = p.segment < 3 > (9); |
| 68 | |||
| 69 | // compute surface measures from tangential derivatives | ||
| 70 |
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480000 | auto x_kappa = x_f_dx.cross(x_f_dy).norm(); |
| 71 | |||
| 72 | // evaluate kernel | ||
| 73 |
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480000 | auto kernel = evaluateKernel(point, x_f); |
| 74 | |||
| 75 | // assemble Galerkin solution | ||
| 76 |
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480000 | auto cauchy_value = fun_ev.evaluate(element, p); |
| 77 | |||
| 78 | // integrand without basis functions | ||
| 79 |
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480000 | auto integrand = kernel * cauchy_value * x_kappa * ws; |
| 80 | |||
| 81 |
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960000 | return integrand; |
| 82 | } | ||
| 83 | |||
| 84 | /** | ||
| 85 | * \brief Fundamental solution of the homogenised Laplace problem | ||
| 86 | */ | ||
| 87 | 480000 | double evaluateKernel(const Eigen::Vector3d &x, | |
| 88 | const Eigen::Vector3d &y) const { | ||
| 89 |
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480000 | return k_mod(x - y) |
| 90 |
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480000 | + evaluate_solid_sphericals(x - y, this->cs, this->deg, false); |
| 91 | } | ||
| 92 | |||
| 93 | private: | ||
| 94 | /** The degree of the spherical harmonics expansion */ | ||
| 95 | unsigned int deg; | ||
| 96 | /** The coefficients of the spherical harmonics expansion */ | ||
| 97 | Eigen::VectorXd cs; | ||
| 98 | }; | ||
| 99 | |||
| 100 | } // namespace Bembel | ||
| 101 | |||
| 102 | #endif // BEMBEL_SRC_HOMOGENISEDLAPLACE_SINGLELAYERPOTENTIAL_HPP_ | ||
| 103 |