On Fri, 7 Sep 2012, Andrew E Slaughter wrote: > I am working on solving the level set equation using DG methods, form the > looks of example Miscellaneous Example 5 this should be possible.
It certainly should be. > Currently, I am simply trying to formulate the mass matrix, which is simply > the integral of N^T N over the domain, where N is the shape function > vector. I would like this matrix to be diagonal so it can be inverted > locally allowing me to solve the system with an explicit scheme. Does > libMesh have a set of basis functions that could offer me his behavior? Not yet. We'd love a patch adding them. ;-) I'm not sure how you'd want to go about it, though. Discontinuous orthogonal polynomials are easy to derive on rectangles, but they'd no longer be orthogonal once they went through a non-affine transformation onto physical elements. I suppose you could just work with triangles/tets; if the inner product is a plain L2 integration then orthogonality ought to be preserved by affine maps. Start with the MONOMIAL bases and then do Gram-Schmidt to get an orthonormal basis? > The book I am following for this problem recommends "orthogonal > hierarchical shape functions". So, I tried to using L2_HIERARCHIC > via the add_system(...) command, but the mass matrix was not > diagonal. Could it be a problem with how I am assembling the matrix > via quadrature points, my assemble() function is shown at the end. I > am new to FEM and mostly self-taught so I am naive in many aspects. No - the L2_HIERARCHIC shapes are discontinuous and hierarchic, but they aren't orthogonal in L2 - that name was just supposed to distinguish them from the "default" continuous (H1-conforming) hierarchics that share the same local numbering and shapes. I suppose you could do a numerical stabilized Gram-Schmidt process on *any* set of discontinuous bases (maybe start from XYZ?), doing projections with the same quadrature you use for integration. That would be expensive enough that you'd want to do it once and cache the results, but you might want to cache shape function evaluations anyway if you're trying an explicit solve. --- Roy ------------------------------------------------------------------------------ Live Security Virtual Conference Exclusive live event will cover all the ways today's security and threat landscape has changed and how IT managers can respond. Discussions will include endpoint security, mobile security and the latest in malware threats. http://www.accelacomm.com/jaw/sfrnl04242012/114/50122263/ _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
