Correct the surface integration of triangles, tetrahedra and hexahedra - #114
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## main #114 +/- ##
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+ Coverage 63.53% 64.79% +1.26%
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Lines 1744 1744
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Three defects in the surface quadrature, all found by integrating a traction over element faces: 1. MappedH1OrL2SurfaceInterpolants divided |t1 × t2| by the reference triangle area 1/2, but |t1 × t2| is already twice the physical triangle area, so the Jacobian of every triangular face was twice the face area and every traction on a tetrahedron face was doubled. The ratio of physical to reference area is |t1 × t2| for a triangle and |t1 × t2|/4 for a quadrilateral, whose t2 is the diagonal. 2. The surface quadrature points of hexahedron faces 1, 3, 5 and 6 lay on faces 5, 6, 1 and 3 of face_vertices (the Exodus side order), and the tabulated normals followed the same wrong order; the Gauss-Lobatto rule also left face 6 unassigned. A traction on those faces was integrated with the shape functions of the wrong face, at about half its value. 3. The edge quadrature points of triangle edges 1 and 3 used the coordinate -1 of an unshifted edge on the shifted reference triangle, so they lay outside the element. The tests integrate the surface Jacobian over every face of the linear, quadratic and enriched tetrahedra and of the hexahedron, on the reference element and on an affine image, and compare with the face area; check on every face of every element that the shape functions of the face nodes sum to one at the face quadrature points; and check the tabulated normals of the tetrahedron and hexahedron against the face geometry. Signed-off-by: Alejandro Mota <amota@sandia.gov>
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Three defects in the surface quadrature, all found by integrating a traction over element faces:
MappedH1OrL2SurfaceInterpolantsdivided |t1 × t2| by the reference triangle area 1/2, but |t1 × t2| is already twice the physical triangle area, so the Jacobian of every triangular face was twice the face area and every traction on a tetrahedron face was doubled. The ratio of physical to reference area is |t1 × t2| for a triangle and |t1 × t2|/4 for a quadrilateral, whose t2 is the diagonal.face_vertices(the Exodus side order), and the tabulated normals followed the same wrong order; the Gauss-Lobatto rule also left face 6 unassigned. A traction on those faces was integrated with the shape functions of the wrong face, at about half its value.Tests: the surface Jacobian integrates to the face area on every face of the linear, quadratic and enriched tetrahedra and of the hexahedron (reference and affine image); on every face of every element the shape functions of the face nodes sum to one at the face quadrature points; the tabulated normals of the tetrahedron and hexahedron equal the geometric face normals. Version 0.14.8.