TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator

Si, Hang

doi:10.1145/2629697

Cited by 1,331 publications

(830 citation statements)

References 102 publications

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“…To accelerate the calculations, the algorithms are implemented with the parallel adaptive finite element package PHG [65]. The molecular surface and volume meshes, that are necessary for FEM computation, are generated by TMSmesh [7,8] and Tetgen [57].…”

Section: Methodsmentioning

confidence: 99%

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

et al. 2016

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The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al Phys. Rev. Lett. 1997, 79, 435-438; Kilic et al Phys. Rev. E 2007, 75, 021502; Lu and Zhou Biophys. J. 2011, 100, 2475-2485; Liu and Eisenberg J. Chem. Phys. 2014, 141, 22D532) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both LHSPNP and SMPNP models the stratification of one counterion species can be observed under certain bulk concentrations.

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Section: Methodsmentioning

confidence: 99%

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

et al. 2016

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“…Namely, the CDT of Ω with vertices in X minimizes the E ρ ODT (X, T ) among all constrained triangulations of X [28]. To compute the constrained Delaunay triangulation, we use the method in [30]. (4) See (3.1) and the complete formula in section 4.2.…”

Section: Reaching a Local Minimum With L-bfgsmentioning

confidence: 99%

“…We use the TetGen library [30] for generating 3D Delaunay triangulation. All the experiments are conducted on a laptop computer with a 2.66 GHz Intel processor and 4 GB memory.…”

Section: Implementation and Evaluation Our Algorithm Is Implementedmentioning

confidence: 99%

“…For tetrahedral mesh generation, we explore a number of widely used tools, in particular, TetGen [30], GHS3D [15], Gmsh [17], and NetGen [26]. Table 1 shows the statistics of the qualities of the meshes generated by different methods and the error norms of the solutions.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The most time-consuming part of the ODT method is building the constrained Delaunay triangulation. We test the algorithms of CDT and DT implemented in TetGen [30] with different numbers of points, sampled in a bunny model (Figure 21). The CDT algorithm is about 20% slower than computing DT.…”

Section: Timingmentioning

confidence: 99%

See 2 more Smart Citations

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

Chen¹,

Wang²,

Lévy³

et al. 2014

SIAM J. Sci. Comput.

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Abstract. This paper proposes a new algorithm to generate a graded three-dimensional tetrahedral mesh. It revisits the class of methods based on optimal Delaunay triangulation (ODT) and proposes a proper way of injecting a background density function into the objective function minimized by ODT. This continuous/analytic point of view leads to an objective function that is continuous and Delaunay consistent, in contrast with the discrete/geometrical point of view developed in previous work. To optimize the objective function, this paper proposes a hybrid algorithm that combines a local search (quasi-Newton) with a global optimization (simulated annealing). The benefits of the method are both improved performances and an improved quality of the result in terms of dihedral angles. This results from the combination of two effects. First, the local search has a faster speed of convergence than previous work due to the better behavior of the objective function, and second, the algorithm avoids getting stuck in a poor local minimum. Experimental results are evaluated and compared using standard metrics.

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An upscaling procedure for fractured reservoirs with embedded grids

Fumagalli

Pasquale²,

Zonca

et al. 2016

Water Resources Research

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Upscaling of geological models for reservoir simulation is an active and important area of research. In particular, we are interested in reservoirs where the rock matrix exhibits an intricate network of fractures, which usually acts as a preferential path to the flow. Accounting for fractures' contribution in the simulation of a reservoir is of paramount importance. Here we have focused on obtaining effective parameters (e.g., transmissibility) on a 3-D computational grid on the reservoir scale, which account for the presence, at a finer spatial scale, of fractures and a network of fractures. We have essentially followed the idea illustrated in Karimi-Fard et al. (2006), yet this work has some notable aspects of innovation in the way the procedure has been implemented, and in its capability to consider rather general corner-point grids, like the ones normally used in reservoir simulations in the industry, and complex and realistic fracture networks, possibly not fully connected inside the coarse cells. In particular, novel contribution is the employment of an Embedded Discrete Fracture Model (EDFM) for computing fracture-fracture and matrix-fracture transmissibilities, with a remarkable gain in speedup. The output is in the form of transmissibility that, although obtained by considering single-phase flow, can be used for coarse-scale multiphase reservoir simulations, also via industrial software, such as Eclipse, Intersect, or GPRS. The results demonstrate the effectiveness and computational efficiency of the numerical procedure which is now ready for further testing and industrialization.

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TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator

Cited by 1,331 publications

References 102 publications

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

An upscaling procedure for fractured reservoirs with embedded grids

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