Hello Bruno, Thanks for the reply.
I read the the link you gave and that helped me learn and understand how things work behind the scene in deal.ii. But, I dont understand 1 thing. Lets say my domain just consists of a single element in 1D. I use quadratic shape functions so this makes a total of 3 shape functions. Now, lets say I want to use isoparametric mapping. If x is the mapping and zeta is the coordinate in the parent element, and x1, x2 (middle node), x3 are the coordinates of the three nodes in the real space. so, Jacobian needs to calculate, dx / dzeta = x1 * dN1 / dzeta + x2 * dN2 / dzeta + x3 * dN3 / dzeta. So, going by what you described, if x2 is unknown, how can the mapping class calculate the information? Is it because it uses the manifold information (which is a straight boundary by default) attached to it to get the nodal coordinates of the middle node and then calculate the Jacobian and other information? Thanks. On Monday, December 11, 2017 at 8:39:20 AM UTC-5, Bruno Turcksin wrote: > > Hi, > > On Sunday, December 10, 2017 at 9:55:49 PM UTC-5, RAJAT ARORA wrote: > >> My question is: >> Is the mesh movement independent of the order of the polynomial used to >> interpolate the solution? >> >> What is confusing me is that I learned that there are nodes (other than >> vertices) in the element when using higher order elements. So, when moving >> mesh, these nodes must also be moved. In other words, these nodes are part >> of the mesh. But if the move mesh function is correct for higher order >> shape functions as well, than this means, my mesh just knows about the >> vertices of the elements. >> > The mesh is independent of the order of the polynomial. The easiest way > to realize it is that you don't need to know which kind of finite element > you are using to create a mesh. If it worked like you said and the nodes > would be part of the mesh, you would need to know the finite element to > build the mesh. There is no reason to have the nodes part of the mesh. The > only thing you need is to be able to map the position of the nodes in the > unit cell to their position in the mesh. This is done using Mapping. > Mapping allows you decouple the mesh with the finite element that you are > using. Take a look here > http://dealii.org/developer/doxygen/deal.II/group__FE__vs__Mapping__vs__FEValues.html > > Best, > > Bruno > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
