DARSS: a hybrid mesh smoother for all hexahedral meshes

International Journal for Numerical Methods in Engineering, 2009

An octree-based mesh generation method is proposed to create reasonable-quality, geometry-adapted unstructured hexahedral meshes automatically from triangulated surface models without any sharp geometrical features. A new, easy-to-implement, easy-to-understand set of refinement templates is developed to perform local mesh refinement efficiently even for concave refinement domains without creating hanging nodes. A buffer layer is inserted on an octree core mesh to improve the mesh quality significantly. Laplacian-like smoothing, angle-based smoothing and local optimization-based untangling methods are used with certain restrictions to further improve the mesh quality. Several examples are shown to demonstrate the capability of our hexahedral mesh generation method for complex geometries.

1998

The 3D meshing process begins with the definition of the outer geometry. With a CAD system and a 2d quadrilateral mesh generator, a closed all-quadrilateral mesh is obtained, which is the start point for the process that this communication describes.

2017

This article introduces a method to generate a hex-dominant mesh from an input tet mesh. We first compute a global parameterization, then we isolate the ``void'' (also called ``gap'' or ``cavity''), that is the zone where the global parameterization is singular or too much distorted. Once properly isolated, the void can be meshed with different algorithms. Thus, our main technical contribution is an algorithm that computes the boundary of the void and makes it compatible with both the hexahedra generated in the regular part of the parameterization and the input boundary. We tested our method on a large collection of objects (200+) with different settings. In most cases, we obtained very good quality results compared to the state-of-the-art solutions. In addition to improving the state-of-the-art in hex-dominant meshing, a second contribution of this work is to introduce a pipeline architecture, which can be used to compare present and future algorithms involv...

Proceedings of the Eighth International Conference on Engineering Computational Technology

In this paper, we extend a simultaneous untangling and smoothing technique previously developed for triangular and tetrahedral meshes to quadrilateral and hexahedral ones. Specifically, we present a technique that iteratively untangles and smooths a given quadrilateral or hexahedral mesh by minimizing an objective function defined in terms of a modification of an algebraic quality measure. The proposed method optimizes the mesh quality by a local node relocation process. That is, without modifying the mesh connectivity. Finally, we present several examples to show that the proposed technique obtains valid meshes composed by high-quality quadrilaterals and hexahedra, even when we start from tangled meshes.

The Visual Computer, 2001

In a landmark paper, Catmull and Clark described a simple generalization of the subdivision rules for bi-cubic B-splines to arbitrary quadrilateral surface meshes. This smooth subdivision scheme has become a mainstay of surface modeling systems. Joy and MacCracken described a generalization of this surface scheme to volume meshes. Unfortunately, little is known about the smoothness and regularity of this scheme

ACM Transactions on Graphics, 2017

We introduce a robust and automatic algorithm to simplify the structure and reduce the singularities of a hexahedral mesh. Our algorithm interleaves simplification operations to collapse sheets and chords of the base complex of the input mesh with a geometric optimization, which improves the elements quality. All our operations are guaranteed not to introduce elements with negative Jacobians, ensuring that our algorithm always produces valid hex-meshes, and not to increase the Hausdorff distance from the original shape more than a user-defined threshold, ensuring a faithful approximation of the input geometry. Our algorithm can improve meshes produced with any existing hexahedral meshing algorithm --- we demonstrate its effectiveness by processing a dataset of 194 hex-meshes created with octree-based, polycube-based, and field-aligned methods.

Finite Elements in Analysis and Design, 2017

In this paper, we describe a robust meshing algorithm for obtaining a mixed mesh with large number of hexahedral/prismatic elements grown over the domain boundary respecting the user imposed anisotropic metric where physics matter the most and in areas where it is required to have the least number of elements. The inner section away from the boundaries is filled with the terminal octants of a non-conformal octree. The remaining unmeshed portion of the domain within the hexahedral/prismatic faces is filled with narrow bands of tetrahedra. The novel idea of the meshing algorithm is the formation of the cavity as slim as possible between the exposed faces of the outer most boundary layers and the octant faces of the inner most terminal octants, in such a way that the length scales of the cavity mesh spacings would allow the frontal tetrahedral meshing algorithm robustly succeeding to fill the cavity respecting its boundary faces without recovery issues. The algorithm could be applied to non-cubical, arbitrary geometries that can also be non-manifold. Each domain region is meshed recursively and within which, the tetrahedral filling algorithm constructs as many manifold cavity shells as the problem constrains are imposed by the boundary layers and the mesh size settings. The final hexahedral dominant mesh is exported to a face-based finite volume format (OpenFoam) so that the non-manifold nature of the mesh is captured by flux based numerical solvers consistently and accurately.

1997

Automatic mesh generation and adaptive refinement methods for complex three-dimensional domains have proven to be very successful tools for the efficient solution of complex applications problems. These methods can, however, produce poorly shaped elements that cause the numerical solution to be less accurate and more difficult to compute. Fortunately, the shape of the elements can be improved through several mechanisms, including face- and edge-swapping techniques, which change local connectivity, and optimization-based mesh smoothing methods, which adjust mesh point location. We consider several criteria for each of these two methods and compare the quality of several meshes obtained by using different combinations of swapping and smoothing. Computational experiments show that swapping is critical to the improvement of general mesh quality and that optimization-based smoothing is highly effective in eliminating very small and very large angles. High-quality meshes are obtained in a...

Proceedings of the 18th International Meshing Roundtable, 2009

We proposed a new, easy-to-implement, easy-to-understand set of refinement templates in our previous paper to create geometry-adapted all-hexahedral meshes easily [

Computers & Graphics, 2017

We introduce a simple and practical technique to untangle and improve hexahedral (hex-) meshes. We achieve that by enabling the deformation of the boundary surfaces during the untangling process, which provides more space to reach a valid solution. To improve the element quality, an angle optimization strategy is proposed, which has much simpler formulation than the existing method. The deformed volume after optimization is then pulled back to the original one using an inversion-free deformation. In contrast to the current methods, we perform the untangling and quality improvement within a few local regions surrounding elements with undesired quality, which can effectively improve the minimum scaled Jacobian (MSJ) quality of the mesh over the existing method. We demonstrate the effectiveness of our methods by applying it to the hex-meshes generated by a range of methods.