5.2 Size Functions

5.2.1 Overview

Size functions allow you to control the size of mesh intervals for edges and mesh elements for faces or volumes. Size functions are similar to boundary layers in that they control the mesh characteristics in the proximity of the entities to which they are attached. They differ from boundary layers with respect to the manner in which they are defined and the manner in which they control the mesh. Whereas boundary layers prescribe specific mesh patterns and the sizes of mesh elements within those patterns, size functions control the following properties:

• Maximum mesh-element edge lengths (fixed-type size function)
• Angles between normals for adjacent mesh elements (curvature-type size function)
• Number of mesh elements employed in the gaps between two geometric entities (proximity-type size function)
The following sections describe the GAMBIT commands used to create, modify, summarize, and delete size functions.

5.2.2 Size Function Commands

The Tools/Size-Function subpad includes the following commands.

 Symbol Command(s) Description Create Size Function Creates and attaches a size function Modify Size Function Modifies an existing size function View Size Function Displays an existing size function in the graphics window Summarize Size Functions Displays summary information for an existing size function Delete Size Functions Deletes an existing size function

The following sections describe the commands listed above.

Create Size Function

The Create Size Function operation (sfunction create command) creates a size function and attaches it to a specified entity. Size functions allow you to control the size of the mesh in regions surrounding a specified entity. Specifically, they can be used to limit the mesh-interval size on any edge or the mesh-element size on any face or volume.

As an example of the effect of size functions on simple volume meshes, consider the meshed cube shown in Figure 5-3.

Figure 5-3: Example size function attached to a cube corner vertex

In this example, a size function has been attached to the volume and defined with respect to one of the eight corner vertices (the source vertex) on the cube. When the volume is meshed using tetrahedral elements, the size function restricts the size of the element edges in proximity to the source vertex. As a result, the tetrahedral elements in the region surrounding the source vertex are small in comparison to those used to mesh the volume as a whole, and the mesh-element edge length increases with distance from the source vertex.

 NOTE (1): To apply a size function when meshing a model, GAMBIT first divides the bounding box into a set of hexahedral subsections and computes the size-function values at the corners of each subsection. To determine the size of any mesh element that exists within a given subsection, GAMBIT interpolates between the values assigned to the subsection corners. The total number of background-grid subsections affects the speed and accuracy of any size-function application. If the background grid contains only a few subsections, computational time is minimized, but the computed mesh-element sizes might only crudely approximate the intended effects of the size function. Conversely, if the number of subsections is very large, the interpolated mesh-element sizes might accurately reflect the intended effects of the size function, but computational time might be prohibitive. You can control the level to which GAMBIT divides the background grid by means of the TOOLS.SFUNCTION.BGRID_NONLINEAR_ERR_PERCENT default variable. This default variable specifies the maximum allowable percentage difference between the exact and interpolated size-function values computed at the center of any subsection. If the difference exceeds the specified value for any subsection, GAMBIT further divides the subsection into a set of smaller subsections. By applying this method iteratively, GAMBIT subdivides the background grid until the percentage difference for all subsections is less than the specified maximum value. NOTE (2): You can generate the background grid for a size function without performing a meshing operation by means of the sfunction bgrid command (see Section 5.2.2 in the GAMBIT Command Refer­ence Guide). For example, the command ```sfunction bgrid attachvolumes "volume.2" ``` generates a background grid for a volume labeled volume.2. When you execute the sfunction bgrid command, GAMBIT searches for all upper- and lower-topology entities associated with the entity specified in the command and generates a background grid for any of the upper- or lower-topology entities that are affected by an existing size function. When you mesh an entity the mesh of which is affected by a size function without first executing the sfunction bgrid command, GAMBIT automat­ically executes the command before meshing the entity. As a result, GAMBIT executes and journals two commands in the process of meshing the entity. The two commands are not "grouped" together and, therefore, must be undone separately to reverse the total meshing/size-function operation.

Size-Function Specifications

To create a size function, you must define the following specifications:

• Type
• Entities
• Parameters
The type specification determines the algorithm used by the size function to control the mesh-element edge size. The entities specification determines which geometric entities are used as the source and attachment entities for the size function. The size function parameters define the exact characteristics of the size function. (NOTE: The entities and parameters required to specify a size function differ according to size-function type.)

