Refinement Algorithm Research Articles

Dynamic Optimization Using Local Collocation Methods and Improved Multiresolution Technique

Dynamic optimization has wide applications in scientific and industrial researches. Multiresolution techniques provide an efficient way to solve dynamic optimization problems but have some disadvantages. An improved multiresolution technique is developed in this paper to overcome these disadvantages. The proposed technique consists of local collocation methods and a multiresolution-based mesh refinement method. New, generalized dyadic meshes are proposed to overcome the dyadic limitation, and the mesh refinement method is improved so that it can start with the coarsest generalized dyadic mesh. Additionally, the proposed technique involves a mesh refinement algorithm to remove the redundant mesh points in the constant control regions by analyzing the control slopes. The technique is applied to three chemical process control optimization problems and compared with other methods to demonstrate its effectiveness. Numerical results show that the proposed technique can solve chemical process control optimization problems accurately and efficiently and has advantages over other methods.

Solving QBF by Abstraction

Many verification and synthesis approaches rely on solving techniques for quantified Boolean formulas (QBF). Consequently, solution witnesses, in the form of Boolean functions, become more and more important as they represent implementations or counterexamples. We present a recursive counterexample guided abstraction and refinement algorithm (CEGAR) for solving and certifying QBFs that exploits structural reasoning on the formula level. The algorithm decomposes the given QBF into one propositional formula for every block of quantifiers that abstracts from assignments of variables not bound by this quantifier block. Further, we show how to derive an efficient certification extraction method on top of the algorithm. We report on experimental evaluation of this algorithm in the solver QuAbS (Quantified Abstraction Solver) which won the most recent QBF competition (QBFEVAL'18). Further, we show the effectiveness of the certification approach using synthesis benchmarks and a case study for synthesizing winning strategies in Petri Games.

Asymmetric Adaptive Particle Refinement in SPH and Its Application in Soil Cutting Problems

In this study, a novel asymmetric adaptive particle refinement algorithm in smoothed particle hydrodynamics (SPH) is developed for soil cutting problems. Each candidate particle that located at the cutting blade of the structure is split into two “children” particles to minimize the oscillation of the contact force. And thus reduce the local instability. To minimize the density refinement error, a numerical method to determine the optimal smoothing lengths for “children” particles is given. To verify the accuracy of proposed algorithm, the adaptive refinement procedure are implemented into two models: one for soil cutting test on plane strain condition and the other for sample drilling test on axisymmetric condition. The observed flow pattern of the soil and contact forces are compared with laboratory experimental data available in the literature. Results indicate that the proposed asymmetric adaptive refinement algorithm could significantly avoid severe local instability and contributes to high-accuracy simulation.

Анализ пределов применимости алгоритма уточнения параметров конечно-элементной модели на основе расчета коэффициентов чувствительности

Анализ пределов применимости алгоритма уточнения параметров конечно-элементной модели на основе расчета коэффициентов чувствительности

Algorithms of the Minimum Spanning Tree in Gas Supply Systems

In this paper, a method for tracing gas networks using the Kruskal algorithm and the Steiner algorithm is considered. The result of the work of algorithms on the example of a bio meta network between agricultural enterprises located on the territory of the Belgorod region is demonstrated. The economic result is determined using Steiner’s refinement algorithm.

A Novel Variational Meshless Method With Radial Basis Functions for Waveguide Eigenvalue Problems

A novel variational meshless method is presented to calculate a large number of modes of a homogeneous waveguide with an arbitrary shape. The proposed technique is based on the variational principle combined with the meshless method using radial basis functions (RBFs). Compared with the more traditional point-matching meshless method with RBFs, the proposed technique leads to a well-conditioned matrix problem, and no preconditioning is needed. An iterative refinement algorithm is also presented, which generates automatically new collocation points and locally defined shape parameters for the RBFs, until a prescribed convergence is reached. As proved through many examples, including waveguides with sharp corners, the variational meshless method permits to calculate a large number of waveguide modes with high precision in a very short computing time.

Local refinement for analysis-suitable++ T-splines

We develop an optimized local refinement algorithm for analysis-suitable++ T-splines (AS++ T-splines) which produces less propagation of control points. We then demonstrate its use as an adaptive framework for isogeometric analysis. AS++ T-splines are a class of T-splines which include analysis-suitable T-spline as a special case, are linearly independent, form a weighted partition of unity and are optimal convergent. These properties, coupled with the local refinement algorithm, make the AS++ T-spline appealing as a better basis both for design and analysis.

