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Add Levi-Civita tensor to Aspect #5318

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Jul 14, 2023
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Add Levi-Civita tensor to Aspect #5318

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Add Levi-Cevita tensor to Aspect
MFraters Jul 14, 2023
c41d6aa
Update include/aspect/utilities.h
MFraters Jul 14, 2023
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26 changes: 26 additions & 0 deletions include/aspect/utilities.h
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Original file line number Diff line number Diff line change
Expand Up @@ -1276,6 +1276,32 @@ namespace aspect
Tensor<1,21>
to_voigt_stiffness_vector(const SymmetricTensor<4,3> &input);


namespace internal
{
constexpr Tensor<3,3> create_levi_civita_tensor_3d()
{
Tensor<3,3> permutation_operator_3d;
permutation_operator_3d[0][1][2] = 1;
permutation_operator_3d[1][2][0] = 1;
permutation_operator_3d[2][0][1] = 1;
permutation_operator_3d[0][2][1] = -1;
permutation_operator_3d[1][0][2] = -1;
permutation_operator_3d[2][1][0] = -1;
Comment on lines +1284 to +1290
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Oh yes, that's nice -- you don't actually need to replace the zeros!

return permutation_operator_3d;
}
}

/**
* The Levi-Civita tensor, also called a permutation or "totally antisymmetric" tensor.
* See https://en.wikipedia.org/wiki/Levi-Civita_symbol for a definition.
* See https://en.wikipedia.org/wiki/Levi-Civita_symbol for more info.
*/
template<int dim>
constexpr Tensor<dim,dim> levi_civita;

template <> constexpr Tensor<3,3> levi_civita<3> = internal::create_levi_civita_tensor_3d();

}

}
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36 changes: 36 additions & 0 deletions unit_tests/utilities.cc
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Expand Up @@ -575,4 +575,40 @@ TEST_CASE("CPO elastic tensor transform functions")
}
}
}

/**
* test Levi-Cevita tensor function
*/
{

REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[0][0][0] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[0][0][1] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[0][0][2] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[0][1][0] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[0][1][1] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[0][1][2] == Approx(1.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[0][2][0] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[0][2][1] == Approx(-1.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[0][2][2] == Approx(0.0));

REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[1][0][0] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[1][0][1] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[1][0][2] == Approx(-1.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[1][1][0] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[1][1][1] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[1][1][2] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[1][2][0] == Approx(1.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[1][2][1] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[1][2][2] == Approx(0.0));

REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[2][0][0] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[2][0][1] == Approx(1.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[2][0][2] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[2][1][0] == Approx(-1.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[2][1][1] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[2][1][2] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[2][2][0] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[2][2][1] == Approx(0.0));
REQUIRE(aspect::Utilities::Tensors::levi_civita<3>[2][2][2] == Approx(0.0));
}
}