Hi David, Greetings again.
I found the answer from this link <http://www.joinville.udesc.br/portal/professores/pablo/materiais/CIL26_0053.pdf> and yes, we will get a globally smooth distribution at the cost of much more computation. Thank you, Shawn On Fri, Nov 2, 2018 at 10:01 PM Yuxiang Wang <yw...@virginia.edu> wrote: > Hi David, > > Thank you for your response! Yes I was indeed reading your example and > thinking about it. Your insight helps a lot. Thank you so much! > > Since we are discussing on this topic, if you wouldn't mind, I'd like to > ask one more question: > > During the L2 projection process, we solved the system per element. If we > assemble the element mass matrices and the RHS to a global one with all > elements, and similarly solve the global equation, would we be getting a > globally smoothed stress distribution? > > I'd really love to hear your comment. Thanks in advance! > > Best, > Shawn > > On Fri, Nov 2, 2018 at 7:27 PM David Knezevic <david.kneze...@akselos.com> > wrote: > >> On Fri, Nov 2, 2018 at 9:50 PM Yuxiang Wang <yw...@virginia.edu> wrote: >> >>> Dear all, >>> >>> I have been using the matrix notation (following the Bathe textbook) with >>> libmesh recently to code finite element solutions for basic continuum >>> structural elements. I realized that I need to compute those matrices >>> twice >>> - once when I assemble the global stiffness matrix, and another time >>> when I >>> get the solutions and need to post-process to compute the >>> stresses/strains. >>> Being curious, do we have any best practices (or special considerations) >>> to >>> save those matrices so that we don't have to compute them twice? For >>> example, should I just create a huge vector of DenseMatrix, and each >>> matrix >>> for each quadrature point? Or that libmesh has some tools for this book >>> keeping? >>> >>> Explanation for what I meant by "matrix notation" and what are those >>> finite >>> element matrices: for example, for each quadrature point I have an >>> interpolation matrix [H], a strain-displacement matrix [B] (constructed >>> from derivatives of [H]). With the constitutive tensor matrix being [C], >>> we >>> can easily get the element stiffness matrix by [K] = >>> integrate([B]^T[C][B]). After the solution [uhat] is obtained, we can >>> also >>> get the strain and stress by again [strain] = [B][uhat] or [stress] = >>> [C][B][uhat]. >>> >>> Just wondering whether anyone else has done this before and whether there >>> would be a better practice to do it more elegantly. Thanks :) >>> >>> Best, >>> Shawn >> >> >> See systems_of_equations_ex6 for an example of computing stresses in >> libMesh. In that case we do not store and re-use the per-element strain and >> stress matrices (C and B in your notation) You could store and reuse that >> data, but it's not clear to me whether it'd be worth it. You'd presumably >> get some speedup in the evaluation of the stress at the cost of extra >> storage, so you'd have to decide if you want that or not (in my experience >> I would not want that since memory is usually more of a limiting factor >> than speed). >> >> Best, >> David >> > > > -- > Yuxiang "Shawn" Wang, PhD > yw...@virginia.edu > +1 (434) 284-0836 > -- Yuxiang "Shawn" Wang, PhD yw...@virginia.edu +1 (434) 284-0836 _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
