tensor_tools.h

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2023 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner

// This library 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 2.1 of the License, or (at your option) any later version.

// This library 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 this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA



#ifndef LIBMESH_TENSOR_TOOLS_H
#define LIBMESH_TENSOR_TOOLS_H

// Local includes
#include "libmesh/libmesh_common.h"
#include "libmesh/compare_types.h"

#ifdef LIBMESH_HAVE_METAPHYSICL
#include "metaphysicl/dualnumber_decl.h"
#endif

namespace libMesh
{
// Forward declarations
template <typename T> class TypeVector;
template <typename T> class VectorValue;
template <typename T> class TypeTensor;
template <typename T> class TensorValue;
template <unsigned int N, typename T> class TypeNTensor;

namespace TensorTools
{
// 通用情况下的内积计算，适用于标量
template <typename T, typename T2>
inline
typename boostcopy::enable_if_c<ScalarTraits<T>::value && ScalarTraits<T2>::value,
                                typename CompareTypes<T, T2>::supertype>::type
inner_product(const T & a, const T2& b)
{ return a * b; }

// 向量的内积计算
template <typename T, typename T2>
inline
typename CompareTypes<T, T2>::supertype
inner_product(const TypeVector<T> & a, const TypeVector<T2> & b)
{ return a * b; }

// 张量的内积计算
template <typename T, typename T2>
inline
typename CompareTypes<T, T2>::supertype
inner_product(const TypeTensor<T> & a, const TypeTensor<T2> & b)
{ return a.contract(b); }

// 多维张量的内积计算
template <unsigned int N, typename T, typename T2>
inline
typename CompareTypes<T, T2>::supertype
inner_product(const TypeNTensor<N,T> & a, const TypeNTensor<N,T2> & b)
{ return a.contract(b); }

// 计算复数的模的平方
template<typename T>
inline
T norm_sq(std::complex<T> a) { return std::norm(a); }

// 计算实数或复数的模的平方
template<typename T>
inline
auto norm_sq(const T & a) -> decltype(std::norm(a))
{ return std::norm(a); }

// 向量的模的平方计算
template <typename T>
inline
auto norm_sq(const TypeVector<T> & a) -> decltype(std::norm(T()))
{ return a.norm_sq(); }

// VectorValue类型的模的平方计算
template <typename T>
inline
auto norm_sq(const VectorValue<T> & a) -> decltype(std::norm(T()))
{ return a.norm_sq(); }

// 判断数值是否为零
template<typename T>
inline
bool is_zero(const T & a){ return a.is_zero();}

// 增加张量秩的结构
template <typename T>
struct IncrementRank
{
  typedef VectorValue<T> type;
};

// VectorValue类型的张量秩增加
template <typename T>
struct IncrementRank<VectorValue<T>>
{
  typedef TensorValue<T> type;
};

// TypeVector类型的张量秩增加
template <typename T>
struct IncrementRank<TypeVector<T>>
{
  typedef TensorValue<T> type;
};

// TypeTensor类型的张量秩增加
template <typename T>
struct IncrementRank<TypeTensor<T>>
{
  typedef TypeNTensor<3,T> type;
};


template <typename T>
struct IncrementRank<TensorValue<T>>
{
  typedef TypeNTensor<3,T> type;
};

template <unsigned int N, typename T>
struct IncrementRank<TypeNTensor<N,T>>
{
  typedef TypeNTensor<N+1,T> type;
};


// Also need rank-decreasing case
template <typename T>
struct DecrementRank
{
  // The default case is typically an error, but for simpler
  // templated code we need it to be compatible with Number
  // operations...
  typedef T type;
};

template <typename T>
struct DecrementRank<VectorValue<T>>
{
  typedef T type;
};

template <typename T>
struct DecrementRank<TypeVector<T>>
{
  typedef T type;
};

template <typename T>
struct DecrementRank<TensorValue<T>>
{
  typedef VectorValue<T> type;
};

template <typename T>
struct DecrementRank<TypeTensor<T>>
{
  typedef VectorValue<T> type;
};

template <unsigned int N, typename T>
struct DecrementRank<TypeNTensor<N,T>>
{
  typedef TypeNTensor<N-1,T> type;
};