Refinement Algorithms for Adaptive Isogeometric Methods with Hierarchical Splines

The construction of suitable mesh configurations for spline models that provide local refinement capabilities is one of the fundamental components for the analysis and development of adaptive isogeometric methods. We investigate the design and implementation of refinement algorithms for hierarchical B-spline spaces that enable the construction of locally graded meshes. The refinement rules properly control the interaction of basis functions at different refinement levels. This guarantees a bounded number of nonvanishing (truncated) hierarchical B-splines on any mesh element. The performances of the algorithms are validated with standard benchmark problems.

3-D Adaptive Finite-Element Modeling of Marine Controlled-Source Electromagnetics with Seafloor Topography Based on Secondary Potentials

We present a solution of using adaptive nodal finite-element (FE) method to solve the marine controlled-source electromagnetic (CSEM) problem for 3-D earth models in the frequency domain. The forward problem is solved based on the secondary Coulomb-gauged electromagnetic (EM) potentials. We implement an adaptive mesh refinement algorithm according to an a posteriori error estimator based on a gradient-recovery operator of the secondary EM potentials. To increase the quality of the mesh at the receiver locations, the elements containing the receiver locations are constrained by assigning them a maximum volume for the initial mesh. An unstructured tetrahedral mesh used in our approach can provide an accurate description of complex structures such as dipping layers and rough topography that are not accurately fitted using structured meshes. We first validate the adaptive FE approach and demonstrate the convergence of the adaptive grid refinement procedure using a 1-D layered model. The canonical disc model example illustrates the capability of the adaptive FE approach for 3-D CSEM modeling. The bathymetry model shows that the algorithm is well suited to deal with complex seafloor topography, which needs to be simulated exactly to avoid the misinterpretation of marine CSEM data sets.

Resource Demand Misalignment: An Important Factor to Consider for Reducing Resource Over-Provisioning in Cloud Datacenters

Previous resource provisioning strategies in cloud datacenters allocate physical resources to virtual machines (VMs) based on the predicted resource utilization pattern of VMs. The pattern for VMs of a job is usually derived from historical utilizations of multiple VMs of the job. We observed that these utilization curves are usually misaligned in time, which would lead to resource over-prediction and hence over-provisioning. Since this resource utilization misalignment problem has not been revealed and studied before, in this paper, we study the VM resource utilization from public datacenter traces and Hadoop benchmark jobs to verify the commonness of the utilization misalignments. Then, to reduce resource over-provisioning, we propose three VM resource utilization pattern refinement algorithms to improve the original generated pattern by lowering the cap of the pattern, reducing cap provision duration and varying the minimum value of the pattern. We then extend these algorithms to further improve the resource efficiency by considering periodical resource demand patterns that have multiple pulses in a pattern. These algorithms can be used in any resource provisioning strategy that considers predicted resource utilizations of VMs of a job. We then adopt these refinement algorithms in an initial VM allocation mechanism and test them in trace-driven experiments and real-world testbed experiments. The experimental results show that each improved mechanism can increase resource utilization, and reduce the number of PMs needed to satisfy tenant requests. Also, our extended refinement algorithms are effective in improving resource efficiency of the refinement algorithms.

The influence of radial entrance width of the circular cavity on incident shock wave focusing

Despite the achievement of shock wave focusing with certain reflectors, the influence of the radial entrance width of a circular cavity on the flow field has yet to be addressed. In this study, we systematically investigated the effects of the shock wave focusing process in a cavity based on the radial entrance widths. An experimental system was installed to research the evolution of the flow field under conditions with different radial entrance widths of 3.0, 11.1, 19.5, and 33.0 mm. A schlieren system was used to photograph the structures of the flow field in the cavity, and a data acquisition system was used to record the dynamic pressure histories of different points. A numerical simulation was carried out to investigate greater details of the shock wave focusing process. A third-order strong stability-preserving Runge-Kutta method, third-order weighed essential non-oscillation scheme, and an adaptive mesh refinement algorithm were adopted to simulate the shock wave reflection, diffraction, and focus process. Good agreement between the experimental and numerical results was observed. By comparing the evolution process of the flow field under the conditions of four different entrance cavity widths, we found that when the entrance width was 19.5 mm, there was the stronger intensity of the shock wave focusing in the focal region, and the larger pressure value at the apex of the cavity than the other three entrance widths, occur. This study improves our understanding of shock wave focusing.

