844 lines
20 KiB
C++
844 lines
20 KiB
C++
/*---------------------------------------------------------------------------*\
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration |
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\\ / A nd | Copyright (C) 2011 OpenFOAM Foundation
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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This file is part of OpenFOAM.
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OpenFOAM is free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received a copy of the GNU General Public License
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along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
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\*---------------------------------------------------------------------------*/
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#include "SymmTensor.H"
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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namespace Foam
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{
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// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
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//- Construct null
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template <class Cmpt>
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inline Tensor<Cmpt>::Tensor()
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{}
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//- Construct given VectorSpace
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template <class Cmpt>
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inline Tensor<Cmpt>::Tensor(const VectorSpace<Tensor<Cmpt>, Cmpt, 9>& vs)
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:
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VectorSpace<Tensor<Cmpt>, Cmpt, 9>(vs)
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{}
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//- Construct given SphericalTensor
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template <class Cmpt>
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inline Tensor<Cmpt>::Tensor(const SphericalTensor<Cmpt>& st)
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{
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this->v_[XX] = st.ii(); this->v_[XY] = 0; this->v_[XZ] = 0;
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this->v_[YX] = 0; this->v_[YY] = st.ii(); this->v_[YZ] = 0;
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this->v_[ZX] = 0; this->v_[ZY] = 0; this->v_[ZZ] = st.ii();
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}
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//- Construct given SymmTensor
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template <class Cmpt>
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inline Tensor<Cmpt>::Tensor(const SymmTensor<Cmpt>& st)
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{
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this->v_[XX] = st.xx(); this->v_[XY] = st.xy(); this->v_[XZ] = st.xz();
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this->v_[YX] = st.xy(); this->v_[YY] = st.yy(); this->v_[YZ] = st.yz();
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this->v_[ZX] = st.xz(); this->v_[ZY] = st.yz(); this->v_[ZZ] = st.zz();
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}
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//- Construct given the three vector components
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template <class Cmpt>
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inline Tensor<Cmpt>::Tensor
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(
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const Vector<Cmpt>& x,
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const Vector<Cmpt>& y,
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const Vector<Cmpt>& z
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)
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{
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this->v_[XX] = x.x(); this->v_[XY] = x.y(); this->v_[XZ] = x.z();
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this->v_[YX] = y.x(); this->v_[YY] = y.y(); this->v_[YZ] = y.z();
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this->v_[ZX] = z.x(); this->v_[ZY] = z.y(); this->v_[ZZ] = z.z();
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}
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//- Construct from components
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template <class Cmpt>
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inline Tensor<Cmpt>::Tensor
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(
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const Cmpt txx, const Cmpt txy, const Cmpt txz,
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const Cmpt tyx, const Cmpt tyy, const Cmpt tyz,
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const Cmpt tzx, const Cmpt tzy, const Cmpt tzz
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)
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{
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this->v_[XX] = txx; this->v_[XY] = txy; this->v_[XZ] = txz;
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this->v_[YX] = tyx; this->v_[YY] = tyy; this->v_[YZ] = tyz;
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this->v_[ZX] = tzx; this->v_[ZY] = tzy; this->v_[ZZ] = tzz;
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}
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//- Construct from Istream
