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bem_grid.hh
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/**
*
* @author Lucas Frérot <lucas.frerot@epfl.ch>
*
* @section LICENSE
*
* Copyright (©) 2016 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 BEM_GRID_HH
#define BEM_GRID_HH
/* -------------------------------------------------------------------------- */
#include "fftw_engine.hh"
#include "grid.hh"
#include "surface.hh"
#include "legacy_types.hh"
/* -------------------------------------------------------------------------- */
namespace tamaas {
/**
* @brief abstract class for BEMs that use multi component fields
*/
class BemGrid {
public:
/// Constructor
BemGrid(Surface<Real>& surface);
/// Destructor
virtual ~BemGrid();
public:
/* ------------------------------------------------------------------------ */
/* Actual computations */
/* ------------------------------------------------------------------------ */
/// Compute normal vectors to surface
void computeSurfaceNormals();
/// Compute influence coefficients
void computeInfluence();
/// Compute a Lipschitz constant of gradient
void computeInfluenceLipschitz();
/// Apply influence fonctions (p -> u)
void applyInfluenceFunctions(Grid<Real, 2>& input, Grid<Real, 2>& output);
/// Apply inverse influence fonctions (u -> p)
void applyInverseInfluenceFunctions(Grid<Real, 2>& input,
Grid<Real, 2>& output);
/// Compute true tractions
virtual void computeTrueTractions() = 0;
/// Compute true displacements
virtual void computeTrueDisplacements() = 0;
/// Compute equilibrium
virtual void computeEquilibrium(Real tol, const Grid<Real, 1>& p_target) = 0;
/// Compute displacements
void computeDisplacementsFromTractions();
/// Compute tractions
void computeTractionsFromDisplacements();
/// Compute gaps
void computeGaps(Grid<Real, 2>& disp);
/* ------------------------------------------------------------------------ */
/* Field related computations */
/* ------------------------------------------------------------------------ */
/// Project point friction cone
static inline void projectOnFrictionCone(legacy::VectorProxy<Real>& p, Real mu);
/// Project field friction cone
static void projectOnFrictionCone(Grid<Real, 2>& field, Real mu);
/// Project on mean value space
static void enforceMeanValue(Grid<Real, 2>& field,
const Grid<Real, 1>& target);
/// Compute error relative to target mean value
static Real computeMeanValueError(Grid<Real, 2>& field,
const Grid<Real, 1>& target);
/// Compute error vector
static void computeMeanValueError(Grid<Real, 2>& field,
const Grid<Real, 1>& target,
Grid<Real, 1>& error_vec);
/* ------------------------------------------------------------------------ */
/* Getters */
/* ------------------------------------------------------------------------ */
/// Get influence
const GridHermitian<Real, 2>& getInfluence() const { return influence; }
/// Get normals
const Grid<Real, 2>& getSurfaceNormals() const { return surface_normals; }
/// Get tractions
const Grid<Real, 2>& getTractions() const { return tractions; }
/// Get displacements
const Grid<Real, 2>& getDisplacements() const { return displacements; }
/// Get true tractions
const Grid<Real, 2>& getTrueTractions() const;
/// Get true displacements
const Grid<Real, 2>& getTrueDisplacements() const;
/// Get gaps
const Grid<Real, 2>& getGaps() const { return gaps; }
/* ------------------------------------------------------------------------ */
/* Setters */
/* ------------------------------------------------------------------------ */
/// Elasticity parameters
void setElasticity(Real E_, Real nu_) {
E = E_;
nu = nu_;
}
/// Friction coefficient
void setMu(Real mu_) { mu = mu_; }
/// Max iterations
void setMaxIterations(UInt n) { max_iter = n; }
/// Dump frequency
void setDumpFrequency(UInt n) { dump_freq = n; }
protected:
/// Elasticity constants
Real E, nu;
/// Friction coefficient
Real mu;
/// Lipschitz constant of functional gradient
Real lipschitz;
/// Max iterations
UInt max_iter;
/// Surface
Surface<Real> surface;
/// Normal vectors
Grid<Real, 2> surface_normals;
/// Influcence matrices
GridHermitian<Real, 2> influence;
/// Tractions
Grid<Real, 2> tractions;
/// Displacements
Grid<Real, 2> displacements;
/// Gap
Grid<Real, 2> gaps;
/// True tractions
Grid<Real, 2>* true_tractions;
/// True displacements
Grid<Real, 2>* true_displacements;
/// Spectral tractions
GridHermitian<Real, 2> spectral_tractions;
/// Spectral displacements
GridHermitian<Real, 2> spectral_displacements;
/// Dump frequency
UInt dump_freq;
/// FFT Engine
FFTWEngine engine;
};
/* -------------------------------------------------------------------------- */
/* Inline definitions */
/* -------------------------------------------------------------------------- */
inline void BemGrid::projectOnFrictionCone(legacy::VectorProxy<Real>& p, Real mu) {
Real pt = std::sqrt(p(0) * p(0) + p(1) * p(1));
Real pn = p(2);
Real x = (pn + mu * pt) / (1 + mu * mu);
if (pt <= mu * pn && pn >= 0) // inside friction cone
return;
else if (mu * pt <= std::abs(pn) &&
pn < 0) // inside "project to origin" cone (undefined normal)
// else if (pn < 0) // project to origin all points with pn < 0
p = 0;
else { // projectable on cone
p(0) *= mu / pt * x;
p(1) *= mu / pt * x;
p(2) = x;
}
}
/* -------------------------------------------------------------------------- */
} // namespace tamaas
#endif // __BEM_GRID_HH__

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