3D mesh refinement procedure using the bisection and rivara algorithms with mesh quality assessment

Mesh refinement procedures for the solution of three dimensional problems are described. The computational\ud domain is represented by an assembly of tetrahedral elements and the mesh refinement is acheived by the bisection\ud and Rivara methods using an explicit mesh density function coupled with an automatic 3D mesh generator.\ud A couple of benchmark examples is used to compare the performance of both refinement methods in terms of mesh\ud and size qualities, number of generated elements and CPU time consume

Geometrical and topological issues in octree based automatic meshing

Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is discussed. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary representation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractor. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed

Adaptive Resolution for Topology Modifications in Physically-based Animation

This paper shows the interest of basing a mechanical mesh upon an efficient topological model in order to give any simulation the ability to refine this mesh locally and apply topological modifications such as cutting, tear and matter destruction.Refinement and modifications can indeed be combined in order to get a more precise result.The powerful combinatorial map model provides the mathematical background which ensures that the quasi-manifold property is guaranteed for the mesh after any topological modification.The obtained results offer the versatility and time efficiency that are expected in applications such as surgical simulation

Algorithms and data structures for adaptive multigrid elliptic solvers

Adaptive refinement and the complicated data structures required to support it are discussed. These data structures must be carefully tuned, especially in three dimensions where the time and storage requirements of algorithms are crucial. Another major issue is grid generation. The options available seem to be curvilinear fitted grids, constructed on iterative graphics systems, and unfitted Cartesian grids, which can be constructed automatically. On several grounds, including storage requirements, the second option seems preferrable for the well behaved scalar elliptic problems considered here. A variety of techniques for treatment of boundary conditions on such grids are reviewed. A new approach, which may overcome some of the difficulties encountered with previous approaches, is also presented

Finite Element Analysis for Linear Elastic Solids Based on Subdivision Schemes

Finite element methods are used in various areas ranging from mechanical engineering to computer graphics and bio-medical applications. In engineering, a critical point is the gap between CAD and CAE. This gap results from different representations used for geometric design and physical simulation. We present two different approaches for using subdivision solids as the only representation for modeling, simulation and visualization. This has the advantage that no data must be converted between the CAD and CAE phases. The first approach is based on an adaptive and feature-preserving tetrahedral subdivision scheme. The second approach is based on Catmull-Clark subdivision solids

Three-dimensional unstructured grid generation via incremental insertion and local optimization

Algorithms for the generation of 3D unstructured surface and volume grids are discussed. These algorithms are based on incremental insertion and local optimization. The present algorithms are very general and permit local grid optimization based on various measures of grid quality. This is very important; unlike the 2D Delaunay triangulation, the 3D Delaunay triangulation appears not to have a lexicographic characterization of angularity. (The Delaunay triangulation is known to minimize that maximum containment sphere, but unfortunately this is not true lexicographically). Consequently, Delaunay triangulations in three-space can result in poorly shaped tetrahedral elements. Using the present algorithms, 3D meshes can be constructed which optimize a certain angle measure, albeit locally. We also discuss the combinatorial aspects of the algorithm as well as implementational details

Steiner-point free edge cutting of tetrahedral meshes with applications in fracture

Realistic 3D finite strain analysis and crack propagation with tetrahedral meshes require mesh refinement/ division. In this work, we use edges to drive the division process. Mesh refinement and mesh cutting are edge- based. This approach circumvents the variable mapping procedure adopted with classical mesh adaptation algorithms. The present algorithm makes use of specific problem data (either level sets, damage variables or edge deformation) to perform the division. It is shown that global node numbers can be used to avoid the Schönhardt prisms. We therefore introduce a nodal numbering that maximizes the trapezoid quality created by each mid-edge node. As a by-product, the requirement of determination of the crack path using a crack path criterion is not required. To assess the robustness and accuracy of this algorithm, we propose 4 benchmarks. In the knee-lever example, crack slanting occurs as part of the solution. The corresponding Fortran 2003 source code is provided