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kelvin_helper.hh
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/**
* @file
* @section LICENSE
*
* Copyright (©) 2016-2021 EPFL (École Polytechnique Fédérale de Lausanne),
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program 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 Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <https://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef KELVIN_HELPER_HH
#define KELVIN_HELPER_HH
/* -------------------------------------------------------------------------- */
#include "grid.hh"
#include "grid_hermitian.hh"
#include "influence.hh"
#include "integration/accumulator.hh"
#include "logger.hh"
#include "model.hh"
#include "model_type.hh"
#include <tuple>
/* -------------------------------------------------------------------------- */
namespace tamaas {
namespace detail {
/* -------------------------------------------------------------------------- */
/// Trait for kelvin local types
template <typename T>
struct KelvinTrait;
template <UInt dim>
struct KelvinTrait<influence::Kelvin<dim, 0>> {
using source_t = VectorProxy<Complex, dim>;
using out_t = VectorProxy<Complex, dim>;
};
template <UInt dim>
struct KelvinTrait<influence::Kelvin<dim, 1>> {
using source_t = SymMatrixProxy<Complex, dim>;
using out_t = VectorProxy<Complex, dim>;
};
template <UInt dim>
struct KelvinTrait<influence::Kelvin<dim, 2>> {
using source_t = SymMatrixProxy<Complex, dim>;
using out_t = SymMatrixProxy<Complex, dim>;
};
template <UInt dim>
struct KelvinTrait<influence::Boussinesq<dim, 0>> {
using source_t = VectorProxy<Complex, dim>;
using out_t = VectorProxy<Complex, dim>;
};
template <UInt dim>
struct KelvinTrait<influence::Boussinesq<dim, 1>> {
using source_t = VectorProxy<Complex, dim>;
using out_t = SymMatrixProxy<Complex, dim>;
};
/* -------------------------------------------------------------------------- */
/// Helper to apply integral representation on output
template <model_type type, typename kelvin_t,
typename = typename KelvinTrait<kelvin_t>::source_t>
struct KelvinHelper {
using trait = model_type_traits<type>;
static constexpr UInt dim = trait::dimension;
static constexpr UInt bdim = trait::boundary_dimension;
using BufferType = GridHermitian<Real, bdim>;
using source_t = typename KelvinTrait<kelvin_t>::source_t;
using out_t = typename KelvinTrait<kelvin_t>::out_t;
virtual ~KelvinHelper() = default;
/**
@brief Apply the regular part of Kelvin to source and sum into output
This function performs the linear integration algorithm using the
accumulator.
*/
void applyIntegral(std::vector<BufferType>& source,
std::vector<BufferType>& out,
const Grid<Real, bdim>& wavevectors, Real domain_size,
const kelvin_t& kelvin) {
// Sanity check
if (source.size() != out.size())
TAMAAS_EXCEPTION(
"Linear integration requires source and out of same sizes");
accumulator.makeUniformMesh(source.size(), domain_size);
auto waverange = range<VectorProxy<const Real, bdim>>(wavevectors);
for (auto&& tuple : accumulator.forward(source, wavevectors)) {
auto&& l = std::get<0>(tuple);
auto&& xl_ = std::get<1>(tuple);
auto&& acc_g0 = std::get<2>(tuple);
auto&& acc_g1 = std::get<3>(tuple);
Loop::loop(
[xl = xl_, &kelvin](auto qv, auto u, auto acc_g0, auto acc_g1) {
Real q = qv.l2norm();
auto dense_G0 = dense(acc_g0), dense_G1 = dense(acc_g1);
auto tmp = kelvin.template applyU1<false, true>(qv, dense_G0);
