LaGriT/documentation/lagrit_manual/commands/radapt.txt

.. _radapt :

&nbsp_place_holder;

> **_RADAPT_**

>

>> The command radapt performs r-adaption on 2D or 3D mesh objects. For simple
smoothing see command smooth. radapt takes a 2D or 3D mesh object and moves
nodes (specifically the nodes selected by ifirst,ilast,istride), without
changing the connectivity of the grid, in order to adapt the mesh to best
capture the behavior of a specified field or to an _adaptionfunction_ (fadpt)
supplied by the user.

> > There are two adaptive smoothing algorithms available:

1. **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.
(Ahmed Khamayseh and Andrew Kuprat, "Anisotropic Smoothing and Solution
Adaption for Unstructured Grids", Int. J. Num. Meth. Eng., Vol. 39, pp.
3163-3174 (1996)).

2. **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. (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))

In the field adaption form, 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. (See **maxiter**_**sm** variable description
below.) The user takes on the task of refreshing the field values by e.g. re-
solving a PDE for the new field values on the new mesh. 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.

In the **user** form, the mesh will r-adapt to the function returned by the
subroutine fadpt which must be supplied by the user.

Specifying **position** 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 code 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 by **radapt**. If convergence is
detected , fewer 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 4).

>

> FORMAT:

>

>> **radapt **/**[position**]/** **[**esug**|**mega**]/[ifirst,ilast,istride]
/[field]/

[**refresh**|**stale**]

**radapt **/ [**position**]/** **[**esug**|**mega** ]/ [ifirst,ilast,istride] / [**user**]
>

> EXAMPLES:

>

>> Using **esug**, adapt all nodes in 2dmesh to the density field. Do not
update data.

>>

>>> **radapt / / esug / **1,0,0 / density

>>

>> Assuming a default 3D cmo, use **mega** to adapt the mesh to the adaption
function supplied by the user via subroutine fadpt. Afterwards dope the
density field with the fadpt function values.

>>

>>> **radapt **/ / / 1,0,0 / **user**

**doping **/** user **/ density / **set **/1,0,0/
>

> FORMAT FOR fadpt:

>

>> 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 (material types) 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.

>

>

SAMPLE FUNCTIONS AND INPUT DECKS

>

>> To demonstrate adaptive smoothing using **mega**, examples are available
which use the files [fadpt_boron.f](../../new_html/fadpt_boron.f),[input.boron
.3dtet](../../new_html/input.boron.3dtet),[input.boron.3dhex](../../new_html/i
nput.boron.3dhex),[fadpt_gyro.f](../../new_html/fadpt_gyro.f), [input.gyro.3dt
et](../../new_html/input.gyro.3dtet),[input.gyro.3dhex](../../new_html/input.g
yro.3dhex).

> > 1. Boron density function fadpt_boron.f. 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:

>>

>>> a. input.boron.3dtet. This deck generates and adapts a tetrahedral mesh to
the boron function.&nbsp_place_holder; A snapshot of the adapted grid may be
seen at [boron.png](../../images/boron.png).

b. input.boron.3dhex. This deck generates and adapts a hexahedral mesh to the
boron function.&nbsp_place_holder;&nbsp_place_holder; A snapshot of the
adapted grid may be seen at [boron.hex.png.](../../images/boron.hex.png)

>>

>> 2. "Gyroscope function" fadpt_gyro.f. This function 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:

>>

>>> a. input.gyro.3dtet. This deck generates and adapts a tetrahedral mesh to
the "gyroscope" function.&nbsp_place_holder;&nbsp_place_holder; A snapshot of
the adapted grid may be seen at [gyro.png](../../images/gyro.png).

b. input.gyro.3dhex. This deck generates and adapts a hexahedral mesh to the
"gyr/scope" function.&nbsp_place_holder;&nbsp_place_holder; A snapshot of the
adapted grid may be seen at [gyro.hex.png](../../images/gyro.hex.png).

>>

>> RELEVANT LaGriT VARIABLE FOR radapt

The **maxiter_sm** variable is provided to control the maximum number of
iterations used by **radapt** on a single call. By default, this variable is
set to 25, but this can be changed by the user. For example,

**assign **/ / /** maxiter_sm **/** **50   
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.