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template <class Cmpt>
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inline Tensor<Cmpt>::Tensor(Istream& is)
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:
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VectorSpace<Tensor<Cmpt>, Cmpt, 9>(is)
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{}
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// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
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template <class Cmpt>
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inline const Vector<Cmpt> Tensor<Cmpt>::x() const
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{
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return Vector<Cmpt>(this->v_[XX], this->v_[XY], this->v_[XZ]);
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}
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template <class Cmpt>
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inline const Vector<Cmpt> Tensor<Cmpt>::y() const
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{
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return Vector<Cmpt>(this->v_[YX], this->v_[YY], this->v_[YZ]);
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}
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template <class Cmpt>
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inline const Vector<Cmpt> Tensor<Cmpt>::z() const
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{
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return Vector<Cmpt>(this->v_[ZX], this->v_[ZY], this->v_[ZZ]);
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}
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template <class Cmpt>
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inline const Cmpt& Tensor<Cmpt>::xx() const
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{
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return this->v_[XX];
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}
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template <class Cmpt>
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inline const Cmpt& Tensor<Cmpt>::xy() const
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{
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return this->v_[XY];
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}
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template <class Cmpt>
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inline const Cmpt& Tensor<Cmpt>::xz() const
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{
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return this->v_[XZ];
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}
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template <class Cmpt>
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inline const Cmpt& Tensor<Cmpt>::yx() const
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{
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return this->v_[YX];
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}
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template <class Cmpt>
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inline const Cmpt& Tensor<Cmpt>::yy() const
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{
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return this->v_[YY];
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}
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template <class Cmpt>
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inline const Cmpt& Tensor<Cmpt>::yz() const
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{
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return this->v_[YZ];
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}
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template <class Cmpt>
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inline const Cmpt& Tensor<Cmpt>::zx() const
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{
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return this->v_[ZX];
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}
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template <class Cmpt>
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inline const Cmpt& Tensor<Cmpt>::zy() const
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{
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return this->v_[ZY];
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}
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template <class Cmpt>
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inline const Cmpt& Tensor<Cmpt>::zz() const
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{
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return this->v_[ZZ];
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}
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template <class Cmpt>
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inline Cmpt& Tensor<Cmpt>::xx()
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{
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return this->v_[XX];
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}
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template <class Cmpt>
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inline Cmpt& Tensor<Cmpt>::xy()
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{
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return this->v_[XY];
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}
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template <class Cmpt>
