Parallel Mesh Research Articles

Multi-threaded parallel tetrahedral mesh improvement by combining atomic operation and graph coloring

In industrial numerical simulations, efficiently generating high-quality tetrahedral meshes remains a significant challenge. Advances in high-performance computing have made parallelization a practical approach to improving the quality of large-scale tetrahedral meshes. This study proposes a fine-grained multithreaded parallel method to accelerate tetrahedral mesh improvement. By utilizing atomic operations, we fundamentally address thread safety concerns. Additionally, through the precise use of atomic operations, task decomposition strategies, and a multithreaded memory model, we minimize the probability of task overlap and data races, thereby enhancing overall parallel mesh improvement efficiency. Experimental results demonstrate that our parallel mesh improver is robust and effective for complex industrial models. On a laptop with 16 threads, we achieved a tenfold increase in tetrahedral mesh improvement speed, with the quality of the improved meshes being comparable to that of the sequential process.

Parallel Topology-aware Mesh Simplification on Terrain Trees

We address the problem of performing a topology-aware simplification algorithm on a compact and distributed data structure for triangle meshes, the Terrain trees. Topology-aware operators have been defined to coarsen a Triangulated Irregular Network (TIN) without affecting the topology of its underlying terrain, i.e., without modifying critical features of the terrain, such as pits, saddles, peaks, and their connectivity. However, their scalability is limited for large-scale meshes. Our proposed algorithm uses a batched processing strategy to reduce both the memory and time requirements of the simplification process, and thanks to the spatial decomposition on the basis of Terrain trees, it can be easily parallelized. Also, since a Terrain tree after the simplification process becomes less compact and efficient, we propose an efficient post-processing step for updating hierarchical spatial decomposition. Our experiments on real-world TINs, derived from topographic and bathymetric LiDAR data, demonstrate the scalability and efficiency of our approach. Specifically, topology-aware simplification on Terrain trees uses 40% less memory and half the time compared to the most compact and efficient connectivity-based data structure for TINs. Furthermore, the parallel simplification algorithm on the Terrain trees exhibits a 12× speedup with an OpenMP implementation. The quality of the output mesh is not significantly affected by the distributed and parallel simplification strategy of Terrain trees, and we obtain similar quality levels compared to the global baseline method.

Construction of triptycene molecular rotors with intermeshing arrangement and low rotational barrier

Abstract Molecular rotors are one of the building blocks of molecular machines and they are nano-sized with mechanically rotating moieties. Among them, intermeshing triptycenes with a gear-like skeleton allow the construction of a molecular rotor that transmits rotational motion. For triptycenes to mesh with each other without loss of rotation, intermeshing them in parallel and adjusting the distance between their axes to 8.1 Å are required. However, with conventional methods, because of the restrictions on bond lengths and atomic radii, achieving an ideal arrangement in which the triptycenes mesh in parallel at 8.1 Å has been difficult. In this work, we synthesized disulfonic acid containing a triptycene as a rotator and combined it with amines of 2 different steric factors (normal-amylamine [nAmA] and guanidine [Gu]), which allowed us to prepare organic salts with varying arrangements of triptycenes. In the organic salt with the planar amine (Gu), the crystal structure was close to the ideal intermeshing arrangement of the triptycene and the distance between their axes was 7.7 Å. The T1ρ 13C spin-lattice relaxation time using solid-state nuclear magnetic resonance (NMR) demonstrated that triptycene rotates efficiently at 24 kHz at 313 K with a low rotational barrier (10.9 kcal/mol) compared with non-intermeshing structures.