Specifying the Size-Function Type

GAMBIT provides the following types of size functions:

• Fixed—specifies specifies the maximum mesh element edge length as a function of distance from a given source entity and uses a constant start size
• Meshed—specifies the maximum mesh element edge length as a function of distance from a given source entity and uses a non-constant start size
• Curvature—specifies the maximum angle between normals for adjacent mesh elements
• Proximity—specifies the number of mesh-element cells to be located in gaps between surfaces in a volume
The following sections describe the effects of each of these size-function types and outline the parameters required for their specification.

Fixed Size Functions

Fixed size functions limit the length of mesh-element edges within a region specified by the distance from an existing entity. To define a fixed size function, you must specify two types of entities:

• Source
• Attachment
The source entity defines the center of the region in which the size function applies. The attachment entity is the entity for which the mesh is to be affected by the size function. Each individual fixed size function is associated with only one source entity but may be associated with one or more attachment entities.

As an example of the difference between source and attachment entities for a fixed size function, consider the configuration shown in Figure 5-3, above. In this example, one corner vertex on the cube is specified as the source entity, and the cube itself is specified as the attachment entity.

Specifying the Source Entity

For fixed size functions, source entity locations and types determine the locations and shapes of the size functions. For example, a fixed size function defined with a vertex as the source entity is centered at the source vertex location and shaped as a sphere. Similarly, a fixed size function defined with a straight edge as the source entity is centered on the edge and is shaped like a cylindrical capsule with rounded ends. GAMBIT allows you to specify vertices, edges, faces, or volumes as source entities.

For the purposes of describing the effect of source-entity type on fixed size functions, source entities can be grouped into two general categories:

• Component source entities
• Non-component source entities
Component source entities constitute components of the entity to be meshed-such as lower-topology vertices, edges, and faces on a given attachment volume. Non-component source entities exist apart from the entity to be meshed-such as vertices, edges, faces, and/or volumes that are located near to the attachment entity but which are not part of its lower topology.

 NOTE: GAMBIT does not distinguish between component and non-component source entities when creating and attaching fixed size functions—that is, identical rules of construction, attachment, and effect apply to both types of source entities. The distinction between component and non-component source entities is employed here as a useful tool for describing the effects of fixed size functions on various meshing scenarios.

Component Source Entities

As noted above, component source entities constitute components of the entities to which their size functions are attached. For example, the vertex that serves as the source entity for the fixed size function shown in Figure 5-3, above, is a component source entity, because it constitutes the corner vertex of the cubic volume to which the size function is attached.

The following paragraphs describe the effects of fixed size functions that employ vertex, edge, and face component source entities on meshes of the cubic volume shown in Figure 5-3. In each case, the cubic volume itself serves as the attachment entity.

 NOTE: Although it is possible to specify a single entity as both the source entity and attachment entity for a given fixed size function, doing so is of little practical use, because the size function does not affect its source entity. For example, if you select the volume shown in Figure 5-3 as both the source entity and attachment entity and mesh the volume with tetrahedral elements, GAMBIT meshes the interior of the volume with elements of an approximately uniform size.

Vertex Component Source Entities

Figure 5-4 shows the effect of a fixed size function defined using a corner vertex of the cube as the source entity. (NOTE: The surface mesh shown in Figure 5-4 is identical to that shown in Figure 5-3, above.) For illustrative purposes, Figure 5-4 includes a cutaway sphere representing the outer boundary of the size-function region. In this case, the fixed size function is centered at the source vertex and is shaped as a sphere. Because the source vertex is a corner vertex of the cube, only one octant of the size function affects the mesh within the cube.

Figure 5-4: Meshed cube—fixed size function with vertex source entity

Edge Component Source Entities

Figure 5-5 shows the effect of a fixed size function defined using one edge of the cube as the source entity. For illustrative purposes, Figure 5-5 includes a cutaway cylindrical capsule representing the outer boundary of the size-function region. The size function is centered along the source edge and is shaped as a cylindrical capsule with rounded ends. In this case, however, neither of the rounded ends intersects the meshable region of the attachment entity, therefore only one quadrant of the cylindrical portion of the capsule affects the volume mesh.

