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			/**
			* @file cell_base.hh
			*
			* @author Till Junge <till.junge@epfl.ch>
			*
			* @date 01 Nov 2017
			*
			* @brief Base class representing a unit cell cell with single
			* projection operator
			*
			* Copyright © 2017 Till Junge
			*
			* µSpectre is free software; you can redistribute it and/or
			* modify it under the terms of the GNU General Public License as
			* published by the Free Software Foundation, either version 3, or (at
			* your option) any later version.
			*
			* µSpectre 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
			* General Public License for more details.
			*
			* You should have received a copy of the GNU General Public License
			* along with GNU Emacs; see the file COPYING. If not, write to the
			* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
			* Boston, MA 02111-1307, USA.
			*/

			#ifndef CELL_BASE_H
			#define CELL_BASE_H

			#include "common/common.hh"
			#include "common/ccoord_operations.hh"
			#include "common/field.hh"
			#include "common/utilities.hh"
			#include "materials/material_base.hh"
			#include "fft/projection_base.hh"
			#include "cell/cell_traits.hh"

			#include <vector>
			#include <memory>
			#include <tuple>
			#include <functional>
			#include <array>

			namespace muSpectre {
			/**
			* Cell adaptors implement the matrix-vector multiplication and
			* allow the system to be used like a sparse matrix in
			* conjugate-gradient-type solvers
			*/
			template <class Cell>
			class CellAdaptor;

			/**
			* Base class for cells that is not templated and therefore can be
			* in solvers that see cells as runtime-polymorphic objects. This
			* allows the use of standard
			* (i.e. spectral-method-implementation-agnostic) solvers, as for
			* instance the scipy solvers
			*/

			class Cell
			{
			public:
			//! sparse matrix emulation
			using Adaptor = CellAdaptor<Cell>;

			//! dynamic vector type for interactions with numpy/scipy/solvers etc.
			using Vector_t = Eigen::Matrix<Real, Eigen::Dynamic, 1>;

			//! dynamic matrix type for setting strains
			using Matrix_t = Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic>;

			//! ref to constant vector
			using ConstVector_ref = Eigen::Map<const Vector_t>;

			//! output vector reference for solvers
			using Vector_ref = Eigen::Map<Vector_t>;

			//! Default constructor
			Cell() = default;

			//! Copy constructor
			Cell(const Cell &other) = default;

			//! Move constructor
			Cell(Cell &&other) = default;

			//! Destructor
			virtual ~Cell() = default;

			//! Copy assignment operator
			Cell& operator=(const Cell &other) = default;

			//! Move assignment operator
			Cell& operator=(Cell &&other) = default;

			//! for handling double initialisations right
			bool is_initialised() const {return this->initialised;}

			//! returns the number of degrees of freedom in the cell
			virtual Dim_t get_nb_dof() const = 0;

			//! return the communicator object
			virtual const Communicator & get_communicator() const = 0;

			/**
			* formulation is hard set by the choice of the projection class
			*/
			virtual const Formulation & get_formulation() const = 0;

			/**
			* returns the material dimension of the problem
			*/
			virtual Dim_t get_material_dim() const = 0;

			/**
			* returns the number of rows and cols for the strain matrix type
			* (for full storage, the strain is stored in material_dim ×
			* material_dim matrices, but in symmetriy storage, it is a column
			* vector)
			*/
			virtual std::array<Dim_t, 2> get_strain_shape() const = 0;

			/**
			* returns a writable map onto the strain field of this cell. This
			* corresponds to the unknowns in a typical solve cycle.
			*/
			virtual Vector_ref get_strain_vector() = 0;

			/**
			* returns a read-only map onto the stress field of this
			* cell. This corresponds to the intermediate (and finally, total)
			* solution in a typical solve cycle
			*/
			virtual ConstVector_ref get_stress_vector() const = 0;


			/**
			* evaluates and returns the stress for the currently set strain
			*/
			virtual ConstVector_ref evaluate_stress() = 0;

			/**
			* evaluates and returns the stress and stiffness for the currently set strain
			*/
			virtual std::array<ConstVector_ref, 2> evaluate_stress_tangent() = 0;


			/**
			* applies the projection operator in-place on the input vector
			*/
			virtual void apply_projection(Eigen::Ref<Vector_t> vec) = 0;

