Invalid Elements Research Articles

Automatic p-version mesh generation for curved domains

To achieve the exponential rates of convergence possible with the p-version finite element method requires properly constructed meshes. In the case of piecewise smooth domains, these meshes are characterized by having large curved elements over smooth portions of the domain and geometrically graded curved elements to isolate the edge and vertex singularities that are of interest. This paper presents a procedure under development for the automatic generation of such meshes for general three-dimensional domains defined in solid modeling systems. Two key steps in the procedure are the determination of the singular model edges and vertices, and the creation of geometrically graded elements around those entities. The other key step is the use of general curved element mesh modification procedures to correct any invalid elements created by the curving of mesh entities on the model boundary, which is required to ensure a properly geometric approximation of the domain. Example meshes are included to demonstrate the features of the procedure.

Accounting for curved domains in mesh adaptation

AbstractThis paper presents a procedure to project vertices created by refining straight sided tetrahedra to appropriate locations on curved model boundaries. Although many of the vertices introduced by refinement of mesh edges and faces on the boundary of the model can easily be projected to the model geometry, there are situations where this projection creates invalid elements. To ensure the ability to place those vertices on the model boundary an efficient two‐step procedure has been developed. The first step applies local mesh modification operations such as collapse and swap to incrementally project vertices. It is shown that the effective application of mesh modifications that will yield a mesh in which the vertex in question can be projected to the boundary must focus on ensuring the vertex in question moves at least as far as the plane on which the mesh would have element shapes degrade to zero volume. The second step applies a generalized local cavity triangulation algorithm to ensure the success of the process when the set of local mesh modifications considered is unable to project the vertex to the boundary. Copyright © 2003 John Wiley & Sons, Ltd.

A Robust Method for Unstructured Volume/Surface Mesh Movement

In this paper, a simple and robust method of unstructured dynamic mesh with surface mesh movement method for unstructured triangle/tetrahedral meshes is proposed. The method is developed to avoid the generation of squashed invalid elements by considering each elemental shape. With several three-dimensional applications, it is demonstrated that the present method significantly improves robustness for problems concerning large body motion without much penalty in CPU time. The use of the present method for mesh movements on curved surfaces is also discussed. Its capability is demonstrated for the surface mesh movement in the tail-fuselage juncture region of an airplane.

Smoothing by optimisation for a quadrilateral mesh with invalid elements

In this paper, a smoothing algorithm is introduced which can be applied to a mesh with invalid elements. The first step of the method is to allow those invalid elements to be disconnected from the remaining mesh. This means that the nodes on the invalid elements are all split into two, one on the invalid element, the other on the remaining mesh. The invalid element can then be shaped to become valid. The distance between the two copies of the same node is called offset. In later iterative steps, the nodes will be moved into order to reduce the offset back to zero and at the same time improve the quality of the mesh.