[dune-fem] Two questions about the normal to a triangle and the CG operator

[Sacconi, Andrea]

Hi all,

I have a couple of questions on different topics:

1) suppose that our mesh is made of triangles (in R^3, not in R^2, so each vertex has 3 coordinates); given an arbitrary triangle of such a mesh, I need to extract the unit normal to that triangle.
Is there a method that computes it directly? Like the quantities "center", "volume", "integrationElement", etc?

I mean, I know conceptually how to do it by hand, but I'd like to know if there is a reliable function that does it, on a generic triangle (not the reference one).

2) suppose I'm solving a system of equations using a Schur complement approach, similar to the Uzawa implementation for Stokes.
I'd like to use a CG solver to solve the problem, but the linear matrix of such an operator cannot be assembled, since it'd involve the explicit inversion of a matrix. Only the action of the operator, i.e. the matrix-vector product for any arbitrary vector of the domain of the operator can be implemented.

Which CG solver can I use? What is the difference between these operators

Dune::ISTLCGOp< DiscreteFunction, Dune::ISTLMatrixOperator< DiscreteFunction, DiscreteFunction, MatrixTraits > >
Dune::CGInverseOperator < DiscreteFunction >
Dune::ConjugateGradientSolver < Operator >

By the way, I'm going to solve an operator represented by semi-positive-definite matrix; do all of these satisfy the property that if you feed the CG with a compatible initial guess all the iterates belong to the right space?

Thanks a lot!

Andrea
__________________________________________________________

Andrea Sacconi
PhD student, Applied Mathematics
AMMP Section, Department of Mathematics, Imperial College London,
London SW7 2AZ, UK
a.sacconi11 at imperial.ac.uk
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