Platform: All Platforms Versions: All versions

## Problem Description

There is an option to Form Union or Form Assembly at the end of the Geometry sequence. What does this mean and when should I switch between them?

## Solution

The Geometry branch within the Model Builder consists of a sequence of Geometric operations. This can include sketches, geometric primitives, imported CAD files, Boolean operations, etc., that are used to describe the geometry that you want to model. At the end of this sequence, there is a Finalization step that can be set to either Form Union or Form Assembly. This choice has consequences in the CAD description, the physics settings, and the mesh used to discretize the geometry. This Knowledgebase describes the differences.

#### Form Union

This is the default geometry finalization method. It is equivalent to taking a Boolean union of all objects in the geometry sequence, thus creating a single geometry object composed of many different domains. Any overlapping geometry objects will become a single object composed of different domains for each enclosed volume. This is illustrated in the image below, where three blocks of different sizes overlap in space. The result of the Form Union operation is shown with the different resultant domains in different colors.

In the physics settings, each of these different domains can have different material properties. By default, continuity of the fields and the fluxes will be maintained across the interior boundaries and it is possible to add a variety of different discontinuity or jump conditions at interior boundaries for the various physics.

When meshing, the mesh will be conforming everywhere. Different element sizes can be applied in different regions, but the mesh will exactly match at the boundaries, as shown in the image below.

Having a mesh that is conforming is required for all of the three-dimensional Electromagnetic Waves interfaces as well as the three-dimensional Magnetic Fields interface; these interfaces require the elements to be conforming at all boundaries.

The physical implication of the Form Union step is that the domains in the model cannot slide or move relative to each other. This is an appropriate default assumption for most modeling within COMSOL Multiphysics, but it is not valid when using any of the following physics interfaces:

• Solid Mechanics, when Contact features are included
• Multibody Dynamics
• Rotating Machinery, Magnetic
• Rotating Machinery, Fluid Flow

When any of the above physics interfaces are being used, or when you want to have a non-conforming mesh between adjacent domains, the Geometry should be finalized with the Form Assembly setting.

#### Form Assembly

Form Assembly differs from Form Union in that it does not compute a Boolean union of the geometry objects. It assumes that all geometry objects are non-overlapping. Therefore, you cannot use the Form Assembly operation when there are any spatial overlaps between objects. The number of domains in the model will not change as a consequence of the Form Assembly.

The Form Assembly will only identify the touching, adjacent, boundaries of all objects and by default will form so-called Identity Pairs or Contact Pairs out of them. The default behavior is to create these Pairs automatically, although they can also be set up manually. Both types of Pairs can also be created with Imprints which will project the outline of the faces onto each other. This is shown in the exploded view of the assembly below, with the faces that compose the Pair highlighted.

By default, a single Pair will be created of all mating faces between two parts, even if they are non-adjacent. It is possible to override this behavior by choosing to Split disconnected pairs so that one pair is created for each mating surface pair, as shown above.

By default, there is no continuity of the fields or the fluxes across a boundary Pair. Continuity at Pair boundaries must be explicitly applied. Discontinuity or jump conditions can also be applied.

When using any of the Rotating Machinery interfaces, the option to Form Identity Pairs, without Imprints and without Splitting of Disconnected Pairs, is the appropriate choice.

The choice between creating an Identity and a Contact Pair is governed by the physics which you want to solve. Creating Contact Pairs should only be done when solving a Solid Mechanics problem with Contact features. This means that surfaces can come in and out of contact and can slide relative to each other, and that forces and fluxes will be transferred between the surfaces only when they are in mating contact.

It is also possible to choose to create no pairs at all, and this is appropriate when solving a Multibody Dynamics problem.

The Form Assembly functionality is also helpful if you want to have different meshes in adjacent domains, to understand the differences we first look at the different types of meshes that will be created.

#### Assembly Meshing

A comparison of the meshes created with Form Union, Form Assembly with Imprints, and Form Assembly without Imprints is shown below. The Form Union mesh is conforming across mating faces. That is, the mesh elements on either side of the boundaries share the same nodes and faces. With such a mesh, the continuity of the fields and fluxes is naturally satisfied via the finite element method.

The mesh created when using Form Assembly is non-conforming so the mesh on the two sides of the Pair will be different. The faces of the elements are not the same, nor will the node points be the same.

With the Imprints enabled the mesh is still non-conforming but the edges of the mating boundaries are respected. Although the nodes on either side of the Pair will not be shared, the meshes on either side will both have nodes along the mating edges. The resultant mesh will more accurately represent the mating faces.

When using non-conforming meshes the Pair Continuity condition can be added which will approximately enforce continuity of the fields and fluxes. However, a non-congruent mesh is less accurate than a congruent mesh and becomes increasingly less accurate as the relative element sizes across the Pair differ. Thus, the Form Union mesh will be the most accurate but will require the most memory to solve and the Form Assembly without Imprints will be the least accurate and will use relatively less memory to solve.

In addition to the specific areas already mentioned, it is recommended to investigate using non-conforming meshes for problems involving thermal and structural analyses. Such models can often consist of assemblies of parts that may have quite different feature sizes, and hence different element sizes. These cases are likely to show the greatest benefit, in terms of lesser memory usage while still giving good accuracy, when using the Assembly Meshing capabilities.

#### Video Gallery Resources

Form Union and Form Assembly Geometry Finalization Methods

Creating Contact Pairs for Structural Contact Modeling with Form Assembly

Using Form Assembly in Multibody Dynamics Models

Using Form Assembly in Rotating Machinery Models