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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.<br>
Is there a method that computes it directly? Like the quantities "center", "volume", "integrationElement", etc?<br>
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I am assuming you do not mean the conormal (e.g. tangent to the "surface") but the "surface normal"? That is not part of the Geometry<br>
interface at the moment. So you need to use the cross product (as far<br>
as I am aware that product does not exist in the DenseVector interface - perhaps you could make a suggestion...)<br>
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2)<br>
<br>
Dune::ISTLCGOp< DiscreteFunction, Dune::ISTLMatrixOperator< DiscreteFunction, DiscreteFunction, MatrixTraits > ><br>
Dune::CGInverseOperator < DiscreteFunction ><br>
Dune::ConjugateGradientSolver < Operator ><br>
<br>
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?<br>
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The first one uses the ISTL backend to solve the system and thus requires setting up the matrix (using the ISTL BlockMatrix classes).<br>
Also the DiscreteFunction has to be the BlockVectorDiscreteFuncrtion<br>
because for that the DOFs are stored in the as ISTL blockvector.<br>
<br>
The second is an implementation directly in dune-fem which only requires do implement the application of the operator on the vector.<br>
We use that for on-the-fly inversion - but as a consequence there is no fancy preconditioning available...<br>
<br>
Both should be fine for not quite positive definite or not quite symmetric matrixes - as long as it holds on a subspace and the initial<br>
guess is in that space.<br>
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Best<br>
Andreas<br>
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