Virtual Node Method Research Articles

Virtual node graph neural network for full phonon prediction.

Understanding the structure-property relationship is crucial for designing materials with desired properties. The past few years have witnessed remarkable progress in machine-learning methods for this connection. However, substantial challenges remain, including the generalizability of models and prediction of properties with materials-dependent output dimensions. Here we present the virtual node graph neural network to address the challenges. By developing three virtual node approaches, we achieve Γ-phonon spectra and full phonon dispersion prediction from atomic coordinates. We show that, compared with the machine-learning interatomic potentials, our approach achieves orders-of-magnitude-higher efficiency with comparable to better accuracy. This allows us to generate databases for Γ-phonon containing over 146,000 materials and phonon band structures of zeolites. Our work provides an avenue for rapid and high-quality prediction of phonon band structures enabling materials design with desired phonon properties. The virtual node method also provides a generic method for machine-learning design with a high level of flexibility.

Piezoelectric MEMS-based physical reservoir computing system without time-delayed feedback

Abstract In this study, a physical reservoir computing system, a hardware-implemented neural network, was demonstrated using a piezoelectric MEMS resonator. The transient response of the resonator was used to incorporate short-term memory characteristics into the system, eliminating commonly used time-delayed feedback. In addition, the short-term memory characteristics were improved by introducing a delayed signal using a capacitance-resistor series circuit. A Pb(Zr,Ti)O3-based piezoelectric MEMS resonator with a resonance frequency of 193.2 Hz was employed as an actual node, and computational performance was evaluated using a virtual node method. Benchmark tests using random binary data indicated that the system exhibited short-term memory characteristics for two previous data and nonlinearity. To obtain this level of performance, the data bit period must be longer than the time constant of the transient response of the resonator. These outcomes suggest the feasibility of MEMS sensors with machine-learning capability.

Theoretical and Numerical Investigations on Static Characteristics of Aerostatic Porous Journal Bearings

To investigate the static characteristics of aerostatic journal bearings with porous bushing, the flow model—in which the compressibility of lubricating gas is considered—is established based on the Reynolds lubrication equation, Darcy equation for porous material, and continuity equation. With the finite difference method, difference schemes for non-uniform grids, relaxation method, and virtual node method, the numerical method for the governing equations of compressible flow in porous journal bearings is proposed. The effects of nominal clearance of bearings and compressibility of gas on the static characteristics are analyzed. Under the same minimum film thickness and the same gas compressibility, as the nominal clearance widens, the load capacity, mass flow rate, and power consumption increase. Under the same minimum film thickness and the same nominal clearance, with the increase in gas polytropic index, the load capacity strengthens, while the mass flow rate and power consumption decline. This study could provide a reference for the design of porous journal bearings.

Leakage-free optimization of micro herringbone grooved journal bearings with a virtual node method

PurposeThis study aims to develop a new method to treat the numerical singularity at the critical nodes of two skew coordinates, and optimize the leakage of micro herringbone grooved journal bearings (MHGJBs) with this method.Design/methodology/approachA side leakage numerical algorithm is proposed by using the skew meshes with a virtual node (SMVN) method to evaluate the effects of groove angle, bank/groove ratio, groove depth and groove number on load capacity, friction and side leakage of MHGJB.FindingsThe SMVN method is effective in treating the numerical singularity at the critical nodes of two skew coordinates. Besides, a group of optimized parameters of micro herringbone groove is obtained which can not only minimize the side leakage but also improve the load capacity and friction force.Originality/valueA virtual node method was proposed, which can significantly improve the calculation accuracy in the side leakage model.

A finite element post-processor for fatigue assessment of welded structures based on the Master S-N curve method

The Master S-N curve method enables the use of computationally efficient coarse FE models without overlooking accuracy in fatigue life estimates of welded structures. However, the use of the method in daily design practice of engineering offices faces the barrier of a largely available finite element post-processor. This paper intends to fill the gap on how to implement a finite element structural stress post-processor for the Master S-N curve method in FEM software. Previous overlooked aspects of the Master S-N curve method in literature such as how to deal with solid and quadratic elements and how to smooth stress singularities with the Generalized virtual node method or using a rounded weld end are fully explained. Three demonstration examples of welded connections are illustrated and validated: (a) a uniaxial longitudinal welded attachment using linear/quadratic solid elements, (b) a flat plate subjected to high bending stresses and using a simplified representation of the weld end with quadratic shell elements, and (c) a welded tube subjected to multiaxial loading using shell and solid elements. The proposed algorithms show the full capabilities of the developed Structural Stress Post-processor for fatigue analysis of welded structures under constant amplitude loading and multiaxial stress states.