Parallel and automatic mesh sizing field generation for complicated CAD models

PurposeThe purpose of this paper is to present an automatic approach for mesh sizing field generation of complicated computer-aided design (CAD) models.Design/methodology/approachIn this paper, the authors present an automatic approach for mesh sizing field generation. First, a source point extraction algorithm is applied to capture curvature and proximity features of CAD models. Second, according to the distribution of feature source points, an octree background mesh is constructed for storing element size value. Third, mesh size value on each node of background mesh is calculated by interpolating the local feature size of the nearby source points, and then, an initial mesh sizing field is obtained. Finally, a theoretically guaranteed smoothing algorithm is developed to restrict the gradient of the mesh sizing field.FindingsTo achieve high performance, the proposed approach has been implemented in multithreaded parallel using OpenMP. Numerical results demonstrate that the proposed approach is remarkably efficient to construct reasonable mesh sizing field for complicated CAD models and applicable for generating geometrically adaptive triangle/tetrahedral meshes. Moreover, since the mesh sizing field is defined on an octree background mesh, high-efficiency query of local size value could be achieved in the following mesh generation procedure.Originality/valueHow to determine a reasonable mesh size for complicated CAD models is often a bottleneck of mesh generation. For the complicated models with thousands or even ten thousands of geometric entities, it is time-consuming to construct an appropriate mesh sizing field for generating high-quality mesh. A parallel algorithm of mesh sizing field generation with low computational complexity is presented in this paper, and its usability and efficiency have been verified.

Optimization of solar air heaters performance using parallel porous wire mesh: energy, exergy, and enviro-economic analyses

This research conducts an experimental analysis of a solar air heater (SAH) with and without a porous wire mesh, focusing on energy, exergy, and enviro-economic aspects. Measurements are carried out using both a conventional solar air collector and modified one by adding a porous wire mesh. Various wire mesh lengths (20, 40, and 60 cm) are used to determine the optimum one considering different mass flow rates (ṁ = 0.022, 0.033, and 0.045 kg/s). The impact of specific loss sources on exergy efficiency, including exergy destruction between the environment and system components, between the fluid and absorber, and between the absorber and the sun is pointed out. The findings reveal a remarkable enhancement in thermal efficiency, reaching 86 % by using a 60 cm wire mesh atṁ = 0.045 kg/s. The integration of the wire mesh into the SAH results in reduced exergy efficiency due to increased losses and exergy destruction rates. Using 60 cm wire mesh yields beneficial effects on thermo-hydraulic performance by enhancing convection heat transfer and increasing the overall effectiveness of the collector. Enviro-economic analysis shows significant environmental benefits. In Case4, operating at ṁ = 0.045 kg/s, the highest embodied energy value is observed and the highest annual useful energy output of 5480 kWh/year at the lowest energy cost of 0.0105 ($/kWh) is achieved. Additionally, the incorporation of a 60 cm porous wire mesh leads to an annual mitigation of approximately 1370.21 tons of CO2 and an improved environmental cost of 68.51 $/year compared to the conventional solar air collector's cost (28.15 $/year).

Optimal surrogate boundary selection and scalability studies for the shifted boundary method on octree meshes

The accurate and efficient simulation of Partial Differential Equations (PDEs) in and around arbitrarily defined geometries is critical for many application domains. Immersed boundary methods (IBMs) alleviate the usually laborious and time-consuming process of creating body-fitted meshes around complex geometry models (described by CAD or other representations, e.g., STL, point clouds), especially when high levels of mesh adaptivity are required. In this work, we advance the field of IBM in the context of the recently developed Shifted Boundary Method (SBM). In the SBM, the location where boundary conditions are enforced is shifted from the actual boundary of the immersed object to a nearby surrogate boundary, and boundary conditions are corrected utilizing Taylor expansions. This approach allows choosing surrogate boundaries that conform to a Cartesian mesh without losing accuracy or stability. Our contributions in this work are as follows: (a) we show that the SBM numerical error can be greatly reduced by an optimal choice of the surrogate boundary, (b) we mathematically prove the optimal convergence of the SBM for this optimal choice of the surrogate boundary, (c) we deploy the SBM on massively parallel octree meshes, including algorithmic advances to handle incomplete octrees, and (d) we showcase the applicability of these approaches with a wide variety of simulations involving complex shapes, sharp corners, and different topologies. Specific emphasis is given to Poisson’s equation and the linear elasticity equations.

