Spherical Mesh Research Articles

Parallelized Solution Method of the Three-dimensional Gravitational Potential on the Yin–Yang Grid

Abstract We present a new method for solving the 3D gravitational potential of a density field on the Yin–Yang grid. Our algorithm is based on a multipole decomposition and is completely symmetric with respect to the two Yin–Yang grid patches. It is particularly efficient on distributed-memory machines with a large number of compute tasks, because the amount of data being explicitly communicated is minimized. All operations are performed on the original grid without the need for interpolating data onto an auxiliary spherical mesh.

The model of feature extraction for free-form surface based on topological transformation

• A topology-based rigid spherical quadrilateral mesh method is proposed in this paper. • The nondifferentiable problem of free-form surface is solved based on topological transformation. • The model of feature extraction for free-form surface based on topological transformation is built. • The tangent bundle of smooth free-form surface manifold is analyzed. Free-form surface reconstruction is the key technology of mathematical modeling of engineering. It is important for accurate reconstruction of the entity model that conforms to the design. In order to improve the measurement accuracy of the workpiece, a method for free-form surface feature recognition based on topological transformation is proposed in this paper. Firstly, the information of scanning points is expressed as the form of topological space. Based on this, a method of surface constructing that selects the natural-quadratic-surface as the manifold of free-form surface is proposed. Then, the free-form surface that is constructed from the original point cloud is transformed into a smooth free-form surface which is homeomorphic to the original free-form surface based on the theory of topological embedding. The features of the transformed free-form surface can be easily analyzed and recognized. Finally, the qualitative description of an arbitrary point on the surface is obtained by analyzing the tangent bundle of smooth free-form surface manifolds. The feature recognition of free-form surface for workpiece is realized. The experimental results on workpiece model are reported in this paper, which validate the effectiveness of the proposed method.

Planet–disc interactions with discontinuous Galerkin methods using GPUs

We present a two-dimensional Cartesian code based on high order discontinuous Galerkin methods, implemented to run in parallel over multiple GPUs. A simple planet-disc setup is used to compare the behaviour of our code against the behaviour found using the FARGO3D code with a polar mesh. We make use of the time dependence of the torque exerted by the disc on the planet as a mean to quantify the numerical viscosity of the code. We find that the numerical viscosity of the Keplerian flow can be as low as a few $10^{-8}r^2\Omega$, $r$ and $\Omega$ being respectively the local orbital radius and frequency, for fifth order schemes and resolution of $\sim 10^{-2}r$. Although for a single disc problem a solution of low numerical viscosity can be obtained at lower computational cost with FARGO3D (which is nearly an order of magnitude faster than a fifth order method), discontinuous Galerkin methods appear promising to obtain solutions of low numerical viscosity in more complex situations where the flow cannot be captured on a polar or spherical mesh concentric with the disc.

Fast spherical centroidal Voronoi mesh generation: A Lloyd-preconditioned LBFGS method in parallel

Centroidal Voronoi tessellation (CVT)-based mesh generation is a very effective technique for creating high-quality Voronoi meshes and their dual Delaunay triangulations that often play a crucial role in applications, including ocean and atmospheric simulations using finite volume schemes. In the next generation climate models, the spacing scales change dramatically across the whole sphere and require ultra-high resolution and smooth transitions from coarse to fine grid regions. Thus fast and robust spherical CVT (SCVT) meshing algorithms become highly desirable. In this paper, we first propose a Lloyd-preconditioned limited-memory BFGS method for constructing SCVTs that is also applicable to the construction of CVTs of general domains. This method is then parallelized based on overlapping domain decomposition, enabling excellent scalability on distributed systems. Results of several computational experiments show that the new method could incur computational time costs one order of magnitude smaller compared with some existing methods for generating large-scale highly variable-resolution meshes, while also providing significant improvements in mesh quality.

Irregular-regular mode oscillations inside plasma bubble and its fractal analysis in glow discharge magnetized plasma

Experimental evidence of different kinds of oscillations in floating potential fluctuations of glow discharge magnetized plasma is being reported. A spherical gridded cage is inserted into the ambient plasma volume for creating plasma bubbles. Plasma is produced between a spherical mesh grid and chamber. The spherical mesh grid of 80% optical transparency is connected to the positive terminal of power supply and considered as anode. Two Langmuir probes are kept in the ambient plasma to measure the floating potential fluctuations in different positions within the system, viz., inside and outside the spherical mesh grid. At certain conditions of discharge voltage (Vd) and magnetic field, irregular to regular mode appears, and it shows chronological changes with respect to magnetic field. Further various nonlinear analyses such as Recurrence Plot, Hurst exponent, and Lyapunov exponent have been carried out to investigate the dynamics of oscillation at a range of discharge voltages and external magnetic fields. Determinism, entropy, and Lmax are important measures of Recurrence Quantification Analysis which indicate an irregular to regular transition in the dynamics of the fluctuations. Furthermore, behavior of the plasma oscillation is characterized by the technique called multifractal detrended fluctuation analysis to explore the nature of the fluctuations. It reveals that it has a multifractal nature and behaves as a long range correlated process.

