GridBuilder

GridBuilder is an efficient meshing tool for complex supermeshes including line and point features. GridBuilder is loosely based on an approach outlined by Sadek, 1980. The GridBuilder algorithm is fully included in FEFLOW.

The meshing is done polygon by polygon, starting with the polygon for which the finest mesh is expected based on the number of elements proposed and the number of border nodes.

 

	GridBuilder produces regular meshes with a smooth transition between areas with fine and coarse meshes.
	Can fail under certain conditions, especially if line features are present.

 

Briefly, the steps GridBuilder follows are:

1. Extend supermesh lines so that the domain is subdivided into a number of subregions which are defined by closed polygons.
2. Nodes, whose spacing satisfies user-specified criteria, are generated along the polygon edges.
3. Each subregion is filled with triangular elements.
4. An automatic mesh-relaxation scheme is applied to smooth the mesh.

Line features

Line features may be used with GridBuilder, but care must be exercised when considering the order in which they are defined and in how they are terminated. As described in step 1 above, GridBuilder will automatically extend any line as necessary. The figure below illustrates the various possibilities that can arise. In this figure, an existing supermesh polygon is defined with black lines and yellow nodes, and 3 lines are defined with red lines and black nodes. Potential line extensions are shown as dashed red lines.

 

Case 1: Only a single point at the end of this line lies inside a supermesh polygon. The line is truncated by creating a new point at the intersection of the boundary of the polygon and the line segment, indicated by the arrow drawn at point A.

Case 2: Two points at the end of a line lie inside a supermesh polygon. The line is extended until it intersects the boundary of the polygon, indicated by point B.

Problems or unexpected results related to line input could occur if, for example:

• A line is contained by a supermesh polygon and the extended lines at each end intersect each other. This will cause GridBuilder to fail. This is shown consider as Case 3, where the extensions intersect at point C, inside the polygon.

• A line extension unexpectedly cuts across a later defined line. Changing the order of line definition should alleviate this.

The easiest way to avoid these types of problems is to extend the line manually or avoid their use altogether, and define the mesh using polygons only.

Points

At each existing point, a node will be placed in the finite-element mesh.

Mesh smoothing problems

Problems can arise as a result of the automatic mesh-smoothing algorithm applied by GridBuilder. In cases where supermesh polygons or lines contain sharp kinks, the relaxation procedure can result in a corrupt mesh. This is usually indicated by a log message about negative areas.

One way to alleviate this problem is to define a new sub element boundary or line that eliminates the sharp kink, as shown here where the dashed red line is used to modify the existing boundary.

Gradation

GridBuilder recognizes individual supermesh polygon borders where the user requests more (i.e. smaller) elements. It will also handle cases in which polygon or line edge gradation result in a significant difference in element size between the boundary and the interior of a polygon, by grading the mesh automatically away from the boundary, as shown in the following figure.

 

Properties

Property	Description
Mesh Anisotropy	With an anisotropy factor of 1 (default), the x and y coordinates of the polygons, lines and points are handed over to the mesh generator as original values. Applying another factor, the y coordinates are scaled with this factor for the mesh generation. Thus, it is possible, to obtain a finer mesh vertically than horizontally or vice versa. It has to be kept in mind, however, that distorted elements may be generated by applying very small or very large factors.
Polygon Refinement	Refinement factor for supermesh polygon borders. A value of 1 corresponds to no refinement.
Edge Refine Mode	Switch for refining at ALL or SELECTED supermesh polygon border edges. Selection of edges can be done via the tool button on top of the Meshing panel.
Line Refinement	Refinement factor for supermesh lines. A value of 1 corresponds to no refinement.
Point Refinement	Refinement factor for supermesh points. A value of 1 corresponds to no refinement.