Figure 5-5: Meshed cube—fixed size function with edge source entity

Face Component Source Entities

Figure 5-6 shows the effect of a fixed size function defined using one face of the cube as the source entity. For illustrative purposes, Figure 5-6 includes a cutaway volume that represents the outer boundary of the size-function region. The size function is centered on the face and is shaped as a square wafer with rounded ends.

Because the source entity is only one face of the cube, the rounded edges and corners of the wafer-shaped region do not affect the volume mesh at all. Consequently, the fixed size function acts similarly to a boundary layer in that the mesh-element size increases at a fixed rate in the direction normal to the source face.

Figure 5-6: Meshed cube—fixed size function with face source entity

Non-Component Source Entities

As noted above, GAMBIT does not require that source entities constitute components of their corresponding attachment entities. For example, it is possible to create a fixed size function that employs one bounding edge of a given volume as the source entity and a separate (nearby) volume as the attachment entity. It is also possible to create and employ an edge the explicit purpose of which is to serve as a source entity and to locate the edge either inside or outside its corresponding attachment entities.

As an example of a non-component source entity, consider the configuration shown in Figure 5-7. The configuration consists of a cubic volume and a separate vertex located outside the volume. If you employ the non-component vertex as the source entity for a size function attached to the volume, then mesh the volume using tetrahedral elements, GAMBIT creates a mesh such as that shown in the figure. (NOTE: For illustrative purposes, Figure 5-7 includes a cutaway sphere that represents the outer boundary of the size function.) In this case, only the outer portion of one octant of the size function affects the mesh on the attachment entity. Consequently, the effect of the size function on the mesh is less pronounced than that shown in Figure 5-4, above.

Figure 5-7: Meshed cube with fixed size function—non-component source entity

As a second example of the effect of a non-component source entity, consider the configuration shown in Figure 5-8. In this case, the non-component source vertex is located within a cubic volume to which the fixed size function is attached.

Figure 5-8: Internal, non-component source entity

If you define a fixed size function using the same parameters employed for the examples shown above and mesh the volume using tetrahedral elements, GAMBIT creates a mesh such as that shown in Figure 5-9. (NOTE: Figure 5-9 shows an internal plane cut of 3-D tetrahedral elements, rather than the surface mesh shown in the figures above, and includes a cutaway representation of the outer boundary of the size function.)

Figure 5-9: Meshed volume—internal, non-component source entity

In this case, the mesh elements are small in immediate proximity to the source vertex and increase in size to the size-function boundary. As noted above, the mesh-element sizes outside the boundary are determined by parameters input on the Mesh Volumes form.

Specifying the Attachment Entity

Fixed size functions can be attached to any edge, face, or volume entity, including any edge or face that constitutes a component of a higher-topology entity. All of the examples described above involve fixed size functions for which the attachment entity constitutes the entity to be meshed—that is, the cubic volume. It is possible, however, to attach a fixed size function to one or more edges or faces of the volume, rather than to the volume itself, and to thereby influence the volume mesh characteristics indirectly.

As an example of the effect of attaching a fixed size function to a component of a higher-topology entity, consider the mesh configuration shown in Figure 5-10. This example involves a fixed size function in which a corner vertex is specified as the source entity and an adjacent edge is specified as the attachment entity. The parameters for the size function are identical to those used in the examples described above.

Figure 5-10: Meshed cubic volume—fixed size function attached to an edge

Because the size function is attached to one edge of the cube, rather than to the entire cubic volume, it directly influences the mesh-element edge length only on the edge to which it is attached. Consequently, the meshes on the faces that share the attachment edge as a boundary are strongly influenced by the size function, but the mesh on the face with which those faces share a common vertex (the source vertex) is largely unaffected.

As a second example of the effect of attaching a fixed size function to a component of a higher-topology entity, consider the mesh configuration shown in Figure 5-11, in which a corner vertex again serves as the source entity but the fixed size function is attached to an adjacent face. In this case, the size function directly influences the mesh-element sizes on the attachment face and strongly influences the meshes on the two faces that share a corner vertex (the source vertex) with the attachment face.

Figure 5-11: Meshed cubic volume—fixed size function attached to a face

Specifying the Parameters

To define and create a fixed size function, you must specify the following parameters:

• Start size
• Growth rate
• Max. size
The Start size is the mesh-element edge length in the region immediately adjacent to the source entity. The Growth rate represents the increase in mesh-element edge length with each succeeding layer of elements. For example, a growth rate of 1.2 results in a 20% increase in mesh-element edge length with each succeeding layer of elements. The Max. size specification represents the maximum allowable mesh-element edge length for the attachment entity either inside or outside the outer boundary of the size function.