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inline Cmpt& Tensor<Cmpt>::xz()
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{
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return this->v_[XZ];
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}
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template <class Cmpt>
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inline Cmpt& Tensor<Cmpt>::yx()
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{
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return this->v_[YX];
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}
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template <class Cmpt>
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inline Cmpt& Tensor<Cmpt>::yy()
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{
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return this->v_[YY];
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}
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template <class Cmpt>
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inline Cmpt& Tensor<Cmpt>::yz()
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{
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return this->v_[YZ];
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}
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template <class Cmpt>
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inline Cmpt& Tensor<Cmpt>::zx()
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{
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return this->v_[ZX];
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}
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template <class Cmpt>
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inline Cmpt& Tensor<Cmpt>::zy()
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{
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return this->v_[ZY];
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}
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template <class Cmpt>
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inline Cmpt& Tensor<Cmpt>::zz()
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{
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return this->v_[ZZ];
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}
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//- Return tensor transpose
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template <class Cmpt>
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inline Tensor<Cmpt> Tensor<Cmpt>::T() const
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{
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return Tensor<Cmpt>
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(
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xx(), yx(), zx(),
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xy(), yy(), zy(),
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xz(), yz(), zz()
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);
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}
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// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
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template <class Cmpt>
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inline void Tensor<Cmpt>::operator=(const SphericalTensor<Cmpt>& st)
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{
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this->v_[XX] = st.ii(); this->v_[XY] = 0; this->v_[XZ] = 0;
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this->v_[YX] = 0; this->v_[YY] = st.ii(); this->v_[YZ] = 0;
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this->v_[ZX] = 0; this->v_[ZY] = 0; this->v_[ZZ] = st.ii();
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}
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template <class Cmpt>
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inline void Tensor<Cmpt>::operator=(const SymmTensor<Cmpt>& st)
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{
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this->v_[XX] = st.xx(); this->v_[XY] = st.xy(); this->v_[XZ] = st.xz();
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this->v_[YX] = st.xy(); this->v_[YY] = st.yy(); this->v_[YZ] = st.yz();
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this->v_[ZX] = st.xz(); this->v_[ZY] = st.yz(); this->v_[ZZ] = st.zz();
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}
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// * * * * * * * * * * * * * * * Global Operators * * * * * * * * * * * * * //
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//- Hodge Dual operator (tensor -> vector)
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template <class Cmpt>
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inline Vector<Cmpt> operator*(const Tensor<Cmpt>& t)
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{
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return Vector<Cmpt>(t.yz(), -t.xz(), t.xy());
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}
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//- Hodge Dual operator (vector -> tensor)
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template <class Cmpt>
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inline Tensor<Cmpt> operator*(const Vector<Cmpt>& v)
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{
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return Tensor<Cmpt>
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(
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0, -v.z(), v.y(),
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v.z(), 0, -v.x(),
