What is a smoother!
 

Hello Folks!

Waht ist smoother, or for what does it stand for? I read it everywhere but nowhere is ti explained.

Cheers,

Claus

A smoother allows to change the shape of a mesh preserving its topology.
Usually is used to improve the quality of a volume mesh after meshing (with fixed boundaries or with boundary nodes sliding on boundary surfaces).
It can be used to accommodate the movement of mesh boundary.
There are several algorithm take a look to this presentation:
http://www.torvergata-karting.it/fil...Biancolini.pdf
Take a look to related industrial solution: http://www.rbf-morph.com/

In CFD, I encounter two smoother concepts.

1. Mesh smoother. as just mentioned by meb.
2. Numerical smoother for matrix computation, similar to a preconditioner.

Thanks meb, for your answer!

But my question was related, as bearcat posted, to matrix computation. For instance, Gauss Seidel appears in same context. What is Gauss Seidel supposed to smooth?

Cheers,

Claus

For example in multigrid methods... There you have a hierarchy of discretizations and in cycles, you interpolate the solution between the different levels and do a direct solve at the coarsest scale. After the restriction- or prolongation steps, you usually do a couple of Gauss Seidel iterations to reduce high frequency errors. That is what they call 'smoothing'.

Hey Walli!

Thanks a lot! That is the answer I was looking for. However, I want to digger deeper to understand this method totally. Could you please give me some references?

Cheers,

Claus

Hi Claus,

Gauss-Seidel, and more generally other "preconditioners" and "smoothers" can be thought of as operators on your solution vector, that given enough iterations, would eventually drive your solution error towards zero (of course subject to discretization and machine error). Typically they work well at quickly eliminating the highest spatial frequency component of the error on a given mesh, but slow down asymptotically in their attenuation of error at lower spatial frequency ("coarser") scales. That's where multigrid techniques come in - generally with multigrid you cycle through coarser and finer meshes, thus attenuating error across length scales more uniformly. Where you can afford the extra memory, interpolation, and code complexity overhead they can be very worthwhile at improving convergence rate.

I can recommend Chapter 12 of Hirsch's "Numerical Computation of Internal and External Flows - Volume I - Fundamentals of Numerical Discretization" as a good introduction to the numerical analysis of iterative solvers and the multigrid approach.