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Add H(curl div) sobolev space and the covariant contravariant Piola mapping #312

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Add H(curl div) sobolev space and the covariant contravariant Piola mapping #312

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988c85d
Support covariant contravariant piola mapping for H(curl div)
pbrubeck May 6, 2024
8387a75
Add GLS H(curl div) element
pbrubeck May 6, 2024
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1 change: 1 addition & 0 deletions tsfc/finatinterface.py
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Original file line number Diff line number Diff line change
Expand Up @@ -61,6 +61,7 @@
"Nedelec 2nd kind H(curl)": finat.NedelecSecondKind,
"Raviart-Thomas": finat.RaviartThomas,
"Regge": finat.Regge,
"Gopalakrishnan-Lederer-Schoberl": finat.GopalakrishnanLedererSchoberl,
"BDMCE": finat.BrezziDouglasMariniCubeEdge,
"BDMCF": finat.BrezziDouglasMariniCubeFace,
# These require special treatment below
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11 changes: 11 additions & 0 deletions tsfc/ufl_utils.py
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Expand Up @@ -403,6 +403,10 @@ def apply_mapping(expression, element, domain):

G(X) = det(J)^2 K g(x) K^T i.e. G_il(X)=(detJ)^2 K_ij g_jk K_lk

'covariant contravariant piola' mapping for g:

G(X) = det(J) J^T g(x) K^T i.e. G_il(X) = det(J) J_ji g_jk(x) K_lk

If 'contravariant piola' or 'covariant piola' (or their double
variants) are applied to a matrix-valued function, the appropriate
mappings are applied row-by-row.
Expand Down Expand Up @@ -442,6 +446,13 @@ def apply_mapping(expression, element, domain):
*k, i, j, m, n = indices(len(expression.ufl_shape) + 2)
kmn = (*k, m, n)
rexpression = as_tensor(detJ**2 * K[i, m] * expression[kmn] * K[j, n], (*k, i, j))
elif mapping == "covariant contravariant piola":
J = Jacobian(mesh)
K = JacobianInverse(mesh)
detJ = JacobianDeterminant(mesh)
*k, i, j, m, n = indices(len(expression.ufl_shape) + 2)
kmn = (*k, m, n)
rexpression = as_tensor(detJ * J[m, i] * expression[kmn] * K[j, n], (*k, i, j))
elif mapping == "symmetries":
# This tells us how to get from the pieces of the reference
# space expression to the physical space one.
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