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# Written by Robert C. Kirby
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# Copyright 2005 by The University of Chicago
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# Distributed under the LGPL license
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# This work is partially supported by the US Department of Energy
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# under award number DE-FG02-04ER25650
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# last edited 9 May 2005
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import shapes, functional, polynomial, points, functionalset
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def PhiK( shape , n , U ):
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"""The set PhiK defined by Brezzi & Fortin of vector-valued
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polynomials of degree n with vanishing divergence and
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vanishing normal components around the boundary."""
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U = polynomial.OrthogonalPolynomialArraySet( shape , n )
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# need Phi and U to share a common base, so I have to
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# take degree n and then throw away some to get degree n-1
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Phi = polynomial.OrthogonalPolynomialSet( shape , n )
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Phi_lower = Phi[:shapes.polynomial_dimension( shape , n-1 )]
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DCPE = functional.DirectionalComponentPointEvaluation
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d = shapes.dimension( shape )
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pts_per_edge = [ [ x \
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for x in points.make_points( shape , \
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for i in shapes.entity_range( shape , d-1 ) ]
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pts_flat = reduce( lambda a,b:a+b , pts_per_edge )
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ls = [ functional.IntegralMomentOfDivergence( U , phi ) \
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for phi in Phi_lower ]
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nrml = shapes.normals[ shape ][ i ]
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ls_cur = [ DCPE(U,nrml,pt) for pt in pts_per_edge[i] ]
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fset = functionalset.FunctionalSet(U,ls)
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return polynomial.ConstrainedPolynomialSet( fset )
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FIAT/PhiK.py