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-v.y(), v.x(), 0
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);
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}
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//- Inner-product between two tensors
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template <class Cmpt>
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inline typename innerProduct<Tensor<Cmpt>, Tensor<Cmpt> >::type
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operator&(const Tensor<Cmpt>& t1, const Tensor<Cmpt>& t2)
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{
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return Tensor<Cmpt>
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(
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t1.xx()*t2.xx() + t1.xy()*t2.yx() + t1.xz()*t2.zx(),
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t1.xx()*t2.xy() + t1.xy()*t2.yy() + t1.xz()*t2.zy(),
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t1.xx()*t2.xz() + t1.xy()*t2.yz() + t1.xz()*t2.zz(),
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t1.yx()*t2.xx() + t1.yy()*t2.yx() + t1.yz()*t2.zx(),
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t1.yx()*t2.xy() + t1.yy()*t2.yy() + t1.yz()*t2.zy(),
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t1.yx()*t2.xz() + t1.yy()*t2.yz() + t1.yz()*t2.zz(),
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t1.zx()*t2.xx() + t1.zy()*t2.yx() + t1.zz()*t2.zx(),
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t1.zx()*t2.xy() + t1.zy()*t2.yy() + t1.zz()*t2.zy(),
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t1.zx()*t2.xz() + t1.zy()*t2.yz() + t1.zz()*t2.zz()
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);
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}
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//- Inner-product between a tensor and a vector
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template <class Cmpt>
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inline typename innerProduct<Tensor<Cmpt>, Vector<Cmpt> >::type
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operator&(const Tensor<Cmpt>& t, const Vector<Cmpt>& v)
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{
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return Vector<Cmpt>
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(
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t.xx()*v.x() + t.xy()*v.y() + t.xz()*v.z(),
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t.yx()*v.x() + t.yy()*v.y() + t.yz()*v.z(),
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t.zx()*v.x() + t.zy()*v.y() + t.zz()*v.z()
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);
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}
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//- Inner-product between a vector and a tensor
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template <class Cmpt>
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inline typename innerProduct<Vector<Cmpt>, Tensor<Cmpt> >::type
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operator&(const Vector<Cmpt>& v, const Tensor<Cmpt>& t)
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{
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return Vector<Cmpt>
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(
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v.x()*t.xx() + v.y()*t.yx() + v.z()*t.zx(),
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v.x()*t.xy() + v.y()*t.yy() + v.z()*t.zy(),
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v.x()*t.xz() + v.y()*t.yz() + v.z()*t.zz()
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);
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}
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//- Outer-product between two vectors
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template <class Cmpt>
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inline typename outerProduct<Vector<Cmpt>, Vector<Cmpt> >::type
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operator*(const Vector<Cmpt>& v1, const Vector<Cmpt>& v2)
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{
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return Tensor<Cmpt>
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(
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v1.x()*v2.x(), v1.x()*v2.y(), v1.x()*v2.z(),
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v1.y()*v2.x(), v1.y()*v2.y(), v1.y()*v2.z(),
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v1.z()*v2.x(), v1.z()*v2.y(), v1.z()*v2.z()
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);
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}
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//- Division of a vector by a tensor, i.e. dot-product with the tensor inverse
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template <class Cmpt>
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inline typename innerProduct<Vector<Cmpt>, Tensor<Cmpt> >::type
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operator/(const Vector<Cmpt>& v, const Tensor<Cmpt>& t)
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{
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return inv(t) & v;
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}
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// * * * * * * * * * * * * * * * Global Functions * * * * * * * * * * * * * //
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//- Return the trace of a tensor
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template <class Cmpt>
