I took some notes when my boss told me the smoothing function months ago. He thought we should treat interior points equally with boundary points and thus penalty method is garbage in his words:). For a domain [0, 1] x [0, 1], we can multiply unknown u with a function such as x(1-x)y(1-y), making the boundary all zeros.
I am a guy from computer science. Understanding FE is hard for me. Hope I can get some hints here. Thank you. --Junchao Zhang On Mon, Jan 11, 2016 at 5:46 PM, Geordie McBain <gdmcb...@freeshell.org> wrote: > 2016-01-12 8:44 GMT+11:00 Junchao Zhang <junchao.zh...@gmail.com>: > > Hello, > > I am learning FEM by reading the Libmesh example adaptivity_ex2.C and > > have two questions. > > > 2) The code uses the penalty method to impose boundary conditions. I > was > > told the penalty method is bad and a smoothing function with zero on > > boundary is preferred. Could someone point me to literatures or examples > on > > smoothing? > > Hello. I'm not sure that 'the penalty method is bad'. There can be > some technical issues with it in specialized problems, but if you're > only just learning FEM, I wouldn't worry about them for the moment. A > good introductory reference for the penalty method is the section > 'Essential boundary conditions' on pp. 121-122 of > > Becker, E. B., G. F. Carey, & J. T. Oden (1981). Finite Elements, > An Introduction, > Volume 1 of The Texas Finite Element Series. Englewood Cliffs, New > Jersey: Prentice-Hall > > which includes: 'The penalty method is not only easy to implement and > mathematically sound but it is also easy to motivate by physical > arguments.' > > I haven't heard of the 'smoothing function' idea, but if you do need > or would prefer to avoid the penalty method, libMesh does have the > DirichletBoundary, as in introduction_ex4.C. > ------------------------------------------------------------------------------ Site24x7 APM Insight: Get Deep Visibility into Application Performance APM + Mobile APM + RUM: Monitor 3 App instances at just $35/Month Monitor end-to-end web transactions and take corrective actions now Troubleshoot faster and improve end-user experience. Signup Now! http://pubads.g.doubleclick.net/gampad/clk?id=267308311&iu=/4140 _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
