## Re: [Libmesh-users] boundary condition

 Re: [Libmesh-users] boundary condition From: Roy Stogner - 2006-10-17 14:01:25 ```On Tue, 17 Oct 2006, li pan wrote: > I have a question of boundary condition. I want to set > Dirichlet boundary condition. The boundary surface in > any kinds of plane. The nodes on the plane can only > slid but not move out of the plane. Can I still use > penalty method? How can I do it? Yes: Instead of penalizing the vector between each boundary node and its desired point, penalize the normal distance between each boundary node and its desired plane. Instead of weighting that penalty residual against a full vector of test functions, weight it against the inner product of that vector and the normal derivative to the plane. If the boundary nodes need to be constrained not to move past the edges of a bounded region of a plane, things can get a little harder, but depending on what the rest of your PDE is (it sounds like you're doing mesh smoothing, right?) this may not be a problem. --- Roy ```

 [Libmesh-users] boundary condition From: li pan - 2006-10-17 13:02:50 ```Dear all, I have a question of boundary condition. I want to set Dirichlet boundary condition. The boundary surface in any kinds of plane. The nodes on the plane can only slid but not move out of the plane. Can I still use penalty method? How can I do it? best pan __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com ```
 [Libmesh-users] boundary condition From: li pan - 2006-10-18 16:03:59 ```if I just want to set boundary condition to some of the nodes on one side, e.g. only one node on a triangle, how can I do it in normal approach. Namely, first loop over element, then loop over side, the variables. Can I do like this? fix_node is the node where boundary condition will be set. for loop over element for loop over side for loop over all qpoints for i=0; i
 Re: [Libmesh-users] boundary condition From: Roy Stogner - 2006-10-17 14:01:25 ```On Tue, 17 Oct 2006, li pan wrote: > I have a question of boundary condition. I want to set > Dirichlet boundary condition. The boundary surface in > any kinds of plane. The nodes on the plane can only > slid but not move out of the plane. Can I still use > penalty method? How can I do it? Yes: Instead of penalizing the vector between each boundary node and its desired point, penalize the normal distance between each boundary node and its desired plane. Instead of weighting that penalty residual against a full vector of test functions, weight it against the inner product of that vector and the normal derivative to the plane. If the boundary nodes need to be constrained not to move past the edges of a bounded region of a plane, things can get a little harder, but depending on what the rest of your PDE is (it sounds like you're doing mesh smoothing, right?) this may not be a problem. --- Roy ```
 Re: [Libmesh-users] boundary condition From: li pan - 2006-10-17 15:41:09 ```could anybody give me an example to apply penalty boundary method in this case? best regards pan --- Roy Stogner wrote: > On Tue, 17 Oct 2006, li pan wrote: > > > I have a question of boundary condition. I want to > set > > Dirichlet boundary condition. The boundary surface > in > > any kinds of plane. The nodes on the plane can > only > > slid but not move out of the plane. Can I still > use > > penalty method? How can I do it? > > Yes: Instead of penalizing the vector between each > boundary node and > its desired point, penalize the normal distance > between each boundary > node and its desired plane. Instead of weighting > that penalty > residual against a full vector of test functions, > weight it against > the inner product of that vector and the normal > derivative to the > plane. > > If the boundary nodes need to be constrained not to > move past the > edges of a bounded region of a plane, things can get > a little harder, > but depending on what the rest of your PDE is (it > sounds like you're > doing mesh smoothing, right?) this may not be a > problem. > --- > Roy > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com ```
 Re: [Libmesh-users] boundary condition From: li pan - 2006-10-17 16:13:19 ```I think, I'd better explain my problem first :) I don't have a desired point, nor a desired direction. I only know the boundary nodes can move within the plane. That is to say, no displacement in normal direction. This is like dealing with contact problem. Maybe I can't solve it through setting boundary condition? best pan --- Roy Stogner wrote: > On Tue, 17 Oct 2006, li pan wrote: > > > I have a question of boundary condition. I want to > set > > Dirichlet boundary condition. The boundary surface > in > > any kinds of plane. The nodes on the plane can > only > > slid but not move out of the plane. Can I still > use > > penalty method? How can I do it? > > Yes: Instead of penalizing the vector between each > boundary node and > its desired point, penalize the normal distance > between each boundary > node and its desired plane. Instead of weighting > that penalty > residual against a full vector of test functions, > weight it against > the inner product of that vector and the normal > derivative to the > plane. > > If the boundary nodes need to be constrained not to > move past the > edges of a bounded region of a plane, things can get > a little harder, > but depending on what the rest of your PDE is (it > sounds like you're > doing mesh smoothing, right?) this may not be a > problem. > --- > Roy > > ------------------------------------------------------------------------- > Using Tomcat but need to do more? Need to support > web services, security? > Get stuff done quickly with pre-integrated > technology to make your job easier > Download IBM WebSphere Application Server v.1.0.1 > based on Apache Geronimo > http://sel.as-us.falkag.net/sel?cmd=lnk&kid=120709&bid=263057&dat=121642 > _______________________________________________ > Libmesh-users mailing list > Libmesh-users@... > https://lists.sourceforge.net/lists/listinfo/libmesh-users > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com ```
 Re: [Libmesh-users] boundary condition From: Roy Stogner - 2006-10-17 16:29:22 ```On Tue, 17 Oct 2006, li pan wrote: > I think, I'd better explain my problem first :) > I don't have a desired point, nor a desired direction. > I only know the boundary nodes can move within the > plane. That is to say, no displacement in normal > direction. This is like dealing with contact problem. > Maybe I can't solve it through setting boundary > condition? Well, what are your system's variables? If your x, y, and z displacement u has components ux, uy, and uz, with test functions tx, ty, and tz corresponding to vectors in each direction, and you're on a surface whose normal vector n has components nx, ny, and nz, and you want the displacement to be zero in the normal direction, then you should be able to add the following (penalized by 1 over epsilon) term to your residual: (ux * nx + uy * ny + uz * nz, tx * nx + ty * ny + tz * nz) Where (.,.) is the L2 inner product over the penalized boundary. This should be (modulo a constant factor of 2) what you get from variational calculus on the scalar residual (u*n)^2, unless I didn't have enough coffee this morning and I've done my math wrong. Isn't this kind of an odd boundary condition for a contact problem, though? The reason I assumed you were doing mesh smoothing is because you didn't talk about any friction terms, and most solid contact problems don't involve teflon sliding over wet ice. ;-) --- Roy ```