Prediction of shock heating during ultrasound-induced bubble collapse using real-fluid equations of state

Numerical simulations of collapsing air bubbles considering complex and more accurate equations of state (EoS) for estimating the properties of both the liquid and gas are presented. The necessity for utilising such EoSs in bubble collapse simulations is illustrated by the unphysical (spurious) liquid temperature jump formed in the vicinity of the bubble-air interface when simplified EoSs are used. The solved fluid flow equations follow the mechanical equilibrium multiphase method of Kapila. The solver is coded in the AMReX platform, enabling high-performance computation with parallel processing and Adaptive Mesh Refinement for speeding up simulations. It is initially demonstrated that the frequently used Stiffened Gas (SG) EoS overpredicts the liquid temperature at high compression. More sophisticated EoS models, such as the International Association for the Properties of Water and Steam (IAPWS), the Modified Noble Abel Stiffened Gas (MNASG) and a modified Tait EoS introduced here, are also implemented into the flow solver and their differences are highlighted for bubble collapse cases for the first time. Subsequently, application of the developed model to cases of practical interest is showcased. More specifically, simulations of bubble collapse near a solid wall are presented for conditions simulating shock wave lithotripsy (SWL). It is concluded that for such cases, a maximum increase of 25 K of the liquid temperature in contact along the solid wall is caused during the collapse of the air bubble due to shock wave focusing effects. It is also highlighted that the maximum liquid heating varies depending on the initial bubble-wall stand-off distance.

A three-dimensional solver for simulating detonation on curvilinear adaptive meshes

A generic solver in a parallel Cartesian adaptive mesh refinement framework is extended to simulate detonations on three-dimensional structured curvilinear meshes. A second-order accurate finite volume method is used with grid-aligned Riemann solvers for thermally perfect gas mixtures. Detailed, multi-step chemical kinetic mechanisms are employed and numerically incorporated with a splitting approach. The adaptive mesh refinement technique is applied to a mapped mesh using modified prolongation and restriction operators. The flux along the coarse-fine interface is considered in a correction procedure to ensure the conservation of the solver. The numerical accuracy, conservation and robustness of the simulations are verified and validated with suitable benchmark tests. The new solver is then used to simulate detonation problems in non-Cartesian geometries. A simulation is conducted of the three-dimensional detonation propagation in a 90-degree pipe bend. A detonation in a round tube is also simulated in a Galilean frame of reference. Both a rectangular mode and a spinning mode are observed in the simulations. In addition, the fundamental problem of detonation wave/boundary layer interaction is studied. The results show that the new solver can simulate high-speed reactive flows efficiently by the combined use of a curvilinear mapping with mesh adaptation.

The Cartesian Grid Active Flux Method with Adaptive Mesh Refinement

We present the first implementation of the Active Flux method on adaptively refined Cartesian grids. The Active Flux method is a third order accurate finite volume method for hyperbolic conservation laws, which is based on the use of point values as well as cell average values of the conserved quantities. The resulting method has a compact stencil in space and time and good stability properties. The method is implemented as a new solver in ForestClaw, a software for parallel adaptive mesh refinement of patch-based solvers. On each Cartesian grid patch the single grid Active Flux method can be applied. The exchange of data between grid patches is organised via ghost cells. The local stencil in space and time and the availability of the point values that are used for the reconstruction, leads to an efficient implementation. The resulting method is third order accurate, conservative and allows the use of subcycling in time.

A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes

The Cahn-Hilliard Navier-Stokes (CHNS) system provides a computationally tractable model that can be used to effectively capture interfacial dynamics in two-phase fluid flows. In this work we present a semi-implicit, projection-based finite element framework for solving the CHNS system. We use a projection-based semi-implicit time discretization for the Navier-Stokes equation and a fully-implicit time discretization for the Cahn-Hilliard equation. We use a conforming continuous Galerkin (cG) finite element method in space equipped with a residual-based variational multiscale (RBVMS) formulation. Pressure is decoupled using a projection step, which results in two linear positive semi-definite systems for velocity and pressure, instead of the saddle point system of a pressure-stabilized method. All the linear systems are solved using an efficient and scalable algebraic multigrid (AMG) method. We deploy this approach on a massively parallel numerical implementation using parallel octree-based adaptive meshes. The overall approach allows the use of relatively large time steps with much faster time-to-solve than similar fully-implicit methods. We present comprehensive numerical experiments showing detailed comparisons with results from the literature for canonical cases, including the single bubble rise and Rayleigh-Taylor instability.

