The generation of hexahedral meshes for assembly geometry: survey and progress

Tautges, Timothy J.

doi:10.1002/nme.139

Cited by 75 publications

(28 citation statements)

References 37 publications

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“…Although all-hexahedral mesh generation for a general geometry is still a di cult task compared with other elements such as tetrahedral, pyramid, etc., there are several reasons for using all-hexahedral elements [11]. First, hexahedral meshes perform quite well when local mesh is strongly anisotropic such as boundary layers.…”

Section: Sahinmentioning

confidence: 99%

A preconditioned semi‐staggered dilation‐free finite volume method for the incompressible Navier–Stokes equations on all‐hexahedral elements

Şahin

2005

Numerical Methods in Fluids

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SUMMARYA new semi-staggered ÿnite volume method is presented for the solution of the incompressible NavierStokes equations on all-quadrilateral (2D)=hexahedral (3D) meshes. The velocity components are deÿned at element node points while the pressure term is deÿned at element centroids. The continuity equation is satisÿed exactly within each elements. The checkerboard pressure oscillations are prevented using a special ÿltering matrix as a preconditioner for the saddle-point problem resulting from second-order discretization of the incompressible Navier-Stokes equations. The preconditioned saddle-point problem is solved using block preconditioners with GMRES solver. In order to achieve higher performance FORTRAN source code is based on highly e cient PETSc and HYPRE libraries. As test cases the 2D=3D lid-driven cavity ow problem and the 3D ow past array of circular cylinders are solved in order to verify the accuracy of the proposed method.

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Section: Sahinmentioning

confidence: 99%

A preconditioned semi‐staggered dilation‐free finite volume method for the incompressible Navier–Stokes equations on all‐hexahedral elements

Şahin

2005

Numerical Methods in Fluids

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“…Poor quality mesh creates numerical instability (i.e., increase in the computational cost, lack of convergence, and the inaccuracy of the results). Different researchers have worked on hexahedral meshing and have emphasized on quality meshing for greater numerical stability (e.g., [26][27][28][29]). The successful application of the SEM includes the effective mesh operation, which includes descretization and mapping.…”

Section: Spectral Element Discretizationmentioning

confidence: 99%

High-Order FEM Formulation for 3-D Slope Instability

Chandra¹,

Prakash²,

Yatabe³

2013

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High-order finite element method (FEM) formulation also referred to as spectral element method (SEM) formulation is currently implemented in this paper for 3-dimensional (3-D) elasto-plastic problems in stability assessment of largescale slopes (vegetated and barren slopes) in different instability conditions such as seismic and saturation. We have reviewed the SEM formulation, and have sought its applicability for vegetated slopes. Utilizing p (high-order polynomial degree or spectral degrees) and h (mesh operation for quality meshing in required elemental budgets) refining techniques in the existing FEM, the complexity of problem domain can be well addressed in greater numerical stability. Unlike the existing FEM formulation, this high-order FEM employs the same integration and interpolation points to achieve a progressive response of the instability, which drastically reduces the computational costs (formation of diagonalized mass matrix) and offers significant benefits to slope instability computations for serial and parallel implementations. With this formulation, we have achieved the following three qualities in slope instability modeling: 1) geometric flexibility of the finite elements, 2) high computational efficiency, and 3) reliable spectral accuracy. A sample problem has also been presented in this paper, which has accommodated all aforesaid numerical qualities.

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“…Fully automatic hexahedral meshing methods, such as grid-based methods, decomposition-based approaches, and outside-in algorithms, generally cannot achieve high mesh quality and boundary sensitivity with reasonable speed (cf. surveys such as [Tautges 2001;Shepherd 2007]). Our hexahedron-dominant meshing uses the MorseSmale Complex to construct the surface quadrangulation, then follows the framework presented in [Meshkat and Talmor 2000].…”

Section: Related Workmentioning

confidence: 99%

Boundary aligned smooth 3D cross-frame field

Huang

Tong

Wei

et al. 2011

Proceedings of the 2011 SIGGRAPH Asia Conference

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Figure 1: Snapshots of the optimization procedure to construct a boundary aligned 3D cross-frame field. The top row shows the internal streamlines. The next row contains another visualization with cubes spread by a parameterization along the current cross-frame field and rotated by the current local frame R(Φ). The corresponding number of iteration is shown at the bottom. AbstractIn this paper, we present a method for constructing a 3D crossframe field, a 3D extension of the 2D cross-frame field as applied to surfaces in applications such as quadrangulation and texture synthesis. In contrast to the surface cross-frame field (equivalent to a 4-Way Rotational-Symmetry vector field), symmetry for 3D crossframe fields cannot be formulated by simple one-parameter 2D rotations in the tangent planes. To address this critical issue, we represent the 3D frames by spherical harmonics, in a manner invariant to combinations of rotations around any axis by multiples of π/2. With such a representation, we can formulate an efficient smoothness measure of the cross-frame field. Through minimization of this measure under certain boundary conditions, we can construct a smooth 3D cross-frame field that is aligned with the surface normal at the boundary. We visualize the resulting cross-frame field through restrictions to the boundary surface, streamline tracing in the volume, and singularities. We also demonstrate the application of the 3D cross-frame field to producing hexahedron-dominant meshes for given volumes, and discuss its potential in high-quality hexahedralization, much as its 2D counterpart has shown in quadrangulation.

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The generation of hexahedral meshes for assembly geometry: survey and progress

Cited by 75 publications

References 37 publications

A preconditioned semi‐staggered dilation‐free finite volume method for the incompressible Navier–Stokes equations on all‐hexahedral elements

A preconditioned semi‐staggered dilation‐free finite volume method for the incompressible Navier–Stokes equations on all‐hexahedral elements

High-Order FEM Formulation for 3-D Slope Instability

Boundary aligned smooth 3D cross-frame field

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