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inline Cmpt tr(const Tensor<Cmpt>& t)
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{
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return t.xx() + t.yy() + t.zz();
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}
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//- Return the spherical part of a tensor
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template <class Cmpt>
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inline SphericalTensor<Cmpt> sph(const Tensor<Cmpt>& t)
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{
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return (1.0/3.0)*tr(t);
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}
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//- Return the symmetric part of a tensor
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template <class Cmpt>
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inline SymmTensor<Cmpt> symm(const Tensor<Cmpt>& t)
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{
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return SymmTensor<Cmpt>
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(
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t.xx(), 0.5*(t.xy() + t.yx()), 0.5*(t.xz() + t.zx()),
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t.yy(), 0.5*(t.yz() + t.zy()),
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t.zz()
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);
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}
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//- Return twice the symmetric part of a tensor
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template <class Cmpt>
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inline SymmTensor<Cmpt> twoSymm(const Tensor<Cmpt>& t)
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{
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return SymmTensor<Cmpt>
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(
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2*t.xx(), (t.xy() + t.yx()), (t.xz() + t.zx()),
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2*t.yy(), (t.yz() + t.zy()),
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2*t.zz()
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);
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}
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//- Return the skew-symmetric part of a tensor
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template <class Cmpt>
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inline Tensor<Cmpt> skew(const Tensor<Cmpt>& t)
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{
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return Tensor<Cmpt>
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(
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0.0, 0.5*(t.xy() - t.yx()), 0.5*(t.xz() - t.zx()),
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0.5*(t.yx() - t.xy()), 0.0, 0.5*(t.yz() - t.zy()),
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0.5*(t.zx() - t.xz()), 0.5*(t.zy() - t.yz()), 0.0
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);
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}
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//- Return the skew-symmetric part of a symmetric tensor
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template <class Cmpt>
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inline const Tensor<Cmpt>& skew(const SymmTensor<Cmpt>& st)
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{
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return Tensor<Cmpt>::zero;
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}
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//- Return the deviatoric part of a tensor
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template <class Cmpt>
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inline Tensor<Cmpt> dev(const Tensor<Cmpt>& t)
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{
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return t - SphericalTensor<Cmpt>::oneThirdI*tr(t);
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}
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//- Return the deviatoric part of a tensor
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template <class Cmpt>
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inline Tensor<Cmpt> dev2(const Tensor<Cmpt>& t)
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{
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return t - SphericalTensor<Cmpt>::twoThirdsI*tr(t);
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}
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//- Return the determinant of a tensor
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template <class Cmpt>
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inline Cmpt det(const Tensor<Cmpt>& t)
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{
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return
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(
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t.xx()*t.yy()*t.zz() + t.xy()*t.yz()*t.zx()
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+ t.xz()*t.yx()*t.zy() - t.xx()*t.yz()*t.zy()
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- t.xy()*t.yx()*t.zz() - t.xz()*t.yy()*t.zx()
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);
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}
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//- Return the cofactor tensor of a tensor