Evaluation Method for Cohesive Crack Propagation in Fragile Locations of RCC Dam Using XFEM

Roller compacted concrete (RCC) dams own a large number of horizontal construction layers, which can easily lead to weak joints among layers and generate interlayer joints with different scales to reduce the dam bearing capacity. In this study, extended finite element method (XFEM) is used to simulate crack propagation, the finite element description is first taken on the strong discontinuity. Subsequently, the displacement function of the crack-tip in the quadrilateral element and the geometric determination method of the crack-tip strengthening region are established. Afterwards, the discrete form of the governing equation is derived and the XFEM increment discretization method of the cohesive crack with the crack-tip reinforcement is proposed using the virtual node method to represent the discontinuity of the fracture element. These methods are validated through simulating mixed-mode cracking of one-sided notched asymmetric four-point bending beam. Eventually, the proposed methods are applied to RCC gravity dam to study the development rule and propagation path of the interlayer joints, so as to evaluate the effect of different lengths of the interlayer joints on the dam structural performance. The estimated critical values of dam deformation are helpful to prevent the dam failure during long term operation.

Topology Virtualization and Dynamics Shielding Method for LEO Satellite Networks

Virtual Node (VN) method is widely adopted to handle satellite network topological dynamics. However, conventional VN method is insufficient when earth rotation and inter-plane phase difference are considered. An improved VN method based on Celestial Sphere Division is proposed to overcome the defects of the conventional method. An optimized inter-satellite link connecting mode is derived to achieve maximal available links. The optimal VN division solution and addressing scheme are designed to generate a nearly static virtual network and solve the asynchronous switches caused by inter-plane phase difference. Comparison results demonstrate the advantages of proposed method.

LSH-based distributed similarity indexing with load balancing in high-dimensional space

Locality-sensitive hashing (LSH) and its variants are well-known indexing schemes for solving the similarity search problem in high-dimensional space. Traditionally, these indexing schemes are centrally managed and multiple hash tables are needed to guarantee the search quality. However, due to the limitation of storage space and processing capacity of the server, the centralized indexing schemes become impractical for massive data objects. Therefore, several distributed indexing schemes based on peer-to-peer (P2P) networks are proposed, whereas how to ensure load balancing is still one of the key issues. To solve the problem, in this paper, we propose two theoretical LSH-based data distribution models in P2P networks for datasets with homogeneous and heterogeneous $$l_2$$ norms, respectively. Unlike earlier schemes, to our knowledge, we focus on load balancing for a single hash table rather than multiple tables, which has not been considered previously. Then, we propose a static distributed indexing scheme with a novel load balancing indexing mapping method based on the cumulative distribution function by our models. Furthermore, we propose a dynamic load rebalancing algorithm using virtual node method of P2P networks to make the static indexing scheme more practical and robust. The experiments based on synthetic and real datasets show that the proposed distributed similarity indexing schemes are effective and efficient for load balancing in similarity indexing of high-dimensional space.

A Novel Virtual Node Hexahedral Element with Exact Integration and Octree Meshing

The method presented in this work is a 3-dimensional polyhedral finite element (3D PFEM) based on virtual node method. Novel virtual node polyhedral elements (termed as VPHE) are developed here, particularly virtual node hexahedral element (termed as VHE). Stiffness matrices of these polyhedral elements consist of simple polynomials. Thus, a new algorithm is introduced in this paper, which enables exact integration of monomials without a need for high number of integration points and weights. The number of nodes for VHE elements is not restricted, as opposed to the conventional hexahedral elements. This feature enables formulation of transition elements (termed as T-VHE) which are useful to adaptive computation. Performances of the new VHE elements in solid mechanics and conductive heat transfer phenomena are examined through numerical simulations. The new T-VHE elements are utilized in octree mesh. The VHE elements are found to produce good results and T-VHE elements help to reduce number of global nodes for the analysis.

Hp-adaptive finite element method for linear elasticity using higher-order virtual node method

Higher-order polygonal finite elements are developed for adaptive analyses of linear elastic problem. These elements are constructed using virtual node method based on partition of unity coupled with polynomial enrichment functions. Because the element shape functions are polynomials, the stiffness matrix is computed precisely with standard Gauss quadrature rules. Several numerical examples of linear elasticity are presented to validate the accuracy and convergence of the proposed elements. One of the advantages of the proposed elements is that they can be used as transition elements with hanging nodes on higher-order approximation meshes. Building on this advantage, h- and hp-adaptive finite element analyses of numerical examples with local singularities are performed on triangular quadtree meshes in order to demonstrate the performance of the adaptive strategies using the proposed elements.