3-Dimensional heat transfer modeling for laser powder bed fusion additive manufacturing using parallel computing and adaptive mesh

In this article, an innovative 3-dimensional (3D) heat-transfer finite element parallel-computing model with adaptive mesh capability, named LPBFSim, for Laser Powder Bed Fusion (LPBF) additive manufacturing is introduced for high precision prediction of melt pool dimensions and single-layer part-level process simulations. Numerical modeling can significantly reduce the expense of the sole deployment of trial-and-error experiments for achieving optimal process parameters. The previously developed single-track model [1] is highly accurate to predict melt pool dimensions for different combinations of process parameters. However, without using parallel computing and an adaptive mesh, it is very challenging to scale it up to a multi-track model or even a part-level model due to the high computational cost. The proposed model is parallelized to be able to run on a cluster and aimed to solve this difficulty while keeping all the accuracy from the previous version. Single-track, multi-track, and single-layer part-level models have been implemented to demonstrate its efficiency and accuracy.

A parallel adaptive finite-element approach for 3-D realistic controlled-source electromagnetic problems using hierarchical tetrahedral grids

SUMMARY To effectively and efficiently interpret or invert controlled-source electromagnetic (CSEM) data which are recorded in areas with the kind of complex geological environments and arbitrary topography that are typical, 3-D CSEM forward modelling software that can quickly solve large-scale problems, provide accurate electromagnetic responses for complex geo-electrical models and can be easily incorporated into inversion algorithms are required. We have developed a parallel goal-oriented adaptive mesh refinement finite-element approach for frequency-domain 3-D CSEM forward modelling with hierarchical tetrahedral grids that can offer accurate electromagnetic responses for large-scale complex models and that can efficiently serve for inversion. The approach uses the goal-oriented adaptive vector finite element method to solve the total electric field vector equation. The geo-electrical model is discretized by unstructured tetrahedral grids which can deal with complex underground geological models with arbitrary surface topography. Different from previous adaptive finite element software working on unstructured tetrahedral grids, we have utilized a novel mesh refinement technique named the longest edge bisection method to generate hierarchically refined grids. As the refined grids are nested into the coarse grids, the refinement technique can precisely map the electrical parameters of inversion grids onto the forward modelling grids so that the extra numerical errors generated by the inconsistency of electrical parameters between inversion grids and forward modelling grids are eliminated. In addition, we use the parallel domain-decomposition technique to further accelerate the computations, and the flexible generalized minimum residual solver (FGMRES) with an auxiliary Maxwell solver pre-conditioner to solve the final large-scale system of linear equations. In the end, we validate the performance of the proposed scheme using two synthetic models and one realistic model. We demonstrate that accurate electromagnetic fields can be obtained by comparison with the analytic solutions and that the code is highly scalable for large-scale problems with millions or even hundreds of millions of unknowns. For the synthetic 3-D model and the realistic model with complex geometry, our solutions match well with the results calculated by an existing 3-D CSEM forward modelling code. Both synthetic and realistic examples demonstrate that our newly developed code is an effective, efficient forward modelling engine for interpreting CSEM field data acquired in areas of complex geology and topography.

A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes

We present a fully-coupled, implicit-in-time framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work, we extend the block iterative method presented in Khanwale et al. [Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes, J. Comput. Phys. (2020)], to a fully-coupled, provably second-order accurate scheme in time, while maintaining energy-stability. The new method requires fewer matrix assemblies in each Newton iteration resulting in faster solution time. The method is based on a fully-implicit Crank-Nicolson scheme in time and a pressure stabilization for an equal order Galerkin formulation. That is, we use a conforming continuous Galerkin (cG) finite element method in space equipped with a residual-based variational multiscale (RBVMS) procedure to stabilize the pressure. We deploy this approach on a massively parallel numerical implementation using parallel octree-based adaptive meshes. We present comprehensive numerical experiments showing detailed comparisons with results from the literature for canonical cases, including the single bubble rise, Rayleigh-Taylor instability, and lid-driven cavity flow problems. We analyze in detail the scaling of our numerical implementation.

