On Thu, 21 Feb 2013, Manav Bhatia wrote:
I have a preference for Lagrange interpolation for the structural
(and some thermal) applications that I am working on, primarily due
to easy application of Dirichlet boundary conditions.
Have you noticed the relatively-new DirichletBoundary class we have?
Hand that a functor, and it'll do the projections onto non-Lagrange
spaces for you. Right now there's still work and testing to be done
for transient Dirichlet conditions (that functor may get evaluated at
time t in places where it should be evaluated at t +/- deltat...) but
for steady Dirichlet conditions it's pretty solid.
Perhaps hierarchic polynomials would also offer a similar feature
(please correct if I am wrong) due to the presence of node and edge
functions whose dof values can be specified, and bubble functions
that are zero on the boundaries.
Unless your Dirichlet values are piecewise-linear, they'll have
non-zero dofs corresponding to those bubble functions. What our
DirichletBoundary stuff gives you is interpolation at nodes, then
constrained L2 projection for edge-interior values, then
further-constrained L2 projection for face-interior values.
I am curious about your comment "mapped the Lagrange bases on to
nodes topologically". Are you implying a software fix of telling the
dof that it is associated with a node, or some sort of a
mathematical mapping process?
Software. Suppose you have a quad on the unit square. Isoparametric
cubic Lagrange elements would have nodes at (1/3,0) and (2/3,0), each
with a single degree of freedom. My suggestion would be to do what we
do with hierarchics: keep the single node at (1/2,0), give it two
degrees of freedom, then use some canonical ordering based on node
positions to determine which DoF is which. This breaks code which
assumes that solution(node->dof_number(0,0,0)) == u(Point(node)), but
mathematically it can still be the same basis being used.
---
Roy
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