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template <class Cmpt>
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inline Tensor<Cmpt> cof(const Tensor<Cmpt>& t)
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|
{
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return Tensor<Cmpt>
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(
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t.yy()*t.zz() - t.zy()*t.yz(),
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t.zx()*t.yz() - t.yx()*t.zz(),
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t.yx()*t.zy() - t.yy()*t.zx(),
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t.xz()*t.zy() - t.xy()*t.zz(),
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t.xx()*t.zz() - t.xz()*t.zx(),
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t.xy()*t.zx() - t.xx()*t.zy(),
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t.xy()*t.yz() - t.xz()*t.yy(),
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t.yx()*t.xz() - t.xx()*t.yz(),
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t.xx()*t.yy() - t.yx()*t.xy()
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);
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}
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//- Return the inverse of a tensor given the determinant
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|
template <class Cmpt>
|
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inline Tensor<Cmpt> inv(const Tensor<Cmpt>& t, const Cmpt dett)
|
|
{
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return Tensor<Cmpt>
|
|
(
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t.yy()*t.zz() - t.zy()*t.yz(),
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t.xz()*t.zy() - t.xy()*t.zz(),
|
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t.xy()*t.yz() - t.xz()*t.yy(),
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t.zx()*t.yz() - t.yx()*t.zz(),
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t.xx()*t.zz() - t.xz()*t.zx(),
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t.yx()*t.xz() - t.xx()*t.yz(),
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t.yx()*t.zy() - t.yy()*t.zx(),
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t.xy()*t.zx() - t.xx()*t.zy(),
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t.xx()*t.yy() - t.yx()*t.xy()
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)/dett;
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}
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|
|
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//- Return the inverse of a tensor
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|
template <class Cmpt>
|
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inline Tensor<Cmpt> inv(const Tensor<Cmpt>& t)
|
|
{
|
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return inv(t, det(t));
|
|
}
|
|
|
|
|
|
//- Return the 1st invariant of a tensor
|
|
template <class Cmpt>
|
|
inline Cmpt invariantI(const Tensor<Cmpt>& t)
|
|
{
|
|
return tr(t);
|
|
}
|
|
|
|
|
|
//- Return the 2nd invariant of a tensor
|
|
template <class Cmpt>
|
|
inline Cmpt invariantII(const Tensor<Cmpt>& t)
|
|
{
|
|
return
|
|
(
|
|
0.5*sqr(tr(t))
|
|
- 0.5*
|
|
(
|
|
t.xx()*t.xx() + t.xy()*t.xy() + t.xz()*t.xz()
|
|
+ t.yx()*t.yx() + t.yy()*t.yy() + t.yz()*t.yz()
|
|
+ t.zx()*t.zx() + t.zy()*t.zy() + t.zz()*t.zz()
|
|
)
|
|
);
|
|
}
|
|
|
|
|
|
//- Return the 3rd invariant of a tensor
|
|
template <class Cmpt>
|
|
inline Cmpt invariantIII(const Tensor<Cmpt>& t)
|
|
{
|
|
return det(t);
|
|
}
|
|
|
|
|
|
// * * * * * * * * * Mixed Tensor SphericalTensor Operators * * * * * * * * //
|
|
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator+(const SphericalTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
st1.ii() + t2.xx(), t2.xy(), t2.xz(),
|
|
t2.yx(), st1.ii() + t2.yy(), t2.yz(),
|
|
t2.zx(), t2.zy(), st1.ii() + t2.zz()
|
|
);
|
|
}
|
|
|
|
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator+(const Tensor<Cmpt>& t1, const SphericalTensor<Cmpt>& st2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
t1.xx() + st2.ii(), t1.xy(), t1.xz(),
|
|
t1.yx(), t1.yy() + st2.ii(), t1.yz(),
|
|
t1.zx(), t1.zy(), t1.zz() + st2.ii()
|
|
);
|
|
}
|
|
|
|
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator-(const SphericalTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
st1.ii() - t2.xx(), -t2.xy(), -t2.xz(),
|
|
-t2.yx(), st1.ii() - t2.yy(), -t2.yz(),
|
|
-t2.zx(), -t2.zy(), st1.ii() - t2.zz()
|
|
);
|
|
}
|
|
|
|
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator-(const Tensor<Cmpt>& t1, const SphericalTensor<Cmpt>& st2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
t1.xx() - st2.ii(), t1.xy(), t1.xz(),
|
|
t1.yx(), t1.yy() - st2.ii(), t1.yz(),
|
|
t1.zx(), t1.zy(), t1.zz() - st2.ii()
|
|
);
|
|
}
|
|
|
|
|
|
//- Inner-product between a spherical tensor and a tensor
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator&(const SphericalTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
st1.ii()*t2.xx(), st1.ii()*t2.xy(), st1.ii()*t2.xz(),
|
|
st1.ii()*t2.yx(), st1.ii()*t2.yy(), st1.ii()*t2.yz(),
|
|
st1.ii()*t2.zx(), st1.ii()*t2.zy(), st1.ii()*t2.zz()
|
|
);
|
|
}
|
|
|
|
|
|
//- Inner-product between a tensor and a spherical tensor
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator&(const Tensor<Cmpt>& t1, const SphericalTensor<Cmpt>& st2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
t1.xx()*st2.ii(), t1.xy()*st2.ii(), t1.xz()*st2.ii(),
|
|
t1.yx()*st2.ii(), t1.yy()*st2.ii(), t1.yz()*st2.ii(),
|
|
t1.zx()*st2.ii(), t1.zy()*st2.ii(), t1.zz()*st2.ii()
|
|
);
|
|
}
|
|
|
|
|
|
//- Double-dot-product between a spherical tensor and a tensor
