use affine root coords as geom if possible #855
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Before 5034398 the geometry of a rectilinear mesh with uniform vertices was an affine transformation of the root coordinates. In patch 5034398 this special case was removed due to a pending change in the transform chains for structured topologies: the replacement of the transformation that places an element in the root space with an index, thereby giving every element unit square root coordinates. The effect of this change is a suboptimal gradient of the geometry to the root coordinates. Since the geometry is now always the inner product of a linear basis with vertices, the gradient of the geometry does not simplify to a constant if the vertices are evenly spaced. This patch restores the special cased geometry for rectilinear meshes defined by numbers of elements by creating a reference geometry out of the (unit square) root coordinates and the element index.
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gertjanvanzwieten
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Mar 1, 2024
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Before 5034398 the geometry of a rectilinear mesh was an affine transformation of the root coordinates. In patch 5034398 this special case was removed due to a pending change in the transform chains for structured topologies: the replacement of the transformation that places an element in the root space with an index, thereby giving every element unit square root coordinates.
The effect of this change is a suboptimal gradient of the geometry to the root coordinates. Since the geometry is now always the inner product of a linear basis with vertices, the gradient of the geometry does not simplify to a constant if the vertices are evenly spaced.
This patch restores the special cased geometry by creating a reference geometry out of the (unit square) root coordinates and the element index and applying an affine transformation.