// Handle the complex-valued case
template <typename T>
struct MakeNumber
{
#ifdef LIBMESH_USE_COMPLEX_NUMBERS
  typedef std::complex<T> type;
#else
  typedef T type;
#endif
};

template <typename T>
struct MakeNumber<std::complex<T>>
{
  // Should this be a compile-time error? we shouldn't need to make numbers out of
  // numbers, but then again having the typedef below enables more generic
  // programming
  typedef std::complex<T> type;
};


template <typename T>
struct MakeNumber<TypeVector<T>>
{
  typedef TypeVector<typename MakeNumber<T>::type > type;
};

template <typename T>
struct MakeNumber<VectorValue<T>>
{
  typedef VectorValue<typename MakeNumber<T>::type > type;
};

template <typename T>
struct MakeNumber<TypeTensor<T>>
{
  typedef TypeTensor<typename MakeNumber<T>::type> type;
};

template <typename T>
struct MakeNumber<TensorValue<T>>
{
  typedef TypeTensor<typename MakeNumber<T>::type> type;
};

template <unsigned int N, typename T>
struct MakeNumber<TypeNTensor<N,T>>
{
#ifdef LIBMESH_USE_COMPLEX_NUMBERS
  typedef TypeNTensor<N,std::complex<T>> type;
#else
  typedef TypeNTensor<N,T> type;
#endif
};

// A utility for determining real-valued (e.g. shape function)
// types from corresponding complex-valued types
template <typename T>
struct MakeReal
{
  typedef T type;
};

template <typename T>
struct MakeReal<std::complex<T>>
{
  typedef T type;
};

template <typename T>
struct MakeReal<TypeVector<T>>
{
  typedef TypeVector<typename MakeReal<T>::type > type;
};

template <typename T>
struct MakeReal<VectorValue<T>>
{
  typedef VectorValue<typename MakeReal<T>::type > type;
};

template <typename T>
struct MakeReal<TypeTensor<T>>
{
  typedef TypeTensor<typename MakeReal<T>::type> type;
};

template <typename T>
struct MakeReal<TensorValue<T>>
{
  typedef TypeTensor<typename MakeReal<T>::type> type;
};

template <unsigned int N, typename T>
struct MakeReal<TypeNTensor<N,T>>
{
  typedef TypeNTensor<N,typename MakeReal<T>::type> type;
};

// 用于使ExactSolution编译通过
Number curl_from_grad(const VectorValue<Number> &);

VectorValue<Number> curl_from_grad(const TensorValue<Number> & grad);

TensorValue<Number> curl_from_grad(const TypeNTensor<3, Number> & grad);

Number div_from_grad(const VectorValue<Number> & grad);

Number div_from_grad(const TensorValue<Number> & grad);

VectorValue<Number> div_from_grad(const TypeNTensor<3, Number> & grad);

template <typename T>
struct MathWrapperTraits
{
  static constexpr bool value = false;
};

template <typename T>
struct MathWrapperTraits<TypeVector<T>>
{
  static constexpr bool value = true;
};

template <typename T>
struct MathWrapperTraits<VectorValue<T>>
{
  static constexpr bool value = true;
};

template <typename T>
struct MathWrapperTraits<TypeTensor<T>>
{
  static constexpr bool value = true;
};

template <typename T>
struct MathWrapperTraits<TensorValue<T>>
{
  static constexpr bool value = true;
};

template <unsigned int N, typename T>
struct MathWrapperTraits<TypeNTensor<N, T>>
{
  static constexpr bool value = true;
};

template <typename T, typename enable = void>
struct MakeBaseNumber {};

template <typename T>
struct MakeBaseNumber<T, typename std::enable_if<ScalarTraits<T>::value>::type> {
  typedef typename MakeNumber<T>::type type;
};

template <template <typename> class Wrapper, typename T>
struct MakeBaseNumber<
    Wrapper<T>,
    typename std::enable_if<MathWrapperTraits<Wrapper<T>>::value>::type> {
  typedef typename MakeBaseNumber<T>::type type;
};

template <typename T, typename Enable = void>
struct TensorTraits
{
  static_assert(always_false<T>,
                "Instantiating the generic template of TensorTraits. You must specialize "
                "TensorTraits for your type.");
  static constexpr unsigned char rank = 0;
};

template <typename T>
struct TensorTraits<T, typename std::enable_if<ScalarTraits<T>::value>::type>
{
  static constexpr unsigned char rank = 0;
};

template <typename T>
struct TensorTraits<TypeVector<T>>
{
  static constexpr unsigned char rank = 1;
};

template <typename T>
struct TensorTraits<VectorValue<T>>
{
  static constexpr unsigned char rank = 1;
};

template <typename T>
struct TensorTraits<TypeTensor<T>>
{
  static constexpr unsigned char rank = 2;
};

template <typename T>
struct TensorTraits<TensorValue<T>>
{
  static constexpr unsigned char rank = 2;
};

template <typename T, unsigned int N>
struct TensorTraits<TypeNTensor<N, T>>
{
  static constexpr unsigned char rank = static_cast<unsigned char>(N);
};

}//namespace TensorTools

}//namespace libMesh

#endif // LIBMESH_TENSOR_TOOLS_H