			/**
			* freezes all the history variables of the materials
			*/
			virtual void save_history_variables() = 0;

			/**
			* evaluates the directional and projected stiffness (this
			* corresponds to G:K:δF in de Geus 2017,
			* http://dx.doi.org/10.1016/j.cma.2016.12.032). It seems that
			* this operation needs to be implemented with a copy in oder to
			* be compatible with scipy and EigenCG etc (At the very least,
			* the copy is only made once)
			*/
			virtual Vector_ref evaluate_projected_directional_stiffness
			(Eigen::Ref<const Vector_t> delF) = 0;


			/**
			* set uniform strain (typically used to initialise problems
			*/
			virtual void set_uniform_strain(const Eigen::Ref<const Matrix_t> &) = 0;

			//! get a sparse matrix view on the cell
			virtual Adaptor get_adaptor() = 0;
			protected:
			bool initialised{false}; //!< to handle double initialisation right

			private:
			};
			//! DimS spatial dimension (dimension of problem
			//! DimM material_dimension (dimension of constitutive law)
			template <Dim_t DimS, Dim_t DimM=DimS>
			class CellBase: public Cell
			{
			public:
			using Parent = Cell;
			using Ccoord = Ccoord_t<DimS>; //!< cell coordinates type
			using Rcoord = Rcoord_t<DimS>; //!< physical coordinates type
			//! global field collection
			using FieldCollection_t = GlobalFieldCollection<DimS>;
			//! the collection is handled in a `std::unique_ptr`
			using Collection_ptr = std::unique_ptr<FieldCollection_t>;
			//! polymorphic base material type
			using Material_t = MaterialBase<DimS, DimM>;
			//! materials handled through `std::unique_ptr`s
			using Material_ptr = std::unique_ptr<Material_t>;
			//! polymorphic base projection type
			using Projection_t = ProjectionBase<DimS, DimM>;
			//! projections handled through `std::unique_ptr`s
			using Projection_ptr = std::unique_ptr<Projection_t>;
			//! expected type for strain fields
			using StrainField_t =
			TensorField<FieldCollection_t, Real, secondOrder, DimM>;
			//! expected type for stress fields
			using StressField_t =
			TensorField<FieldCollection_t, Real, secondOrder, DimM>;
			//! expected type for tangent stiffness fields
			using TangentField_t =
			TensorField<FieldCollection_t, Real, fourthOrder, DimM>;
			//! combined stress and tangent field
			using FullResponse_t =
			std::tuple<const StressField_t&, const TangentField_t&>;
			//! iterator type over all cell pixel's
			using iterator = typename CcoordOps::Pixels<DimS>::iterator;

			//! dynamic vector type for interactions with numpy/scipy/solvers etc.
			using Vector_t = typename Parent::Vector_t;

			//! ref to constant vector
			using ConstVector_ref = typename Parent::ConstVector_ref;

			//! output vector reference for solvers
			using Vector_ref = typename Parent::Vector_ref;


			//! sparse matrix emulation
			using Adaptor = Parent::Adaptor;

			//! Default constructor
			CellBase() = delete;

			//! constructor using sizes and resolution
			CellBase(Projection_ptr projection);

			//! Copy constructor
			CellBase(const CellBase &other) = delete;

			//! Move constructor
			CellBase(CellBase &&other);

			//! Destructor
			virtual ~CellBase() = default;

			//! Copy assignment operator
			CellBase& operator=(const CellBase &other) = delete;

			//! Move assignment operator
			CellBase& operator=(CellBase &&other) = default;

			/**
			* Materials can only be moved. This is to assure exclusive
			* ownership of any material by this cell
			*/
			Material_t & add_material(Material_ptr mat);


			/**
			* returns a writable map onto the strain field of this cell. This
			* corresponds to the unknowns in a typical solve cycle.
			*/
			virtual Vector_ref get_strain_vector() override;

			/**
			* returns a read-only map onto the stress field of this
			* cell. This corresponds to the intermediate (and finally, total)
			* solution in a typical solve cycle
			*/
			virtual ConstVector_ref get_stress_vector() const override;

			/**
			* evaluates and returns the stress for the currently set strain
			*/
			virtual ConstVector_ref evaluate_stress() override;