Mixed mode oscillations in presence of inverted fireball in an excitable DC glow discharge magnetized plasma

The typical phenomena of mixed mode oscillations and their associated nonlinear behaviors have been investigated in collisionless magnetized plasma oscillations in a DC glow discharge plasma system. Plasma is produced between a cylindrical mesh grid and a constricted anode. A spherical mesh grid of 80% optical transparency is kept inside a cylindrical grid to produce an inverted fireball. Three Langmuir probes are kept in the ambient plasma to measure the floating potential fluctuations at different positions of the chamber. It has been observed that under certain conditions of discharge voltages and magnetic fields, the mixed mode oscillation phenomena (MMOs) appears, and it shows a sequential alteration with the variation of the magnetic fields and probe positions. Low frequency instability has been observed consistently in various experimental conditions. The mechanisms of the low frequency instabilities along with the origin of the MMOs have been qualitatively explained. Extensive linear and nonlinear analysis using techniques such as fast Fourier transform, recurrence quantification analysis, and the well-known statistical computing, skewness, and kurtosis are carried out to explore the complex dynamics of the MMO appearing in the plasma oscillations under various discharge conditions and external magnetic fields.

Conservative interpolation between general spherical meshes

Abstract. An efficient, local, explicit, second-order, conservative interpolation algorithm between spherical meshes is presented. The cells composing the source and target meshes may be either spherical polygons or latitude–longitude quadrilaterals. Second-order accuracy is obtained by piece-wise linear finite-volume reconstruction over the source mesh. Global conservation is achieved through the introduction of a supermesh, whose cells are all possible intersections of source and target cells. Areas and intersections are computed exactly to yield a geometrically exact method. The main efficiency bottleneck caused by the construction of the supermesh is overcome by adopting tree-based data structures and algorithms, from which the mesh connectivity can also be deduced efficiently.The theoretical second-order accuracy is verified using a smooth test function and pairs of meshes commonly used for atmospheric modelling. Experiments confirm that the most expensive operations, especially the supermesh construction, have O(NlogN) computational cost. The method presented is meant to be incorporated in pre- or post-processing atmospheric modelling pipelines, or directly into models for flexible input/output. It could also serve as a basis for conservative coupling between model components, e.g., atmosphere and ocean.

Spherical Parameterization Balancing Angle and Area Distortions.

This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid theoretic foundation. An area-preserving spherical parameterization is also discussed, which is based on discrete optimal mass transport theory. Furthermore, a spherical parameterization algorithm, which is based on the polar decomposition method, balancing angle distortion and area distortion is presented. The algorithms are tested on 3D geometric data and the experiments demonstrate the efficiency and efficacy of the proposed methods.

Sensitive elements of vacuum sensors based on porous nanostructured SiO2-SnO2 sol-gel films

The objects of investigation are porous nanostructured SiO2-SnO2 sol-gel films used as sensitive elements on vacuum sensors. The properties of the films with spherical, labyrinth, and percolation mesh structures are analyzed. It is shown that the resistance of sensitive elements based on these films sharply drops at a pressure below the atmospheric value. Processes taking place in the films at subatmospheric pressures are studied. It is found that the desorption of water vapor increases the resistance of the sensitive elements of vacuum sensors, whereas the desorption of carbon dioxide and oxygen decreases the resistance. This agrees with experimental data.

Simulation and experimental analysis of acoustic signal characteristics in laser welding

The characteristics of the acoustic signals generated in laser welding are investigated using a two-dimensional model, which was determined based on a theoretical investigation of the process heat balance. Three kinds of welds with different penetration depths induced by the welding parameters have been presented, and spherical field point meshes have also been built to obtain the spatial distributions of the acoustic radiation. The predicted oscillatory frequencies of the weld pools obtained by the modeling process are 1453.125, 1890.625, and 2750 Hz. To effectively isolate the environmental noise sources at the welding site, soundproofing equipment is designed that could reduce the acoustic pressure level of 10 dBA. Typical experiments using the soundproofing equipment are presented in the form of continuous wave Nd/YAG laser welding of an iron workpiece. Three weld shapes are obtained in the experiments at various welding speeds and the associated oscillatory frequencies are 1503.9, 1894.53, and 2792.96 Hz. The results show that the oscillatory frequencies of the weld pool that were predicted by the two-dimensional modeling process agree with the experimental results to within 4 %, which demonstrates the effectiveness of the proposed model for prediction of the acoustic radiation.

