heat_diffusion.hh
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	#include "diffusion_law.hh"

	#ifndef AKANTU_HEAT_DIFFUSION_HH
	#define AKANTU_HEAT_DIFFUSION_HH

	namespace akantu {

	template <Int dim> class HeatDiffusion : public DiffusionLaw {
	using Parent = DiffusionLaw;

	public:
	HeatDiffusion(DiffusionModel & model, const ID & id,
	const ID & fe_engine_id = "");

	void updateInternalParameters() override;
	void computeDiffusivityGradUOnQuadPoints(ElementType type,
	GhostType ghost_type) override;
	void computeDiffusivityOnQuadPoints(ElementType type,
	GhostType ghost_type) override;

	decltype(auto) getArguments(ElementType type, GhostType ghost_type) {
	return DiffusionLaw::getArguments<dim>(type, ghost_type);
	}

	[[nodiscard]] Real getStableTimeStep(Real element_size) override;

	[[nodiscard]] Real getRho() const override { return density * capacity; }

	[[nodiscard]] Real getEnergy(const ID & energy_id) override;
	[[nodiscard]] Real getEnergy(const ID & energy_id,
	const Element & element) override;

	private:
	auto getThermalEnergy(const Element & element) -> Real;
	auto getThermalEnergy() -> Real;

	template <class iterator, class t_iterator>
	void getThermalEnergy(iterator Eth, t_iterator T_it, t_iterator T_end) const;

	private:
	Real density{0.};

	/// capacity
	Real capacity{0.};

	// conductivity matrix
	Matrix<Real> conductivity;

	// linear variation of the conductivity (for temperature dependent
	// conductivity)
	Real conductivity_variation{0.};

	// reference temperature for the interpretation of temperature variation
	Real T_ref{0.};
	};

	} // namespace akantu

	#endif // AKANTU_HEAT_DIFFUSION_HH