An approximated volume of fluid method with the modified height function method in the simulation of surface tension driven flows

Surface tension in two-phase flow problems plays a dominant role in many micro-flow phenomena and has an important influence on the development of flow instability phenomena that contain free surfaces. In this study, the multi-moment finite volume method is extended for direct numerical simulation of two-phase flow problems. A constraint interpolation profile–CSL (semi-Lagrangian) scheme is used for discretization of the advection part in the momentum equation. A compact volume of fluid method–approximated piecewise linear calculation method without flux limiter is proposed for capturing the moving interface. For modeling the surface tension accurately, the logic in curvature estimation is redesigned based on the height function (HF) method. The isolated volumetric fractions that may reduce accuracy in HF integration are excluded, and the numerical solution shows that the accuracy in the curvature estimation is improved for a coarse mesh. The present method is implemented with a parallel block-structured adaptive mesh refinement (BAMR) strategy; thus, the computational cost can be reduced significantly. Numerical tests show that the present BAMR solver is capable of reproducing the theoretical predictions of capillary wave instability problems with high accuracy. The simulation of droplet collisions further demonstrates the accuracy of the surface tension model. Finally, we extend it to the liquid jet atomization. The wavy disturbance, film breakup, liquid filament pinch-off, and droplet generation are well reproduced. The droplet size distribution satisfies the experimental measurement and theoretical predictions power-law. BAMR shows a huge advantage in computational efficiency than the traditional Cartesian grid. The findings of this study can help for a better understanding of the micro-mechanism of surface tension driven flows.

A Parallel Variational Mesh Quality Improvement Method for Tetrahedral Meshes Based on the MMPDE Method

There are numerous large-scale applications requiring mesh adaptivity, e.g., cardiac electrophysiology, computational fluid dynamics, fracture propagation, and weather prediction. Parallel processing is needed for simulations involving large-scale adaptive meshes. In this paper, we propose a parallel variational mesh quality improvement algorithm for use with distributed memory machines. Our parallel method is based on the sequential method by Huang, Ren, and Russell and the recent implementation by Huang and Kamenski. Their approach is based on the use of the Moving Mesh PDE method to adapt the mesh based on the minimization of an energy functional for mesh equidistribution and alignment. This leads to a system of ordinary differential equations (ODEs) to be solved which determine where to move the interior mesh nodes. The MMPDE method successfully removes/reduces the number of extreme dihedral angles, particularly those less than 2 0 o or greater than 15 0 o . An efficient solution is obtained by solving the ODEs on subregions of the mesh with overlapped communication and computation. Strong and weak scaling experiments on up to 128 cores for meshes with up to 160M elements demonstrate excellent results. • A parallel algorithm and implementation are proposed for variational mesh quality improvement on simplicial meshes. This is the first parallel variational mesh quality improvement method. • The method is based on the sequential moving mesh PDE (MMPDE) method of Huang, Ren, and Russell and the recent implementation by Huang and Kamenski which removes or significantly reduces the number of extreme dihedral angles in a tetrahedral mesh upon smoothing. • Their approach adapts the mesh based on the minimization of an energy functional for mesh equidistribution and alignment. This leads to a system of ODEs to be solved for the velocities of the interior mesh nodes. • An efficient solution is obtained by solving the ODEs in parallel on subregions of the mesh with overlapped communication and computation. • Excellent scalability results are obtained on up to 128 cores for tetrahedral meshes with up to 160M elements and on an industrial example from the tire industry.

SAFT: Shotgun advancing front technique for massively parallel mesh generation on graphics processing unit

AbstractLarge‐scale numerical simulations need efficient parallel mesh generation schemes. Several parallel advancing front algorithms were proposed in the past decades, most of which require domain decomposition. In this article, we present a shotgun algorithm for parallel advancing front mesh generation. Our algorithm is front‐based, therefore does not require domain decomposition. We've implemented the algorithm on GPU, which has thousands of CUDA cores. Different from traditional volume‐based parallelization, each CUDA thread handles one face at a time. We deal with conflicts by discarding illegal new elements which intersect with each other. We name this proposed method “SAFT”, which stands for “shotgun advancing front technique”. Its performance, as well as scalability, has been evaluated on a laptop equipped with one NVIDIA Geforce RTX2060 graphics card. We have been able to generate high‐quality 2D meshes efficiently (233k elements per second).