On the inter-comparison of two tracer transport schemes on icosahedral grids

Two simple finite volume advection schemes based on linear sub-grid reconstruction are implemented over spherical icosahedral–hexagonal grids. One of theses schemes is fully discrete in space and time, while the other one is a semi-discrete scheme with third order Runge–Kutta time integration. For the linear sub-grid reconstruction, we propose two possible candidates for consistent gradient discretization over general grids. These gradients are designed in a finite volume sense with an adequate modification to guarantee convergence in the absence of special grid optimization. To generate our computational mesh from triangular grid, we either use centroids (BT grid) or circumcenters (VT grid) of the spherical triangular mesh. A numerical convergence study is used to show that for a first order convergence of our discrete gradients grid modification is sufficient, whereas to achieve second order convergence grid optimization is mandatory. This study also implicates that BT grid offers a better rate of convergence than VT grid.Monotonicity of the advection schemes is enforced by a slope limiter as well as flux-corrected transport (FCT). We compared aforementioned space–time coupled and space–time decoupled advection schemes in terms of their performance for the recently proposed advection test cases. Our findings advocate that space–time coupled advection scheme is performing better than its counterpart. Furthermore, we used the fully discrete advection scheme to carried out a comparison of slope limitation and FCT approach to achieve monotonicity.

A primal–dual mimetic finite element scheme for the rotating shallow water equations on polygonal spherical meshes

A new numerical method is presented for solving the shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical properties of the continuous equations and thereby capture several desirable physical properties related to balance and conservation. The method relies on two novel features. The first is the use of compound finite elements to provide suitable finite element spaces on general polygonal meshes. The second is the use of dual finite element spaces on the dual of the original mesh, along with suitably defined discrete Hodge star operators to map between the primal and dual meshes, enabling the use of a finite volume scheme on the dual mesh to compute potential vorticity fluxes. The resulting method has the same mimetic properties as a finite volume method presented previously, but is more accurate on a number of standard test cases.

Spherical volume-preserving Demons registration

In order to analyze the brain shift situation accurately, we need to register the medical image and analyze its deformation. In this paper, we introduce a framework with volume-preserving registration for brain shift analysis. First, a volume-preserving mapping is introduced for general manifolds supported by a rigorous continuous theory. The registration is then performed on the spherical tetrahedron mesh with MRI gray values. The registration can retain the equality of local volume elements while registering the manifold to a template at the same time. We use simulated brain shift data to test our method. The results show that our method can efficiently register the brain while preserving the volume of each vertex.

Numerical calculation of the condensational growth of liquid particles in non-dilute and non-ideal media

Condensational growth in aerosols involves simultaneous heat and mass transfer between particles and their surrounding medium. There are several ways of modelling this phenomenon: dilute medium in the vapour species, ideal gas behaviour, ideal mixture, constant thermophysical properties, etc. Most of the solutions proposed for this problem are analytical, at the cost of simplifying many aspects of the phenomenon. This study develops a numerical method for the solution of the steady-state condensational growth of aerosol liquid particles submerged in a gaseous mixture of condensable vapour and inert (non-condensing) gas. Following the principles of the finite volume method, the mass and energy conservation and the droplet heat balance equations are discretized in a spherical mesh around the particle, obtaining their solution by means of a matrix procedure. Heat and mass are transferred satisfying the first-order phenomenological equations. Transport and thermophysical properties of the mixture can be calculated independently, avoiding other assumptions required in analytical procedures. In order to test the method, it was compared with two analytical solutions for the non-dilute condensational growth problem. One of these methods was applied as formulated in the literature, but the other was significantly improved, applying new factors to separate heat and mass transfer as functions of temperature and composition, respectively. The comparison was performed for four condensing substances (H2O, R-134a, n-pentane and n-octane) with air as the inert gas. The results show good agreement under conditions for the ideal gas law, with differences in the case that deviates slightly from this behaviour.

Oxidative stress–induced assembly of PML nuclear bodies controls sumoylation of partner proteins

The promyelocytic leukemia (PML) protein organizes PML nuclear bodies (NBs), which are stress-responsive domains where many partner proteins accumulate. Here, we clarify the basis for NB formation and identify stress-induced partner sumoylation as the primary NB function. NB nucleation does not rely primarily on intermolecular interactions between the PML SUMO-interacting motif (SIM) and SUMO, but instead results from oxidation-mediated PML multimerization. Oxidized PML spherical meshes recruit UBC9, which enhances PML sumoylation, allow partner recruitment through SIM interactions, and ultimately enhance partner sumoylation. Intermolecular SUMO-SIM interactions then enforce partner sequestration within the NB inner core. Accordingly, oxidative stress enhances NB formation and global sumoylation in vivo. Some NB-associated sumoylated partners also become polyubiquitinated by RNF4, precipitating their proteasomal degradation. As several partners are protein-modifying enzymes, NBs could act as sensors that facilitate and confer oxidative stress sensitivity not only to sumoylation but also to other post-translational modifications, thereby explaining alterations of stress response upon PML or NB loss.