tmp *= -q * xl;
tmp += kelvin.template applyU0<false, true>(qv, dense_G0);
tmp += kelvin.template applyU1<false, true>(qv, dense_G1);
tmp *= std::exp(-q * xl);
u += tmp;
},
waverange.headless(), range<out_t>(out[l]).headless(),
range<source_t>(acc_g0).headless(),
range<source_t>(acc_g1).headless());
}
for (auto&& tuple : accumulator.backward(source, wavevectors)) {
auto&& l = std::get<0>(tuple);
auto&& xl_ = std::get<1>(tuple);
auto&& acc_g0 = std::get<2>(tuple);
auto&& acc_g1 = std::get<3>(tuple);
Loop::loop(
[xl = xl_, &kelvin](auto qv, auto u, auto acc_g0, auto acc_g1) {
Real q = qv.l2norm();
auto dense_G0 = dense(acc_g0), dense_G1 = dense(acc_g1);
auto tmp = kelvin.template applyU1<true, true>(qv, dense_G0);
tmp *= -q * xl;
tmp += kelvin.template applyU0<true, true>(qv, dense_G0);
tmp += kelvin.template applyU1<true, true>(qv, dense_G1);
tmp *= std::exp(q * xl);
u += tmp; // should automatically symmetrize if needed
},
waverange.headless(), range<out_t>(out[l]).headless(),
range<source_t>(acc_g0).headless(),
range<source_t>(acc_g1).headless());
}
}
private:
template <bool upper>
struct cutoff_functor {
Real r, xc, dx, cutoff;
kelvin_t kelvin;
void operator()(VectorProxy<const Real, bdim> qv, source_t wj0,
source_t wj1, out_t out_i) const {
using integ = Integrator<1>;
Real q = qv.l2norm();
// Do not compute if element is too far from source
if (std::exp(-q * std::abs(dx)) < std::abs(cutoff))
return;
auto dense_wj0 = dense(wj0);
auto dense_wj1 = dense(wj1);
std::array<Real, 4> G = {integ::template G0<upper, 0>(q, r, dx),
integ::template G1<upper, 0>(q, r, dx),
integ::template G0<upper, 1>(q, r, dx),
integ::template G1<upper, 1>(q, r, dx)};
// Do first shape function
out_i += G[0] * kelvin.template applyU0<upper, true>(qv, dense_wj0);
out_i += G[1] * kelvin.template applyU1<upper, true>(qv, dense_wj0);
// Do second shape function
out_i += G[2] * kelvin.template applyU0<upper, true>(qv, dense_wj1);
out_i += G[3] * kelvin.template applyU1<upper, true>(qv, dense_wj1);
}
};
public:
/**
@brief Apply the regular part of Kelvin to source and sum into output
This function performs the cutoff integration algorithm. Not to be
confused with its overload above.
*/
void applyIntegral(std::vector<BufferType>& source, BufferType& out,
UInt layer, const Grid<Real, bdim>& wavevectors,
Real domain_size, Real cutoff, const kelvin_t& kelvin) {
accumulator.makeUniformMesh(source.size(), domain_size);
auto xi = accumulator.nodePositions()[layer];
auto waverange = range<VectorProxy<const Real, bdim>>(wavevectors);
for (auto bounds : accumulator.elements()) {
const auto j = thrust::get<0>(bounds);
const auto xj0 = thrust::get<1>(bounds);
const auto xj1 = thrust::get<2>(bounds);
const auto r = 0.5 * std::abs(xj0 - xj1);
const auto xc = 0.5 * (xj0 + xj1);
const auto dx = xc - xi;
Logger().get(LogLevel::debug)
<< TAMAAS_DEBUG_MSG("Integration element " << j);
// Treat lower case
if (j < layer) {
const cutoff_functor<false> func{r, xc, dx, cutoff, kelvin};
Loop::loop(func, waverange.headless(),
range<source_t>(source[j]).headless(),
range<source_t>(source[j + 1]).headless(),
range<out_t>(out).headless());
}
// Treat upper case
else {
const cutoff_functor<true> func{r, xc, dx, cutoff, kelvin};
Loop::loop(func, waverange.headless(),
range<source_t>(source[j]).headless(),
range<source_t>(source[j + 1]).headless(),
range<out_t>(out).headless());
