SMOOTH

The smooth command smooths 2D or 3D mesh objects. For adaptive smoothing see the radapt command. smooth takes a 2D or 3D mesh object and moves nodes, without changing the connectivity of the grid, in order to improve the aspect ratios and distribution of elements in the mesh.

An optional control value between zero and one for options esug, mega, geometry, elliptical and random affects the amount of node movement. The default (control =0.) results in the standard smoothing scheme. Increasing control towards 1. causes the scheme to be progressively more controlled (moving the mesh less), until at control =1., there is no mesh movement whatsoever.

By default, the second argument is position. This results in the positions of the nodes being changed. (Other options will be added in the future for implementation of smoothing using node velocities.)

There are nine smoothing algorithms available. esug, elliptic and random  are for 2D grids, laplace, aspect and lpfilter  for 2D or 3D grids, mega, network and geometry are for 3D grids:

1 . esug — Elliptic Smoothing for Unstructured Grids. This is the default for 2D mesh objects. It can only be used on triangular 2D mesh objects. (Ref.: Ahmed Khamayseh and Andrew Kuprat, “Anisotropic Smoothing and Solution Adaption for Unstructured Grids

2.elliptic — Similar to esug but the ‘guards’ which prevent a grid from folding are turned off. (Thus esug is preferred.)

  1. random – a node’s position is set to a randomly weighted average position of its neighbors. ‘Guards’ keep the elements from inverting.

  2. laplace —On a 3D tetahedral mesh moves a node to the average position of its neighbors where neighbor is defined as the set of nodes connected to the candidate node by an edge where the node types (itp1) and node constraints (icr1) are a ‘subset’ of the candidate node type and constraints.  A node will not be moved if the result is an inverted element. The following controls may be supplied:

Command Default Description
rlxwt 0.5 weight for underrelaxed Laplacian smothing
ntimes 5 number of smoothing iterations
nwttry 3 number of attempts to not tangle the mesh by halving the smoothing weight.
useisn 1 1 means interface nodes are smoothed based along a multimaterial edge with all the same materials as the candidate node. 0 means interface nodes are smoothed based on all interface neighbors
extrnbr (inclusive)   inclusivemeans do not restrict neighbors exclusive means restrict neighbors to nodes in pset 

 5. aspect—Adjusts node positions such that the aspect ratio of the elements is improved.  The default damage tolerance for smooth//aspect is infinity, so it can be used as a general smooth which has the effect of improving worst aspect ratio.

6 . lpfilter—This smooths surface networks by a low-pass filtering of the coordinate data.

(filtdeg default = 30, k_pb default = 0.1)

 7. mega — Minimum Error Gradient Adaption. This option creates a smoothed grid which is adapted to the standard function with constant Hessian f(x,y,z)=x2+y2+z2. Can be used on hybrid 3D meshes and guards against mesh folding. Adaption to this function creates a uniform isotropic mesh.  The code variable maxiter_sm (default=25) controls the maximum number of mega iterations.  The value of maxiter_sm may be changed using the assign command (assign/// maxiter_sm/10).  (Ref.: Randolph E. Bank and R. Kent Smith, “Mesh Smoothing Using A Posteriori Error Estimates”, SIAM J. Num. Anal. tol. 34, Issue 3, pp. 9-9 (19).)

  1. geometry — Geometry (“plump element”) adaption. Default for 3D. Can be used on hybrid 3D meshes It uses the mega algorithm but retains only the leading geometry term; the term containing the Hessian has been dropped. This algorithm guards against mesh folding.

  2. network — This option smooths the surface network of a 3D tetrahedral grid.  Volume nodes are not moved.  The material volumes are conserved.  By default a check is performed to verify that no elements are inverted; the user may turn this check off with the nocheck option.  This option will not work correctly (will not conserve volume) on grids which have two areas of a material connected at a single node or edge; each material region must have face connectivity.  The number of iterations is controlled by the niter argument (default is 10) and the weight argument controls the amount of movement (from 0. to 1. default is 1.).  Combining this type of smooth with volume smoothing will help to avoid element inversions.

FORMAT:

smooth /position /esug mega geometry elliptic random/ [ifirst,ilast,istride ]/[control]

smooth /position /lpfilter// [ifirst,ilast,istride] /[filtdeg]/[k_pb]/network

network smoothing applies to a network of curves in 2D or 3D, or to a network of surfaces in 3D.  The materiality of the cells (if any) is ignored.

smooth /position /aspect//[ifirst,ilast,istride/toldamage]

smooth /position/laplace/[ifisrt,ilast,istride]/[rlxwt]/[ntimes]/[nwtty]/[useisn]/[extrnbr]

smooth /position/network/[ifisrt,ilast,istride]/[niter]/[weight]/[check nocheck

EXAMPLES:

  1. Smooth all nodes in the mesh using esug in 2D or geometry in 3D.

     smooth
    
  2. Smooth all nodes in the mesh, using controlled smoothing with control=0.5.

     smooth / / / 1,0,0 / 0.5
    
  3. Smooth a 3D grid by combining network and volume smooths.

     pset/p2/attribute/itp1/1,0,0/0/eq
     smooth /position /network/1,0,0/3/1./heck
     smooth/position/geometry/pset,get,p2
     smooth /position /network/1,0,0/3/1./heck
     smooth/position/geometry/pset,get,p2