Meshed Size Functions

Meshed size functions are similar to fixed size functions with regard to their growth and size-limit parameters and their effect on the meshes of attachment entities. They differ from fixed size functions in that their start sizes can vary with location on the source entity (edge or face). Specifically, the size-function start size for a meshed size function varies according to the size(s) of existing mesh elements on the source entity. (NOTE:The source entity (or entities) must be meshed prior to meshing the attachment entity (or entities).)

As an example of the difference between fixed size functions and meshed size functions, consider the cubic volume shown in Figure 5-12(a), one edge of which is meshed using a double-sided grading scheme with the mesh nodes bunched toward the center of the edge.

Figure 5-12: Cubic volume with meshed edge—mesh without size function

If you mesh the volume (using a tetrahedral meshing scheme) without applying a size function and specify a mesh-interval length one fifth of the length of the cube edges, GAMBIT creates the mesh shown in Figure 5-12(b). In this case, the growth of the tetrahedral elements away from the pre-meshed edge does not follow a regular, defined pattern.

Figure 5-13 shows the effects of fixed and meshed size functions on the meshing of the cube shown in Figure 5-12(a). In both cases, the pre-meshed edge and cubic volume are specified as the source and attachment entities, respectively.

Figure 5-13: Effects of fixed and meshed size functions

For the fixed size function (Figure 5-13(a)), the start size is constant along the length of the source edge, which results in first-row mesh-element layers of approximately constant height all along the edge and a uniform increase in mesh-element size away from the edge. For the meshed size function (Figure 5-13(b)), the start size is larger at the ends of the edge than it is near the center. As a result, GAMBIT the first-row mesh elements are larger near the ends of the edge than near the center, which in turn affects the growth of the mesh-element pattern (and the total number of elements created).

Specifying the Source and Attachment Entities

To define a meshed size function, you must specify two types of entities:

• Source edge(s) or face(s)
• Attachment entity (or entities)
The source specification identifies the pre-meshed entities that define the start sizes for the size function. The attachment entities are the entities the meshes of which are to be affected by the size function. For example, in the example described above, the volume is specified as the attachment entity. GAMBIT allows you to specify edges, faces, or volumes as attachment entities.

Specifying the Parameters

To define a meshed size function, you must specify the following para­meters:

• Growth rate
• Max. size
The Growth rate represents the increase in mesh-element edge length with each succeeding layer of elements emanating from the source entity. The Max. size spec­ification represents the maximum allowable mesh-element edge length for the attachment entity.

Curvature Size Functions

Curvature size functions limit the allowable angle between outward-pointing normals for any two adjacent mesh elements located immediately adjacent to the surface of a source entity. They are particularly useful for geometric configurations that include highly curved surfaces and volume regions which tetrahedral elements of a reasonable size may not fit.

As an example of the effect of a curvature size function, consider the configuration shown in Figure 5-14. The configuration consists of a thin elliptical cylinder meshed with tetrahedral elements of a uniform size. Because the cylinder narrows in its two blade-edge regions, GAMBIT is unable to fully mesh the geometry using mesh elements of the specified size. Consequently, the resulting mesh represents only a crude approximation of the cylinder shape.

Figure 5-14: Meshed elliptical cylinder—without curvature size function

To better approximate the shape of the elliptical cylinder shown in Figure 5-14, it is possible to reduce the specified, uniform mesh-element size such that GAMBIT is able to create elements in the narrow, blade-edge regions. Reducing the mesh-element size, however, can significantly increase the total number of mesh elements required to mesh the geometry and can result in unnecessary mesh refinement in the thick, center region of the cylinder.

As an alternative to reducing the overall mesh-element size, it is possible to refine the mesh by creating and attaching a curvature size function to the cylinder. Figure 5-15 shows the effect of such a size function for which the curved face of the cylinder is specified as the source entity, and the cylinder itself is specified as the attachment entity.