Parallel GPU-accelerated adaptive mesh refinement on two-dimensional phase-field lattice Boltzmann simulation of dendrite growth

Simulations of dendritic solidification involving melt convection and solid motion usually require a considerably higher computational domain than the dendrite size, whose computational efficiency with a uniform mesh is extremely low. In this study, to accelerate those two-dimensional simulations using the phase-field and lattice Boltzmann (PF-LB) methods, we developed a parallel computing method with multiple graphics processing units (GPUs) for the adaptive mesh refinement (AMR) method with dynamic load balancing (parallel-GPU AMR). It was confirmed that parallel-GPU AMR simulations were faster than those with the uniform mesh when the number of grid points in the adaptive mesh was around 40% or less than those in the uniform mesh. We also demonstrate that the developed parallel-GPU AMR can greatly accelerate the PF-LB simulations of dendrite growth with melt convection and solid motion.

Efficiency of parallel anisotropic mesh adaptation for the solution of the bidomain model in cardiac tissue

Electrocardiology models are nonlinear reaction–diffusion type systems, where the numerical simulation requires extremely fine meshes to accurately compute the heart’s electrical activity. Anisotropic mesh adaptation methods have been proven to be efficient for simulating cardiac dynamic by many authors and showed a considerable improvement in the numerical accuracy while reducing the computational expenses. However, the efficiency of these techniques in parallel computing environments has not been shown yet, especially when compared to the performance of parallel uniform meshes. In this paper, we demonstrate the efficiency of a parallel anisotropic mesh adaptation method for the solution of the bidomain model in cardiac tissue. The technique is based on an efficient error estimator appropriate for second or higher order numerical solutions. To demonstrate the effectiveness of the developed methodology, comparisons between the numerical simulations on parallel adapted meshes with those on parallel uniform meshes are presented. The computational efficiency is assessed by computing spiral and scroll waves in cardiac tissue.

An ultralight geometry processing library for parallel mesh refinement

In applications such as parallel mesh refinement, it remains a challenging issue to ensure the refined surface respects the original Computer-Aided Design (CAD) model accurately. In this paper, an ultralight geometry processing library is developed to resolve this issue effectively and efficiently. Here, we say the kernel is ultralight because it has a very small set of data-structures and algorithms by comparison with industrial-level geometry kernels. Within the library, a simplified surface boundary representation (B-rep) and a radial edge structure are developed respectively to depict the geometry model and the surface mesh, plus hash tables that record the connections between the geometry model and the surface mesh. Based on these data structures, a set of efficient algorithms are developed, which initializes the connection tables, projects a point back to the original geometry, etc. With these data-structure and algorithmic infrastructures set up, the callings of eight well-designed Application Programming Interfaces (APIs) are powerful enough to enable the parallel mesh refinement algorithm outputs a mesh respecting the input CAD model accurately. Numerical experiments will be finally presented to evaluate the performance of the overall parallel mesh refinement algorithm and the algorithms in relation with the developed library.

A consistent mass–momentum flux computation method for the simulation of plunging jet

In the present study, a robust and conservative numerical scheme is proposed to simulate the violent two-phase flows with high-density ratios. In this method, the mass conservation equation and the momentum equation are solved in a consistent manner. The tangent of hyperbola for interface capturing scheme is extended for the computation of the mass flux by which the sharpness and conservation property of density field is preserved. Compared with other recently proposed methods, no geometrical computation is involved in deriving the mass flux and the spurious velocity in the interfacial region can be completely avoided. To improve the computational efficiency, the present method is implemented on a parallel block-structured adaptive mesh refinement method with a staggered layout of variables. High-fidelity numerical simulation of plunging jet through the liquid surface is performed. A bubble detection algorithm is developed to track bubbles generated in air entrainment process. The evolution of the bubble cloud, air concentration, bubble-size, and bubble-velocity distributions are predicted and compared quantitatively with the experiment. Numerical results show the air entrainment and penetration depth are highly correlated with the upstream disturbance. The growing interfacial roughness of the jet yields more entrained air in the final stage of jet impingement. It is found that when the initial perturbation is introduced, the overall size of the equivalent bubble radius will expand, and the penetration depth of the bubble cloud will decrease, while a larger volume of air is entrained.