Hi Pierre Yes, you do need to smooth the elements after you've snapped the nodes to interfaces. This is quite easy to do, you just regard the lattice as a balls-and-springs network with the nodes as balls and the element edges as springs of natural length that of the original cubic mesh. You then relax according Newton's laws with friction. The nodes will move to the lowest energy configuration. When relaxing, the nodes which have been snapped are constrained to stay on the surface they were snapped to. This can be done using the Lagrangian formulation with Lagrange multipliers for constraints. I would not use the finite element solver to do this, just implement Newton's laws directly on the particles. The hardest part is, in my opinion, snapping the nodes to interfaces. I think I could write the whole code quite easily but interfacing into Gmsh (200,000 lines of c++) would be beyond me. One, not-so-elegant solution would be for me to write my mesh algorithm as a "solver" in Gmsh. This would read in the .geo file and output the .msh file. John Blackburn .
________________________________ From: Pierre JUILLARD [mailto:[email protected]] Sent: 30 July 2009 06:15 To: John Blackburn Cc: [email protected] Subject: Re: [Gmsh] suggested new meshing algorithm in Gmsh: hex gridding Hi John, Just out of curiosity: Don't you need to "smooth" the elements close to the "snapped" boundary nodes? If yes, doesn't it mean that you also need to reposition the nodes not only close to the interfaces, but also those which are in the geometry? Finally, isn't this algorithm like a morphing algorithm? I actually sent a mail to the mailing list to know what are GMSH' capabilities regarding morphing, but there were not much answer. Regarding this smoothing function, it would make use of the GMSH finite element solver part, and deal with the existing mesh, make it deformed linearly with a given E modulus to make it fit a new shape. You would then have all the nodes positioned accordingly their distance from the originally "snapped" nodes. Regards, Pierre 2009/7/29 John Blackburn <[email protected]> Dear Sir, I have recently been trying out Gmsh and am most impressed with its capabilities. I am writing an FE code of my own which uses hexahedrons. I've noticed that, while Gmsh does generate hex's this is quite a painful process and involves splitting the geometry into many more parts than would be the case for tets. Hex meshes can only be generated for transfinite volumes or ones which can be made from extrusions. I would like to suggest another method to generate (structured) hex meshes which is to have a "logical mesh", which is just a cubic grid of nodes, and then "snap" the nodes onto nearby interface points. You then end up with a mesh with the same topology as the original but distored to fit the required shapes. I would like to add this functionality to Gmsh as I think it would greatly improve the program. However, I am mainly a Fortran programmer. I can code in C with some difficulty but full OO C++ is beyond me! I was wondering, if I send you a detailed write up of the algorithm I have in mind (with all the maths/geometry written out explicitly), could you code it in for me? I suspect this simple algorithm would be easy to implement given Gmsh's existing capablities. Basically two things are needed: * a function to decide whether an arbitrary point (x,y,z) is inside a given volume (defined, as usual by plane or ruled surfaces themselves defeined by curves: just the way Gmsh works now). I'm sure Gmsh already has a function like this? * a funciton to "snap" a point to the nearest point on the volume surface. Note that only points at the interface between two regions are candidates for snapping. I've written a little program to implement this algorithm as I see (in 2-D for the moment but 3-D would not be much more difficult). The program outputs a .MSH file which I've plotted using Gmsh and attached. Notice how the algorithm involves INSERTING shapes into each other: the orange square was defined first, then the green circle, blue circle, and finally, yellow polygon. This is very different from Gmsh's current approach but its a very powerful technique. I also intend to write a final "relaxation" part to the meshing so the unecessarily distorted nodes in the blue circle would return to their original positions. What do you think about incorporating this functionality? Basically, the user would do everything he normally does to prepare the GEO file. Then there would be an extra button on the Mesh menu, "Grid" for example. Best Regards, John Blackburn ------------------------------------------------------------------- This e-mail and any attachments may contain confidential and/or privileged material; it is for the intended addressee(s) only. If you are not a named addressee, you must not use, retain or disclose such information. NPL Management Ltd cannot guarantee that the e-mail or any attachments are free from viruses. NPL Management Ltd. Registered in England and Wales. No: 2937881 Registered Office: Serco House, 16 Bartley Wood Business Park, Hook, Hampshire, United Kingdom RG27 9UY ------------------------------------------------------------------- _______________________________________________ gmsh mailing list [email protected] http://www.geuz.org/mailman/listinfo/gmsh ------------------------------------------------------------------- This e-mail and any attachments may contain confidential and/or privileged material; it is for the intended addressee(s) only. If you are not a named addressee, you must not use, retain or disclose such information. NPL Management Ltd cannot guarantee that the e-mail or any attachments are free from viruses. NPL Management Ltd. Registered in England and Wales. No: 2937881 Registered Office: Serco House, 16 Bartley Wood Business Park, Hook, Hampshire, United Kingdom RG27 9UY -------------------------------------------------------------------
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