From: Roy Stogner <roystgnr@ic...>  20060301 20:25:33

On Wed, 1 Mar 2006, David Xu wrote: > I'd like to know when you expect to have a working 3D hermite > polynomial in place? Well, the bug hunting hasn't been high on my priority list since the 3D version of my method has a couple harder obstacles to overcome first. I can give it more attention if I know there's other people waiting to use the code, but it won't be fixed any time in the next week. > I'm trying to model 3D timeindependent schrodinger equation and > some references tell me using hermite polynomial with C1 continuity > has clear advantage over Lagrange polynomial. I'm not sure the advantages will be clear unless your weak formulation depends on integrals on a W^{2,p} space. C1 elements can give you similar accuracy with fewer DoFs (I think ~8 per element instead of ~27 when comparing C0 and C1 cubic hexes), I suppose. > What's the highest order of Lagrange polynomial supported? Only linears and quadratics are supported with a Lagrange basis on most elements, and AFAIK only pseudolinears are supported on pyramid elements. We've also got a set of hierarchic elements you might be interesed in. They're not very complete, but they do include cubic 3D hexes, without any rectilinear mesh restrictions. >> No. The higher order elements give you the chance to use higher order >> mapping functions, and give libMesh more places to put degrees of >> freedom (because edge and face DoFs are usually necessary for higher >> order shape functions), but if you just convert a QUAD4 mesh into a >> QUAD9 mesh while specifying bilinear shape functions it shouldn't >> change your results beyond whatever different floatingpoint errors >> do to the mapping functions. > > So, is the number of nodes in an element unrelated to the order of > Lagrange polynomial in libmesh? Not unrelated  if you want quadratic Lagrange elements, then you need second order geometric elements like QUAD9. However, if you want linear elements, then you can still use second order geometric elements (to better resolve a curved boundary, for instance). > How do I sepcify the order of gauss quadrature? When you construct a QGauss object, one of the parameters is the degree of polynomials you want to exactly integrate. You can also call FEType::default_quadrature_rule() if you have an FEType corresponding to an element of order p and you want a quadrature rule that exactly integrates polynomials of degree 2p+1. That's the safest way to go if you want compatibility with future more exotic elements, too. Macroelement basis functions require Gaussian rules on each of their subelements for exact integration, for example.  Roy 