			/**
			* evaluates and returns the stress and stiffness for the currently set strain
			*/
			virtual std::array<ConstVector_ref, 2> evaluate_stress_tangent() override;


			/**
			* evaluates the directional and projected stiffness (this
			* corresponds to G:K:δF in de Geus 2017,
			* http://dx.doi.org/10.1016/j.cma.2016.12.032). It seems that
			* this operation needs to be implemented with a copy in oder to
			* be compatible with scipy and EigenCG etc. (At the very least,
			* the copy is only made once)
			*/
			virtual Vector_ref evaluate_projected_directional_stiffness
			(Eigen::Ref<const Vector_t> delF) override;

			//! return the template param DimM (required for polymorphic use of `Cell`
			Dim_t get_material_dim() const override final {return DimM;}

			/**
			* returns the number of rows and cols for the strain matrix type
			* (for full storage, the strain is stored in material_dim ×
			* material_dim matrices, but in symmetriy storage, it is a column
			* vector)
			*/
			std::array<Dim_t, 2> get_strain_shape() const override final;

			/**
			* applies the projection operator in-place on the input vector
			*/
			void apply_projection(Eigen::Ref<Vector_t> vec) override final;



			/**
			* set uniform strain (typically used to initialise problems
			*/
			void set_uniform_strain(const Eigen::Ref<const Matrix_t> &) override;


			/**
			* evaluates all materials
			*/
			FullResponse_t evaluate_stress_tangent(StrainField_t & F);

			/**
			* evaluate directional stiffness (i.e. G:K:δF or G:K:δε)
			*/

			StressField_t & directional_stiffness(const TangentField_t & K,
			const StrainField_t & delF,
			StressField_t & delP);
			/**
			* vectorized version for eigen solvers, no copy, but only works
			* when fields have ArrayStore=false
			*/
			Vector_ref directional_stiffness_vec(const Eigen::Ref<const Vector_t> & delF);
			/**
			* Evaluate directional stiffness into a temporary array and
			* return a copy. This is a costly and wasteful interface to
			* directional_stiffness and should only be used for debugging or
			* in the python interface
			*/
			Eigen::ArrayXXd directional_stiffness_with_copy
			(Eigen::Ref<Eigen::ArrayXXd> delF);

			/**
			* Convenience function circumventing the neeed to use the
			* underlying projection
			*/
			StressField_t & project(StressField_t & field);

			//! returns a ref to the cell's strain field
			StrainField_t & get_strain();

			//! returns a ref to the cell's stress field
			const StressField_t & get_stress() const;

			//! returns a ref to the cell's tangent stiffness field
			const TangentField_t & get_tangent(bool create = false);

			//! returns a ref to a temporary field managed by the cell
			StrainField_t & get_managed_field(std::string unique_name);

			/**
			* general initialisation; initialises the projection and
			* fft_engine (i.e. infrastructure) but not the materials. These
			* need to be initialised separately
			*/
			void initialise(FFT_PlanFlags flags = FFT_PlanFlags::estimate);

			/**
			* for materials with state variables, these typically need to be
			* saved/updated an the end of each load increment, this function
			* calls this update for each material in the cell
			*/
			void save_history_variables() override final;

			iterator begin(); //!< iterator to the first pixel
			iterator end(); //!< iterator past the last pixel
			//! number of pixels in the cell
			size_t size() const {return pixels.size();}

			//! return the subdomain resolutions of the cell
			const Ccoord & get_subdomain_resolutions() const {
			return this->subdomain_resolutions;}
			//! return the subdomain locations of the cell
			const Ccoord & get_subdomain_locations() const {
			return this->subdomain_locations;}
			//! return the domain resolutions of the cell
			const Ccoord & get_domain_resolutions() const {
			return this->domain_resolutions;}
			//! return the sizes of the cell
			const Rcoord & get_domain_lengths() const {return this->domain_lengths;}

			/**
			* formulation is hard set by the choice of the projection class
			*/
			const Formulation & get_formulation() const override final {
			return this->projection->get_formulation();}

			/**
			* get a reference to the projection object. should only be
			* required for debugging
			*/
			Eigen::Map<Eigen::ArrayXXd> get_projection() {
			return this->projection->get_operator();}

			//! returns the spatial size
			constexpr static Dim_t get_sdim() {return DimS;};