|
|
template <class Cmpt>
|
|
inline Cmpt
|
|
operator&&(const SphericalTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
|
|
{
|
|
return(st1.ii()*t2.xx() + st1.ii()*t2.yy() + st1.ii()*t2.zz());
|
|
}
|
|
|
|
|
|
//- Double-dot-product between a tensor and a spherical tensor
|
|
template <class Cmpt>
|
|
inline Cmpt
|
|
operator&&(const Tensor<Cmpt>& t1, const SphericalTensor<Cmpt>& st2)
|
|
{
|
|
return(t1.xx()*st2.ii() + t1.yy()*st2.ii() + t1.zz()*st2.ii());
|
|
}
|
|
|
|
template<class Cmpt>
|
|
class typeOfSum<SphericalTensor<Cmpt>, Tensor<Cmpt> >
|
|
{
|
|
public:
|
|
|
|
typedef Tensor<Cmpt> type;
|
|
};
|
|
|
|
template<class Cmpt>
|
|
class typeOfSum<Tensor<Cmpt>, SphericalTensor<Cmpt> >
|
|
{
|
|
public:
|
|
|
|
typedef Tensor<Cmpt> type;
|
|
};
|
|
|
|
template<class Cmpt>
|
|
class innerProduct<SphericalTensor<Cmpt>, Tensor<Cmpt> >
|
|
{
|
|
public:
|
|
|
|
typedef Tensor<Cmpt> type;
|
|
};
|
|
|
|
template<class Cmpt>
|
|
class innerProduct<Tensor<Cmpt>, SphericalTensor<Cmpt> >
|
|
{
|
|
public:
|
|
|
|
typedef Tensor<Cmpt> type;
|
|
};
|
|
|
|
|
|
// * * * * * * * * * * Mixed Tensor SymmTensor Operators * * * * * * * * * * //
|
|
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator+(const SymmTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
st1.xx() + t2.xx(), st1.xy() + t2.xy(), st1.xz() + t2.xz(),
|
|
st1.xy() + t2.yx(), st1.yy() + t2.yy(), st1.yz() + t2.yz(),
|
|
st1.xz() + t2.zx(), st1.yz() + t2.zy(), st1.zz() + t2.zz()
|
|
);
|
|
}
|
|
|
|
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator+(const Tensor<Cmpt>& t1, const SymmTensor<Cmpt>& st2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
t1.xx() + st2.xx(), t1.xy() + st2.xy(), t1.xz() + st2.xz(),
|
|
t1.yx() + st2.xy(), t1.yy() + st2.yy(), t1.yz() + st2.yz(),
|
|
t1.zx() + st2.xz(), t1.zy() + st2.yz(), t1.zz() + st2.zz()
|
|
);
|
|
}
|
|
|
|
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator-(const SymmTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
st1.xx() - t2.xx(), st1.xy() - t2.xy(), st1.xz() - t2.xz(),
|
|
st1.xy() - t2.yx(), st1.yy() - t2.yy(), st1.yz() - t2.yz(),
|
|
st1.xz() - t2.zx(), st1.yz() - t2.zy(), st1.zz() - t2.zz()
|
|
);
|
|
}
|
|
|
|
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator-(const Tensor<Cmpt>& t1, const SymmTensor<Cmpt>& st2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
t1.xx() - st2.xx(), t1.xy() - st2.xy(), t1.xz() - st2.xz(),
|
|
t1.yx() - st2.xy(), t1.yy() - st2.yy(), t1.yz() - st2.yz(),
|
|
t1.zx() - st2.xz(), t1.zy() - st2.yz(), t1.zz() - st2.zz()
|
|
);
|
|
}
|
|
|
|
|
|
//- Inner-product between a spherical tensor and a tensor
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator&(const SymmTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
st1.xx()*t2.xx() + st1.xy()*t2.yx() + st1.xz()*t2.zx(),
|
|
st1.xx()*t2.xy() + st1.xy()*t2.yy() + st1.xz()*t2.zy(),
|
|
st1.xx()*t2.xz() + st1.xy()*t2.yz() + st1.xz()*t2.zz(),
|
|
|
|
st1.xy()*t2.xx() + st1.yy()*t2.yx() + st1.yz()*t2.zx(),
|
|
st1.xy()*t2.xy() + st1.yy()*t2.yy() + st1.yz()*t2.zy(),
|
|
st1.xy()*t2.xz() + st1.yy()*t2.yz() + st1.yz()*t2.zz(),
|
|
|
|
st1.xz()*t2.xx() + st1.yz()*t2.yx() + st1.zz()*t2.zx(),
|
|
st1.xz()*t2.xy() + st1.yz()*t2.yy() + st1.zz()*t2.zy(),
|
|
st1.xz()*t2.xz() + st1.yz()*t2.yz() + st1.zz()*t2.zz()
|
|
);
|
|
}
|
|
|
|
|
|
//- Inner-product between a tensor and a spherical tensor
|
|
template <class Cmpt>
|
|
inline Tensor<Cmpt>
|
|
operator&(const Tensor<Cmpt>& t1, const SymmTensor<Cmpt>& st2)
|
|
{
|
|
return Tensor<Cmpt>
|
|
(
|
|
t1.xx()*st2.xx() + t1.xy()*st2.xy() + t1.xz()*st2.xz(),
|
|
t1.xx()*st2.xy() + t1.xy()*st2.yy() + t1.xz()*st2.yz(),
|
|
t1.xx()*st2.xz() + t1.xy()*st2.yz() + t1.xz()*st2.zz(),
|
|
|
|
t1.yx()*st2.xx() + t1.yy()*st2.xy() + t1.yz()*st2.xz(),
|
|
t1.yx()*st2.xy() + t1.yy()*st2.yy() + t1.yz()*st2.yz(),
|
|
t1.yx()*st2.xz() + t1.yy()*st2.yz() + t1.yz()*st2.zz(),
|
|
|
|
t1.zx()*st2.xx() + t1.zy()*st2.xy() + t1.zz()*st2.xz(),
|
|
t1.zx()*st2.xy() + t1.zy()*st2.yy() + t1.zz()*st2.yz(),
|
|
t1.zx()*st2.xz() + t1.zy()*st2.yz() + t1.zz()*st2.zz()
|
|
);
|
|
}
|
|
|
|
|
|
//- Double-dot-product between a spherical tensor and a tensor
|
|
template <class Cmpt>
|
|
inline Cmpt
|
|
operator&&(const SymmTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
|
|
{
|
|
return
|
|
(
|
|
st1.xx()*t2.xx() + st1.xy()*t2.xy() + st1.xz()*t2.xz() +
|
|
st1.xy()*t2.yx() + st1.yy()*t2.yy() + st1.yz()*t2.yz() +
|
|
st1.xz()*t2.zx() + st1.yz()*t2.zy() + st1.zz()*t2.zz()
|
|
);
|
|
}
|
|
|
|
|
|
//- Double-dot-product between a tensor and a spherical tensor
|
|
template <class Cmpt>
|
|
inline Cmpt
|
|
operator&&(const Tensor<Cmpt>& t1, const SymmTensor<Cmpt>& st2)
|
|
{
|
|
return
|
|
(
|
|
t1.xx()*st2.xx() + t1.xy()*st2.xy() + t1.xz()*st2.xz() +
|
|
t1.yx()*st2.xy() + t1.yy()*st2.yy() + t1.yz()*st2.yz() +
|
|
t1.zx()*st2.xz() + t1.zy()*st2.yz() + t1.zz()*st2.zz()
|
|
);
|
|
}
|
|
|
|
template<class Cmpt>
|
|
class typeOfSum<SymmTensor<Cmpt>, Tensor<Cmpt> >
|
|
{
|
|
public:
|
|
|
|
typedef Tensor<Cmpt> type;
|
|
};
|
|
|
|
template<class Cmpt>
|
|
class typeOfSum<Tensor<Cmpt>, SymmTensor<Cmpt> >
|
|
{
|
|
public:
|
|
|
|
typedef Tensor<Cmpt> type;
|
|
};
|
|
|
|
|
|
template<class Cmpt>
|
|
class innerProduct<SymmTensor<Cmpt>, Tensor<Cmpt> >
|
|
{
|
|
public:
|
|
|
|
typedef Tensor<Cmpt> type;
|
|
};
|
|
|
|
template<class Cmpt>
|
|
class innerProduct<Tensor<Cmpt>, SymmTensor<Cmpt> >
|
|
{
|
|
public:
|
|
|
|
typedef Tensor<Cmpt> type;
|
|
};
|
|
|
|
|
|
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
|
|
|
|
} // End namespace Foam
|
|
|
|
// ************************************************************************* //
|