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tamaas/src/model/integration/integrator.hh
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integrator.hh
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/**
* @file
*
* @author Lucas Frérot <lucas.frerot@epfl.ch>
*
* @section LICENSE
*
* Copyright (©) 2018 EPFL (Ecole Polytechnique Fédérale de
* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
* Solides)
*
* Tamaas 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 3 of the License, or (at your option) any
* later version.
*
* Tamaas 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 Tamaas. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef INTEGRATOR_HH
#define INTEGRATOR_HH
/* -------------------------------------------------------------------------- */
#include "element.hh"
#include <expolit/expolit>
/* -------------------------------------------------------------------------- */
namespace tamaas {
namespace ex = expolit;
template <UInt interpolation_order>
class Integrator {
using element = ExponentialElement<interpolation_order>;
static constexpr std::pair<Real, Real> bounds{-1, 1};
public:
/// Standard integral of \f$\exp(\pm qy) \phi(y)\f$ over an element of radius
/// \f$r\f$ and center \f$x_c\f$
template <bool upper, UInt shape>
static Real G0(Real q, Real r, Real xc) {
const auto F = element::template g0<upper, shape>(q * r);
return r * std::exp(element::sign(upper) * q * xc) *
ex::definite_integral(bounds, F);
}
/// Standard integral of \f$qy\exp(\pm qy) \phi(y)\f$ over an element of
/// radius \f$r\f$ and center \f$x_c\f$
template <bool upper, UInt shape>
static Real G1(Real q, Real r, Real xc) {
const auto c = q * r;
const auto integrals =
std::make_pair(element::template g0<upper, shape>(c),
element::template g1<upper, shape>(c));
return r * std::exp(element::sign(upper) * q * xc) *
(q * xc * ex::definite_integral(bounds, integrals.first) +
ex::definite_integral(bounds, integrals.second));
}
/// Standard integral of \f$\phi(y)\f$ over an element of radius
/// \f$r\f$ and center \f$x_c\f$. Used for fundamental mode
template <UInt shape>
constexpr static Real F(Real r) {
return r * ex::definite_integral(bounds, element::shapes[shape]);
}
};
} // namespace tamaas
#endif // INTEGRATOR_HH
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