}
}
}
/// Apply free term of distribution derivative
void applyFreeTerm(std::vector<BufferType>& source,
std::vector<BufferType>& out, const kelvin_t& kelvin) {
for (UInt l : Loop::range(source.size())) {
applyFreeTerm(source[l], out[l], kelvin);
}
}
/// Apply free term of distribution derivative (layer)
void applyFreeTerm(BufferType& /*source*/, BufferType& /*out*/,
const kelvin_t& /*kelvin*/) {}
/// Making the output free of communist NaN
void makeFundamentalGreatAgain(std::vector<BufferType>& out) {
for (auto&& layer : out)
makeFundamentalGreatAgain(layer);
}
/// Making the output free of communist NaN (layer)
void makeFundamentalGreatAgain(BufferType& /*out_layer*/) {}
protected:
Accumulator<type, source_t> accumulator;
};
/// Applying free term for double gradient of Kelvin
template <>
inline void
KelvinHelper<model_type::volume_2d, influence::Kelvin<3, 2>>::applyFreeTerm(
BufferType& source, BufferType& out,
const influence::Kelvin<3, 2>& kelvin) {
// No need for headless loops as discontinuity term does not depend on q
Loop::loop(
[&kelvin](auto u, auto w) {
u += kelvin.applyDiscontinuityTerm(dense(w));
},
range<out_t>(out), range<source_t>(source));
}
/// Setting fundamental mode to zero: we've got no other choice here
template <>
inline void KelvinHelper<model_type::volume_2d, influence::Kelvin<3, 0>>::
makeFundamentalGreatAgain(BufferType& layer) {
// Fundamental model lives only in root rank
if (mpi::rank() != 0)
return;
out_t u(&layer(0));
u = 0;
}
/* -------------------------------------------------------------------------- */
template <model_type type>
struct SurfaceTractionHelper {
using trait = model_type_traits<type>;
static constexpr UInt dim = trait::dimension;
static constexpr UInt bdim = trait::boundary_dimension;
using BufferType = GridHermitian<Real, bdim>;
using kelvin_t = influence::Kelvin<3, 2>;
using source_t = typename KelvinTrait<kelvin_t>::source_t;
using out_t = typename KelvinTrait<kelvin_t>::out_t;
/// Compute surface tractions due to eigenstress distribution
template <bool apply_q_power>
void computeSurfaceTractions(std::vector<BufferType>& source,
BufferType& tractions,
const Grid<Real, bdim>& wavevectors,
Real domain_size, const kelvin_t& kelvin,
const influence::ElasticHelper<dim>& el) {
accumulator.makeUniformMesh(source.size(), domain_size);
// only doing backward loop because forward loop gives 0 for l = 0
for (auto&& tuple : accumulator.backward(source, wavevectors)) {
auto&& l = std::get<0>(tuple);
auto&& acc_g0 = std::get<2>(tuple);
auto&& acc_g1 = std::get<3>(tuple);
// Just skip all layers and let the accumulator accumulate
if (l != 0)
continue;
Loop::loop(
[&kelvin, &el](auto qv, auto t, auto acc_g0, auto acc_g1) {
// computing strains
auto dense_G0 = dense(acc_g0), dense_G1 = dense(acc_g1);
auto strains =
kelvin.template applyU0<true, apply_q_power>(qv, dense_G0);
strains +=
kelvin.template applyU1<true, apply_q_power>(qv, dense_G1);
// computing traction vector
Vector<Real, dim> normal{{{0, 0, -1}}};
t = el(strains) * normal;
},
range<VectorProxy<const Real, bdim>>(wavevectors).headless(),
range<VectorProxy<Complex, dim>>(tractions).headless(),
range<source_t>(acc_g0).headless(),
range<source_t>(acc_g1).headless());
}
}
protected:
Accumulator<type, source_t> accumulator;
};
} // namespace detail
} // namespace tamaas
#endif // KELVIN_HELPER_HH

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