Parallel algorithms for planar and spherical Delaunay construction with an application to centroidal Voronoi tessellations

Abstract. A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed. Overlapping allows for the seamless stitching of the partial pieces of the global Delaunay tessellations constructed by individual processors. The algorithm is then modified, by the addition of stereographic projections, to handle the parallel construction of spherical Delaunay and Voronoi tessellations. The algorithms are then embedded into algorithms for the parallel construction of planar and spherical centroidal Voronoi tessellations that require multiple constructions of Delaunay tessellations. This combination of overlapping domain decompositions with stereographic projections provides a unique algorithm for the construction of spherical meshes that can be used in climate simulations. Computational tests are used to demonstrate the efficiency and scalability of the algorithms for spherical Delaunay and centroidal Voronoi tessellations. Compared to serial versions of the algorithm and to STRIPACK-based approaches, the new parallel algorithm results in speedups for the construction of spherical centroidal Voronoi tessellations and spherical Delaunay triangulations.

Performance characteristics of a new spherical metal mesh packing

Various tests and analysis on hydrodynamics and mass transfer properties show that, the newly invented spherical metal mesh packing (SMMP) has excellent properties from three aspects: (i) high void space (∼99%) and lower material cost; (ii) high mass transfer efficiency; (iii) easy installation, good liquid distribution, and prevention of wall flow. Moreover, SMMP is a type of isotropic spherical unit with numerous hollow holes, which realizes the regularization of random packing. The results indicate the potential of developing high-efficiency and energy-saving SMMP-based equipment.

Error-sensitivity analysis of hourglass worm gearing with spherical meshing elements

Abstract This paper aims to study the influence of tooth errors and shaft misalignments on the tooth contact in hourglass worm gearing with spherical meshing elements. The geometries of the worm and worm-gear tooth surfaces are described, and the distribution characteristic of contact lines is explored. Based on the common moving frame of conjugate tooth surfaces, the errors and the variations are quantified, and the error-variation equation is developed; in order to evaluate the influence levels of different errors, the error-sensitivity formulas are deduced and illustrated by a numerical example. The results provide a theoretical basis for the manufacture and the tooth contact analysis of hourglass worm pair with spherical meshing elements.

Spherical Mesh Adaptive Direct Search for Separating Quasi-Uncorrelated Sources by Range-Based Independent Component Analysis

It is seemingly paradoxical to the classical definition of the independent component analysis (ICA), that in reality, the true sources are often not strictly uncorrelated. With this in mind, this letter concerns a framework to extract quasi-uncorrelated sources with finite supports by optimizing a range-based contrast function under unit-norm constraints (to handle the inherent scaling indeterminacy of ICA) but without orthogonality constraints. Albeit the appealing contrast properties of the range-based function (e.g., the absence of mixing local optima), the function is not differentiable everywhere. Unfortunately, there is a dearth of literature on derivative-free optimizers that effectively handle such a nonsmooth yet promising contrast function. This is the compelling reason for the design of a nonsmooth optimization algorithm on a manifold of matrices having unit-norm columns with the following objectives: to ascertain convergence to a Clarke stationary point of the contrast function and adhere to the necessary unit-norm constraints more naturally. The proposed nonsmooth optimization algorithm crucially relies on the design and analysis of an extension of the mesh adaptive direct search (MADS) method to handle locally Lipschitz objective functions defined on the sphere. The applicability of the algorithm in the ICA domain is demonstrated with simulations involving natural, face, aerial, and texture images.

Particle System Based Adaptive Sampling on Spherical Parameter Space to Improve the MDL Method for Construction of Statistical Shape Models

Minimum description length (MDL) based group-wise registration was a state-of-the-art method to determine the corresponding points of 3D shapes for the construction of statistical shape models (SSMs). However, it suffered from the problem that determined corresponding points did not uniformly spread on original shapes, since corresponding points were obtained by uniformly sampling the aligned shape on the parameterized space of unit sphere. We proposed a particle-system based method to obtain adaptive sampling positions on the unit sphere to resolve this problem. Here, a set of particles was placed on the unit sphere to construct a particle system whose energy was related to the distortions of parameterized meshes. By minimizing this energy, each particle was moved on the unit sphere. When the system became steady, particles were treated as vertices to build a spherical mesh, which was then relaxed to slightly adjust vertices to obtain optimal sampling-positions. We used 47 cases of (left and right) lungs and 50 cases of livers, (left and right) kidneys, and spleens for evaluations. Experiments showed that the proposed method was able to resolve the problem of the original MDL method, and the proposed method performed better in the generalization and specificity tests.