CPU-GPU mixed implementation of virtual node method for real-time interactive cutting of deformable objects using OpenCL.

Surgical simulators need to simulate interactive cutting of deformable objects in real time. The goal of this work was to design an interactive cutting algorithm that eliminates traditional cutting state classification and can work simultaneously with real-time GPU-accelerated deformation without affecting its numerical stability. A modified virtual node method for cutting is proposed. Deformable object is modeled as a real tetrahedral mesh embedded in a virtual tetrahedral mesh, and the former is used for graphics rendering and collision, while the latter is used for deformation. Cutting algorithm first subdivides real tetrahedrons to eliminate all face and edge intersections, then splits faces, edges and vertices along cutting tool trajectory to form cut surfaces. Next virtual tetrahedrons containing more than one connected real tetrahedral fragments are duplicated, and connectivity between virtual tetrahedrons is updated. Finally, embedding relationship between real and virtual tetrahedral meshes is updated. Co-rotational linear finite element method is used for deformation. Cutting and collision are processed by CPU, while deformation is carried out by GPU using OpenCL. Efficiency of GPU-accelerated deformation algorithm was tested using block models with varying numbers of tetrahedrons. Effectiveness of our cutting algorithm under multiple cuts and self-intersecting cuts was tested using a block model and a cylinder model. Cutting of a more complex liver model was performed, and detailed performance characteristics of cutting, deformation and collision were measured and analyzed. Our cutting algorithm can produce continuous cut surfaces when traditional minimal element creation algorithm fails. Our GPU-accelerated deformation algorithm remains stable with constant time step under multiple arbitrary cuts and works on both NVIDIA and AMD GPUs. GPU-CPU speed ratio can be as high as 10 for models with 80,000 tetrahedrons. Forty to sixty percent real-time performance and 100-200 Hz simulation rate are achieved for the liver model with 3,101 tetrahedrons. Major bottlenecks for simulation efficiency are cutting, collision processing and CPU-GPU data transfer. Future work needs to improve on these areas.

Large-strain elastic viscoplastic consolidation analysis of very soft clay layers with vertical drains under preloading

A very soft clay layer is highly compressible and exhibits significant creep under loading. The classical linearly elastic constitutive relationship and small-strain assumption are not suitable for the consolidation analysis of very soft clays. This paper presents a new large-strain consolidation model that incorporates the Yin–Graham elastic viscoplastic (EVP) constitutive equation for use in studying the consolidation of very soft clay layers with vertical drains under preloading. First, the large-strain fluid continuity equation and the EVP constitutive equation are incorporated into a quadratic differential equation of pore-water pressure and its integral terms. Second, the alternating-direction implicit (ADI) method and virtual node method are adopted to obtain the finite difference solution. A computer program named “BSSDS” is developed for large-strain EVP consolidation analysis of clay layers with vertical drains, taking into account the complicated in situ conditions, such as resistance of vertical drains, smear effects, variation of permeability with void ratio, and multilayered soils. Third, the new large-strain numerical method is applied to the consolidation modeling of very soft clay layers with vertical drains under preloading at a site that is part of the Hong Kong – Shenzhen Western Corridor Link Project. It is found that the foundation settlements of the new large-strain EVP consolidation model have good agreement with the measured data. Finally, three different consolidation models are used to calculate the average degree of consolidation and settlements of the clay layers. The analysis shows that it is essential to consider both large-strain compression and creep effects in the analysis of very soft clay layers with vertical drains under loading.

New Polyhedral Elements Based on Virtual Node Method for Solid Mechanics and Heat Transfer Applications

Finite element method (FEM) is a well-established method and commonly utilized to solve complex engineering problems which cannot be solved analytically. Various element types have been formulated over the years to facilitate engineering analyses using FEM. In this paper, new polyhedral elements are developed by utilizing virtual node method. This paper covers the formulation of shape functions and integration schemes for the new polyhedral elements. These new polyhedral elements have advantages due to the nature of their shape functions which consist of monomials uavbwc. Integration of functions within the element can be accomplished by utilizing an exact integration technique. These polyhedral elements can be utilized to solve real 3 dimensional problems which arise in solid mechanics and heat transfer phenomena.