Figure 5-15: Meshed elliptical cylinder—including curvature size function

The curvature size function illustrated in Figure 5-15 limits the allowable angle between outward-pointing normals for the faces of any two adjacent mesh elements located immediately adjacent to the highly curved surface. To satisfy the restriction of the size function, GAMBIT necessarily reduces the sizes of elements used in the narrow, blade-edge regions of the cylinder (see Figure 5-16). In the broad, center region of the cylinder, however, the curvature size-function requirement is satisfied by larger elements. As a result, the mesh demonstrates a natural grading in mesh-element size from the narrow regions to the broad region, and the final mesh approximates the cylinder geometry.

Figure 5-16: Elliptical cylinder with curvature size function—mesh plane cut

Specifying the Source and Attachment Entities

To define a curvature size function, you must specify two types of entities:

• Source
• Attachment
The source entity specifies the edge or face adjacent to which the size function applies. The attachment entity is the edge, face, or volume for which the mesh is to be affected by the size function. For example, in the meshed elliptical cylinder shown in Figure 5-15, the curved face of the cylinder is the source entity, and the cylindrical volume itself is the attachment entity.

Specifying the Parameters

To define and create a curvature size function, you must specify the following parameters:

• Angle
• Growth rate
• Max. size
• Min. size
The Angle is the maximum allowable angle between outward-pointing normals for any two adjacent mesh elements located immediately adjacent to the surface of a source entity. The Growth rate represents the increase in mesh-element edge length with each succeeding layer of elements from the attachment edge or face. For example, a growth rate of 1.2 results in a 20% increase in mesh-element edge length with each succeeding layer of elements. The Max. size and Min. size specification represent, respectively, the maximum and minimum allowable mesh-element edge length for the attachment entity either inside or outside the size function boundary.

Proximity Size Functions

Proximity size functions allow you to specify the minimum number of mesh-element layers created in regions that constitute "gaps" in the model. For the purposes of specifying a proximity size function, a "gap" is defined in one of two ways:

• The internal volumetric region between two specified faces
• The area between two opposing boundary edges of a specified face
As an example of the effect of proximity size functions, consider the geomet­ric configuration shown in Figure 5-17(a). The configuration consists of a square block base on top of which stands a narrow, rectangular fin. The length, width, and height of the base are 10, 10, and 7.5 units, respectively. The length, width, and height of the fin are 10, 1, and 2.5 units, respectively.

Figure 5-17: Block and fin—mesh without proximity size function

If you mesh the volume shown in Figure 5-17(a) using a tetrahedral meshing scheme with an interval size of 2 and do not employ a size function, GAMBIT creates the mesh shown in Figure 5-17(b). In this case, GAMBIT creates only one layer of mesh elements in the fin region. As a result, subsequent numerical computations based on the mesh cannot provide detailed inform­ation for locations within the fin. It is possible to refine the mesh in the fin region by reducing the specified global mesh element size for the volume, but doing so can substantially increase the total number of elements in the entire configuration.

You can refine the mesh in the fin region for this example by applying a proximity size function defined by two opposing faces of the fin (see Figure 5-18(a)). For example, if you specify a proximity size function with the fol­lowing parameters:

• Cells/gap = 3
• Growth rate = 1.2
• Maximum size = 2
• Minimum size = 0.01
then attach the size function to the volume and mesh the volume using the tetrahedral meshing scheme described above, GAMBIT creates the mesh shown in Figure 5-18(b).

Figure 5-18: Block and fin—mesh with proximity size function

In this case, GAMBIT meshes the fin region such that it contains at least three layers of mesh elements between the faces used to define the size function. Outside the fin region (in the square block base) the mesh element sizes increase according to the growth-rate and size-limit specifications for the size function.

When employing a proximity size function, GAMBIT determines the maxi­mum element size in the gap region based on two criteria:

• The distances between any specified "source" faces (such as the two faces used to define the size function applied to the fin, above)
• The distances between the opposing boundary edges on the specified "source" faces
GAMBIT uses the smaller of the two computed element sizes to control the maximum element size in the gap region. (NOTE: If you specify only one source face, GAMBIT uses only the distances between opposing boundary edges on the specified face to determine the maximum element size in the gap region.)

As an example of the effect of specifying a single source face for a proximity size function, consider the geometry shown in Figure 5-19(a). The geometry consists of a cube that measures 10 units on a side into which is cut a rectangular slot. The length, width, and height of the slot are 10, 1, and 2.5 units, respectively.