			//! return a sparse matrix adaptor to the cell
			Adaptor get_adaptor() override;
			//! returns the number of degrees of freedom in the cell
			Dim_t get_nb_dof() const override {return this->size()*ipow(DimS, 2);};

			//! return the communicator object
			virtual const Communicator & get_communicator() const override {
			return this->projection->get_communicator();
			}

			protected:
			//! make sure that every pixel is assigned to one and only one material
			void check_material_coverage();

			const Ccoord & subdomain_resolutions; //!< the cell's subdomain resolutions
			const Ccoord & subdomain_locations; //!< the cell's subdomain resolutions
			const Ccoord & domain_resolutions; //!< the cell's domain resolutions
			CcoordOps::Pixels<DimS> pixels; //!< helper to iterate over the pixels
			const Rcoord & domain_lengths; //!< the cell's lengths
			Collection_ptr fields; //!< handle for the global fields of the cell
			StrainField_t & F; //!< ref to strain field
			StressField_t & P; //!< ref to stress field
			//! Tangent field might not even be required; so this is an
			//! optional ref_wrapper instead of a ref
			optional<std::reference_wrapper<TangentField_t>> K{};
			//! container of the materials present in the cell
			std::vector<Material_ptr> materials{};
			Projection_ptr projection; //!< handle for the projection operator

			private:
			};


			/**
			* lightweight resource handle wrapping a `muSpectre::Cell` or
			* a subclass thereof into `Eigen::EigenBase`, so it can be
			* interpreted as a sparse matrix by Eigen solvers
			*/
			template <class Cell>
			class CellAdaptor: public Eigen::EigenBase<CellAdaptor<Cell>> {

			public:
			using Scalar = double; //!< sparse matrix traits
			using RealScalar = double; //!< sparse matrix traits
			using StorageIndex = int; //!< sparse matrix traits
			enum {
			ColsAtCompileTime = Eigen::Dynamic,
			MaxColsAtCompileTime = Eigen::Dynamic,
			RowsAtCompileTime = Eigen::Dynamic,
			MaxRowsAtCompileTime = Eigen::Dynamic,
			IsRowMajor = false
			};

			//! constructor
			CellAdaptor(Cell & cell):cell{cell}{}
			//!returns the number of logical rows
			Eigen::Index rows() const {return this->cell.get_nb_dof();}
			//!returns the number of logical columns
			Eigen::Index cols() const {return this->rows();}

			//! implementation of the evaluation
			template<typename Rhs>
			Eigen::Product<CellAdaptor,Rhs,Eigen::AliasFreeProduct>
			operator*(const Eigen::MatrixBase<Rhs>& x) const {
			return Eigen::Product<CellAdaptor,Rhs,Eigen::AliasFreeProduct>
			(*this, x.derived());
			}
			Cell & cell; //!< ref to the cell
			};

			} // muSpectre


			namespace Eigen {
			namespace internal {
			//! Implementation of `muSpectre::CellAdaptor` * `Eigen::DenseVector` through a
			//! specialization of `Eigen::internal::generic_product_impl`:
			template<typename Rhs, class CellAdaptor>
			struct generic_product_impl<CellAdaptor, Rhs, SparseShape, DenseShape, GemvProduct> // GEMV stands for matrix-vector
			: generic_product_impl_base<CellAdaptor,Rhs,generic_product_impl<CellAdaptor,Rhs> >
			{
			//! undocumented
			typedef typename Product<CellAdaptor,Rhs>::Scalar Scalar;

			//! undocumented
			template<typename Dest>
			static void scaleAndAddTo(Dest& dst, const CellAdaptor& lhs, const Rhs& rhs, const Scalar& /alpha/)
			{
			// This method should implement "dst += alpha * lhs * rhs" inplace,
			// however, for iterative solvers, alpha is always equal to 1, so let's not bother about it.
			// Here we could simply call dst.noalias() += lhs.my_matrix() * rhs,
			dst.noalias() += const_cast<CellAdaptor&>(lhs).cell.
			evaluate_projected_directional_stiffness(rhs);
			}
			};
			}
			}


			#endif /* CELL_BASE_H */

muSpectre/src/cell/cell_base.hha09f468662b6feat/documentation

cell_base.hhView Options

muSpectre/src/cell/cell_base.hh
a09f468662b6feat/documentation

cell_base.hh
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