A novel clustered MongoDB-based storage system for unstructured data with high availability

More and more unstructured data are produced and consumed over network. How to maintain these data and improve the availability and scalability of the storage systems has become a considerable challenge. Although some NoSQL systems such as Dynamo, Cassandra, MongoDB have provided different advantages for unstructured data management, no one can provide flexible query functions like MongoDB, meanwhile guarantee the availability and scalability as Cassandra simultaneously. This paper presents a new high available distributed storage system called MyStore based on an optimized clustered MongoDB for unstructured data. Consistent hash is used to distribute data on multiple MongoDB nodes by applying virtual node method. NWR mode is applied to provide automatic backup operation and guarantee data consistency. And a gossip protocol is taken for exchanging information of failures in the system. Moreover, a user-friendly interface module and an efficient cache module are designed for improving the usability of the system. Based on above strategies, the system can realize high availability for unstructured data storage, while providing complex query functions like rational databases. Moreover, it is applied in a multi-discipline virtual experiment platform named VeePalms that has run practically. Experimental evaluation shows that the methodology is powerful enough not only to enhance the data availability, but also to improve the server's scalability.

Virtual Topology for LEO Satellite Networks Based on Earth-Fixed Footprint Mode

In this letter, a formal model is given to clarify the dynamics and fixity of the virtual topology based on Virtual Node method for Low Earth Orbit (LEO) satellite networks. The formal model can generate few snapshots, well-proportioned snapshot length and less path changes than the physical topology with Satellite-fixed footprint mode. Moreover, it can effectively avoid path stretch and contraction deriving from the satellite's movement. Its application in Multi-layered satellite networks can also overcome the main limitation of conventional Satellite Group and Group Manager method.

A Slot-based Virtual Node Method of Consistent Hashing for Optimization of Index Reconfiguration on Distributed Search

A Slot-based Virtual Node Method of Consistent Hashing for Optimization of Index Reconfiguration on Distributed Search

A second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions

We present a numerical method for the variable coefficient Poisson equation in three-dimensional irregular domains and with interfacial discontinuities. The discretization embeds the domain and interface into a uniform Cartesian grid augmented with virtual degrees of freedom to provide accurate treatment of jump and boundary conditions. The matrix associated with the discretization is symmetric positive definite and equal to the standard 7-point finite difference Poisson stencil away from embedded interfaces and boundaries. Numerical evidence suggests second order accuracy in the L ∞-norm. Our approach improves the treatment of Dirichlet and jump constraints in the recent work of Bedrossian et al. [1] and introduces innovations necessary in three dimensions. Specifically, we construct new constraint-based Lagrange multiplier spaces that significantly improve the conditioning of the associated linear system of equations; we provide a method for cell-local polyhedral approximation to the zero isocontour surface of a level set needed for three-dimensional embedding; and we show that the new Lagrange multiplier spaces naturally lead to a class of easy-to-implement multigrid methods that achieve near optimal efficiency, as shown by numerical examples. For the specific case of a continuous Poisson coefficient in interface problems, we provide an expansive treatment of the construction of a particular solution that satisfies the value jump and flux jump constraints. As in [1], this is used in a discontinuity removal technique that yields the standard 7-point stencil across the interface and only requires a modification to the right-hand side of the linear system.

A second order virtual node method for elliptic problems with interfaces and irregular domains

We present a second order accurate, geometrically flexible and easy to implement method for solving the variable coefficient Poisson equation with interfacial discontinuities or on irregular domains, handling both cases with the same approach. We discretize the equations using an embedded approach on a uniform Cartesian grid employing virtual nodes at interfaces and boundaries. A variational method is used to define numerical stencils near these special virtual nodes and a Lagrange multiplier approach is used to enforce jump conditions and Dirichlet boundary conditions. Our combination of these two aspects yields a symmetric positive definite discretization. In the general case, we obtain the standard 5-point stencil away from the interface. For the specific case of interface problems with continuous coefficients, we present a discontinuity removal technique that admits use of the standard 5-point finite difference stencil everywhere in the domain. Numerical experiments indicate second order accuracy in L ∞.

A novel virtual node method for polygonal elements

A novel polygonal finite element method (PFEM) based on partition of unity is proposed, termed the virtual node method (VNM). To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.

Fatigue Strength Evaluation of Load-Carrying Fillet Weldments under Out-of-Plane Bending Load Using Structural Stress Method

Two types of load carrying fillet weldment, which are typical weld joints in ship structures, were examined under out-of-plane bending load by using structural stress approach. Finite element analyses using both solid and shell elements models have been performed for the assessment of fatigue strength. Basis for the derivation of structural stress method is discussed in detail. The calculated structural stress values for the fatigue strength evaluation of load carrying fillet weldments are independent of mesh size. In this study, drawbacks and doubts associated with applying the structural method such as the guidance of virtual node method and the application of three-dimensional equilibrium condition for solid model have been discussed accompanied by various case studies. In order to solve the problem of the solid model, the alternative method for solid model by using the equilibrium condition of the nodal force has been introduced.