Figure 5-19: Slotted cube—mesh without proximity size function

If you mesh the volume shown in Figure 5-19(a) using a tetrahedral meshing scheme with an interval size of 2 and do not employ a size function, GAMBIT creates the mesh shown in Figure 5-19(b). In this case, GAMBIT creates only one layer of mesh elements on the thin, rectangular face at the bottom of the slot. As a result, subsequent numerical computations based on the mesh cannot provide detailed inform­ation for the region surrounding the slot-bottom face. Again, it is possible to refine the mesh in the slot-bottom region by reducing the specified global mesh element size for the volume, but doing so can substantially increase the total number of elements in the entire configuration.

If you create a proximity size function using the parameters described above and specify the slot-bottom face (see Figure 5-20(a)) as the sole source face then attach the size function to the volume and mesh the volume using the tetrahedral meshing scheme with an interval size of 2, GAMBIT creates the mesh shown in Figure 5-20(b).

Figure 5-20: Slotted cube—mesh with proximity size function

In this case, GAMBIT refines the mesh in the slot-bottom region such that the slot-bottom face contains a minimum of three mesh-element layers between its long, opposing boundary edges.

Specifying the Source and Attachment Entities

To define a proximity size function, you must specify two types of entities:

• Source face(s)
• Attachment entity (or entities)
The source specification identifies the face(s) that define the model gap(s) to which the size function applies. If you specify two or more faces, GAMBIT computes the distance between each pair of opposing faces when determining the maximum element size. As noted above, if you specify only one source face, GAMBIT uses only the distances between opposing boundary edges on the specified face to determine the maximum element size in the gap region.

 NOTE: The Create Size Function form allows you to specify either faces or volumes as source entities. If you specify a volume as a source entity, GAMBIT includes all of the faces associated with the volume as source faces. Consequently, GAMBIT computes the distances between all faces in the volume when applying the proximity size function. For volumes that include many faces, such source-face specification can result in long computation times during meshing.

The attachment entity is the entity the mesh of which is to be affected by the size function. For example, in both examples described above, the volume is specified as the attachment entity. GAMBIT allows you to specify edges, faces, or volumes as attachment entities.

Specifying the Parameters

To define a proximity size function, you must specify the following para­meters:

• Cells/gap
• Growth rate
• Max. size
• Min. size
The Cells/gap specification determines the number of layers of mesh elements to be located in the gaps as defined by the source faces. The Growth rate represents the increase in mesh-element edge length with each succeeding layer of elements outside the gap region. The Max. size and Min. size spec­ifications represent, respectively, the maximum and minimum allowable mesh-element edge length for the attachment entity either inside or outside the size-function gap regions.

Using the Create Size Function Form

To open the Create Size Function form (see below), click the Create Size Function command button on the Tools/Size-Function subpad.

The Create Size Function form includes the following specifications.

 Type: Fixed Meshed Curvature Proximity specifies the type of size function to be created. Entities: Source: Volumes Faces Edges Vertices specifies the type of entity that serves as the source of the size function. (NOTE: The size function type determines which entity types are included in the Source option list.) Volumes Faces Edges Vertices specifies the entity to that serves as the basis for the size function. Attachment: Volume Face Edge specifies the type of entity to which the size function is attached. (NOTE: The size function type determines which entity types are included in the Attachment option list.) Volume Face Edge specifies the entity to which the size function is attached.

Aside from the Type and Entities specifications described above, the only specification on the Create Size Function form that is common to all size-function types is the Label specification located at the bottom of the form, which is as follows:

 Label specifies a label for the size function.

The Parameters section of the Create Size Function form varies according to the Type of size function to be created. The following subsections describe the Parameters options and specifications for each of the three Type options listed above. (NOTE: For a description of size-types and their associated parameters, see "Specifying the Size-Function Type," above.)

Fixed Size-Function Parameters

When you select the Type:Fixed option on the Create Size Function specification form, the Parameters section of the form appears as shown above. The options included in the Type:Fixed Parameters section are as follows.

 Start size specifies the desired edge length for all mesh elements immediately adjacent to the Attachment entity. Growth rate specifies the growth rate for the size function. (NOTE: The growth rate must be greater than unity (1).) Max. size specifies a maximum size for a mesh-element edge inside and outside of the size-function outer boundary.

