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detail.h
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/**
* @file
* @copyright Copyright 2017. Tom de Geus. All rights reserved.
* @license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_DETAIL_H
#define GOOSEFEM_DETAIL_H
namespace GooseFEM {
namespace detail {
template <size_t nd, typename = void>
struct tensor {
};
template <size_t nd>
struct tensor<nd, typename std::enable_if_t<nd == 2>> {
/**
* Inverse of a 2nd order tensor.
*
* @param The tensor.
* @param The inverse (overwritten).
* @return Determinant.
*/
template <class T>
static double inv(const T& A, T& Ainv)
{
double det = A(0, 0) * A(1, 1) - A(0, 1) * A(1, 0);
Ainv(0, 0) = A(1, 1) / det;
Ainv(0, 1) = -1.0 * A(0, 1) / det;
Ainv(1, 0) = -1.0 * A(1, 0) / det;
Ainv(1, 1) = A(0, 0) / det;
return det;
}
};
template <size_t nd>
struct tensor<nd, typename std::enable_if_t<nd == 3>> {
/**
* Inverse of a 2nd order tensor (shape: [3, 3]).
*
* @param The tensor.
* @param The inverse (overwritten).
* @return Determinant.
*/
template <class T>
static double inv(const T& A, T& Ainv)
{
double det = (A(0, 0) * A(1, 1) * A(2, 2) + A(0, 1) * A(1, 2) * A(2, 0) +
A(0, 2) * A(1, 0) * A(2, 1)) -
(A(0, 2) * A(1, 1) * A(2, 0) + A(0, 1) * A(1, 0) * A(2, 2) +
A(0, 0) * A(1, 2) * A(2, 1));
Ainv(0, 0) = (A(1, 1) * A(2, 2) - A(1, 2) * A(2, 1)) / det;
Ainv(0, 1) = (A(0, 2) * A(2, 1) - A(0, 1) * A(2, 2)) / det;
Ainv(0, 2) = (A(0, 1) * A(1, 2) - A(0, 2) * A(1, 1)) / det;
Ainv(1, 0) = (A(1, 2) * A(2, 0) - A(1, 0) * A(2, 2)) / det;
Ainv(1, 1) = (A(0, 0) * A(2, 2) - A(0, 2) * A(2, 0)) / det;
Ainv(1, 2) = (A(0, 2) * A(1, 0) - A(0, 0) * A(1, 2)) / det;
Ainv(2, 0) = (A(1, 0) * A(2, 1) - A(1, 1) * A(2, 0)) / det;
Ainv(2, 1) = (A(0, 1) * A(2, 0) - A(0, 0) * A(2, 1)) / det;
Ainv(2, 2) = (A(0, 0) * A(1, 1) - A(0, 1) * A(1, 0)) / det;
return det;
}
};
} // namespace detail
} // namespace GooseFEM
#endif

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