The command radapt performs r-adaption smoothing on 2D or 3D mesh objects.
For a more general version of smoothing see command SMOOTH.
This command takes a 2D or 3D mesh object and moves nodes (specifically the nodes selected by
ifirst,ilast,istride), without changing the connectivity of the mesh, in order to adapt the mesh to best capture the behavior of a specified field or to an adaption function fadpt supplied by the user.
radapt /[position] / esug or mega/ [ifirst,ilast,istride] / [field]/ [refresh or stale] radapt / [position] / esug or mega/ [ifirst,ilast,istride] / [user]
subroutine fadpt(xvec,yvec,zvec, imtvec, nvec, time, fvec)
xvec, yvec, zvec - Vectors of x, y, and z coordinates of the points where the function is to be evaluated. imtvec - Vector of imt values for the case where function value depends on material type as well as position (ie. functions with discontinuities). nvec - Vector length (= number of places where function is to be evaluated). time - Time (scalar), for time-dependent functions. fvec - Vector of adaption function values.
There are two adaptive smoothing algorithms available:
esug Elliptic Smoothing for Unstructured Grids. This can
only be used on triangular 2D mesh objects. If field is specified in
the command line, esug will attempt to adapt the grid to the
specified field. If the keyword user is specified in the command
line, esug will attempt to adapt the grid to an adaption
function defined by the user-supplied subroutine fadpt.
Ref.: Ahmed Khamayseh and Andrew Kuprat, “Anisotropic Smoothing and Solution Adaption for Unstructured Grids”, Int. J. Num. Meth. Eng., Vol. 39, pp. 3163-3174 (1996)
mega Minimum Error Gradient Adaption. For adaptive
smoothing purposes, mega can only be used on 3D meshes, and only
in conjunction with a user-supplied subroutine fadpt or with a user specified attribute field. If adaption is to an attribute field,
then radapt may be instructed to use the interpolation mode associated with the attribute to refresh the attribute values.
The default is stale in which case the attribute value will not be updated to reflect the new node position. In either case, the
user is cautioned to carefully consider the validity of the data used for the adaption. mega can be used to adapt hybrid meshes
as well as tetrahedral meshes.
Ref.: Randolph E. Bank and R. Kent Smith, “Mesh Smoothing Using A Posteriori Error Estimates”, SIAM J. Num. Anal. Vol. 34, Issue 3, pp. 979-997, 1997.
If field adaption is used, the user has specified a valid field
from the current mesh object, and r-adaption is to be based upon
this field. Typically, if the field has large gradients or curvature
in a particular region, r-adaption using this field will cause nodes
to be attracted to the region of interest. (esug adapts
especially to large gradients, mega adapts especially to large
second derivatives—“curvature”.)
If adaption is to an attribute field, then radapt may be instructed to use the interpolation
mode associated with the attribute field to refresh the
attribute values. The default is stale in which case the
attribute value will not be updated to reflect the new node position
adaption. In this case, the user should reduce the number of
adaption iterations to less than 4, since r-adaption with stale data
becomes meaningless.
If refresh is specified, the r-adaption routine will automatically
interpolate the new field values every iteration, using a call to
the doping command. In this case, the number of adaption
iterations need not be reduced from the default value of 25. In
either case, the user is cautioned to carefully consider the
validity of the data used for the adaption.
If user is specified, the mesh will r-adapt to the function returned
by the subroutine fadpt which must be supplied by the user.
If position is specified, it signifies that the x-y-z values of the nodes
in the current mesh object will be altered. (Other argument values allow for modification options that are not yet implemented.)
If esug is used (currently available in 2D only), the degree of
node adaption will depend on the scale of the specified field. In
this case, the results of adaption of the grid to the field can be
altered by using one or more field commands beforehand to modify the field. For example, by increasing the scale of a field using
field /scale, the esug algorithm will produce grids with
increased numbers of nodes in the regions where the field
experiences relatively large gradients. By volume averaging a field
using field/volavg, esug will cause a more gentle form
of adaption with a better grading of elements. By composing the
values of the field with log or asinh using field
/compose, one can cause esug to shift nodes to where the
logarithm (or hyperbolic arcsine) of the field has interesting
features, rather than where the field itself has interesting
features.
Note: Since the* mega adaptive smoothing algorithm is rigorously based on error minimization, it is in general of little or no value to modify the adaption function for this algorithm. In particular, rescaling has no effect on the output.
The variable MAXITER_SM (Default: 25) can be set using the ASSIGN command before calling RADAPT.
This controls the maximum number of adaption iterations to be performed. If convergence is detected beforehand, less iterations will be
performed. If field data is allowed to become “stale” during the course of r-adaption, MAXITER_SM should be reduced (e.g. less than 5).
radapt / / esug / 1,0,0 / density
Using esug, adapt all nodes in 2dmesh to the density field. Do not update data.
radapt / / / 1,0,0 / user
doping / user / density / set /1,0,0/
Assuming a default 3D cmo, use mega to adapt the mesh to the adaption function supplied by the user via subroutine fadpt. Afterwards dope (interpolate) the density field with the fadpt function values.
assign / / / maxiter_sm / 50
This changes the maximum number of iterations to 50. If radapt detects a sufficient amount of convergence, it will terminate smoothing in less than maxiter_sm iterations.
The following demonstrate adaptive smoothing using mega.
Load the file fadpt_boron.f ahead of the LaGriT libraries; this will cause the default fadpt subroutine to be displaced by the one in this file. The result is that now 3D adaptive smoothing will attempt to adapt 3D tetrahedral or hybrid meshes to the boron density function devised by Kent Smith of Bell Labs. This function has a maximum value of 1.1 x 1018, and drops rapidly to zero; the function attains its largest values on a T-shaped region in space and provides very challenging isosurfaces to capture. Two input decks use this function:
input.boron.3dtet. This deck generates and adapts a tetrahedral mesh to the boron function. A snapshot of the adapted grid may be seen at boron.png .
input.boron.3dhex. This deck generates and adapts a hexahedral mesh to the boron function. A snapshot of the adapted grid may be seen boron_hex.png
This function fadpt_gyro.f, has large second derivatives near three rings of unit diameter which are aligned with each of the three coordinate planes which pass through the origin. Adaption to this function results in the pulling of the grid towards the rings when running the following two input decks:
input.gyro.3dtet. This deck generates and adapts a tetrahedral mesh to the “gyroscope” function. A snapshot of the adapted grid may be seen at gyro.png
input.gyro.3dhex. This deck generates and adapts a hexahedral mesh to the “gyroscope” function. A snapshot of the adapted grid may be seen at gyro.hex.png