Meshed Size-Function Parameters

When you select the Type:Meshed option on the Create Size Function specification form, the Parameters section of the form appears as shown below.

The options included in the Type:Meshed Parameters section are as follows.

 Growth rate specifies the growth rate for the size function. (NOTE: The growth rate must be greater than unity (1).) Max. size specifies a maximum size for a mesh-element edge on the attachment entity.

Curvature Size-Function Parameters

When you select the Type:Curvature option on the Create Size Function specification form, the Parameters section of the form appears as shown below.

The options included in the Type:Curvature Parameters section are as follows.

 Angle specifies the maximum allowable angle between outward-pointing normals for the faces of any two adjacent mesh elements located immediately adjacent to the source entity surface. Growth rate specifies the growth rate for the size function. (NOTE: The growth rate must be greater than unity (1).) Max. size specifies a maximum size for a mesh-element edge inside and outside of the size-function outer boundary. Min. size specifies a minimum size for a mesh-element edge inside and outside of the size-function outer boundary.

Proximity Size-Function Parameters

When you select the Type:Proximity option on the Create Size Function specification form, the Parameters section of the form appears as shown below.

The options included in the Type:Proximity Parameters section are as follows.

 Cells/gap specifies the number of layers of mesh elements to be located in gaps between the source and attachment volumes. Growth rate specifies the growth rate for the size function. (NOTE: The growth rate must be greater than unity (1).) Max. size specifies a maximum size for a mesh element edge inside the radius of the size function. Min. size specifies a minimum size for a mesh element edge inside the radius of the size function.

Modify Size Function

The Modify Size Function operation (sfunction modify command) changes the characteristics of an existing size function.

Using the Modify Size Function Form

To open the Modify Size Function form (see below), click the Modify Size Function command button on the Tools/Size-Function subpad.

The Modify Size Function form is similar to the Create Size Function form (see "Using the Create Size Function Form" ) with the following exceptions.

• It includes an S.Function pick list that allows you to select the size function to be modified.
• It includes a non-editable field that displays the Type of the selected size function.
 NOTE: You cannot modify the size-function Type by means of the Modify Size Function form. To change the size-function Type, delete the existing size function and create a new size functions according to the new specifications.

View Size Function

The View Size Function operation (no corresponding command-line command) displays the shape and location of a size function. The display appears in the GAMBIT graphics windows as an isosurface the shape of which reflects the region(s) of influence for the size functions. GAMBIT allows you to customize the display (Color filled) and/or Crosshatch and to specify the value represented by the isosurface.

 NOTE (1): To display a size function by means of the View Size Function form, you must first specify the size function (S. Function) and initialize the display parameters by means of the Initialize pushbutton. NOTE (2): The shapes and locations of size-function displays vary according to size-function type. For example, a Fixed size function appears as a regularly shaped surface centered at the size-function source entity. By contrast, Curvature size functions appear as centered at the regions most affected by the size function and may manifest as multiple surfaces for a single size function.

Using the View Size Function Form

To open the View Size Function form (see below), click the View Size Function command button on the Tools/Size-Function subpad.

The Modify Size Function form includes the following specifications.
 S. Function specifies the size function to be displayed. Initialize computes the parameters necessary to display the size function. Isosurface display mode: specifies the characteristics of the display. Color filled colors and shades the surface of the displayed size-function region. Crosshatch: includes check boxes that specify whether the size-function display includes cross-hatch marks in the x, y, and z directions. Iso value: specifies the value represented by the size of the displayed size-function surface.

Summarize Size Functions

The Summarize Size Functions operation (sfunction summarize command) displays size-function summary information in the Transcript window.

Using the Summarize Size Functions Form

To open the Summarize Size Functions form (see below), click the Summarize command button on the Tools/Size Function subpad.

The Summarize Size Functions form contains the following specification.

 S.F.s specifies the size function(s) for which summary information is to be displayed. All Pick All specifies all existing size functions. Pick specifies size functions selected by means of the S.F.s list box.

Delete Size Functions

The Delete Size Functions operation (sfunction delete command) deletes one or more existing size functions.

Using the Delete Size Functions Form

To open the Delete Size Functions form (see below), click the Delete command button on the Tools/Size Function subpad.

The Delete Size Functions form includes the following specification.

 S.F.s specifies the size function(s) to be deleted.