Discontinuous Lyapunov functions for a class of piecewise affine systems

In this paper, a Lyapunov-based method is provided to study the local asymptotic stability of planar piecewise affine systems with continuous vector fields. For such systems, the state space is supposed to be partitioned into several bounded convex polytopes. A piecewise affine function, not necessarily continuous on the boundaries of the polytopic partitions, is proposed as a candidate Lyapunov function. Then, sufficient conditions for the local asymptotic stability of the system, including a monotonicity condition at switching instants, are formulated as a linear programming problem. In addition, when the problem does not have a feasible solution based on the original partitions of the system, a new partition refinement algorithm is presented. In this way, more flexibility can be provided in searching for the Lyapunov function. Owing to relaxation of the continuity condition imposed on the system boundaries, the proposed method reaches to less conservative results, compared with the previous methods based on continuous piecewise affine Lyapunov functions. Simulation results illustrate the effectiveness of the proposed method.

Topological Disk Mesh Morphing Based on Area-Preserving Parameterization

Mesh morphing is a technique which gradually deforms a mesh into another one. Mesh parameterization, a powerful tool adopted to establish the one-to-one correspondence map between different meshes, is of great importance in 3D mesh morphing. However, current parameterization methods used in mesh morphing induce large area distortion, resulting in geometric information loss. In this paper, we propose a new morphing approach for topological disk meshes based on area-preserving parameterization. Conformal mapping and Mobius transformation are computed firstly as rough alignment. Then area preserving parameterization is computed via the discrete optimal mass transport map. Features are exactly aligned through radial basis functions. A surface remeshing scheme via Delaunay refinement algorithm is developed to create a new mesh connectivity. Experimental results demonstrate that the proposed method performs well and generates high-quality morphs.

Iterative refinement for symmetric eigenvalue decomposition

An efficient refinement algorithm is proposed for symmetric eigenvalue problems. The structure of the algorithm is straightforward, primarily comprising matrix multiplications. We show that the proposed algorithm converges quadratically if a modestly accurate initial guess is given, including the case of multiple eigenvalues. Our convergence analysis can be extended to Hermitian matrices. Numerical results demonstrate excellent performance of the proposed algorithm in terms of convergence rate and overall computational cost, and show that the proposed algorithm is considerably faster than a standard approach using multiple-precision arithmetic.

Quantitative phase-field lattice-Boltzmann study of lamellar eutectic growth under natural convection.

The influence of natural convection on lamellar eutectic growth was determined by a comprehensive phase-field lattice-Boltzmann study for Al-Cu and CBr_{4}-C_{2}Cl_{6} eutectic alloys. The mass differences resulting from concentration differences led to the fluid flow and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency. By means of carefully designed "numerical experiments", the eutectic growth under natural convection was explored and a simple analytical model was proposed to predict the adjustment of the lamellar spacing. Furthermore, by alternating the solute expansion coefficient, initial lamellar spacing, and undercooling, the microstructure evolution was presented and compared with the classical eutectic growth theory. Results showed that both interfacial solute distribution and average curvature were affected by the natural convection, the effect of which could be further quantified by adding a constant into the growth rule proposed by Jackson and Hunt [Jackson and Hunt, Trans. Metall. Soc. AIME 236, 1129 (1966)].

Joint refinement model for the spin resolved one-electron reduced density matrix of YTiO3 using magnetic structure factors and magnetic Compton profiles data.

In this paper, we propose a simple cluster model with limited basis sets to reproduce the unpaired electron distributions in a YTiO3 ferromagnetic crystal. The spin-resolved one-electron-reduced density matrix is reconstructed simultaneously from theoretical magnetic structure factors and directional magnetic Compton profiles using our joint refinement algorithm. This algorithm is guided by the rescaling of basis functions and the adjustment of the spin population matrix. The resulting spin electron density in both position and momentum spaces from the joint refinement model is in agreement with theoretical and experimental results. Benefits brought from magnetic Compton profiles to the entire spin density matrix are illustrated. We studied the magnetic properties of the YTiO3 crystal along the Ti-O1-Ti bonding. We found that the basis functions are mostly rescaled by means of magnetic Compton profiles, while the molecular occupation numbers are mainly modified by the magnetic structure factors.

Accurate stereo matching based on weighted nonlocal aggregation for enhanced disparity refinement

Disparity refinement is an important step to enhance the accuracy of stereo matching. This paper extends the scheme of a recent successful approach, namely the nonlocal disparity refinement algorithm, to exploit the initial disparity map in the aggregation phase of disparity refinement, in addition to the information of spatial distance and intensity difference. In addition, we propose a constraint function applied to the matching cost that constrains the scope of dissimilarity measures to further improve the accuracy of disparity refinement. Extensive experimental comparisons with several state-of-the-art methods using the Middlebury Stereo Evaluation version 3 datasets show that the proposed scheme has a great advantage in disparity refinement.

A spectral clustering approach to network-aware virtual request partitioning

Virtual request partitioning is an essential subproblem of two common problems in virtual networks, namely, virtual network embedding (VNE) and virtual machine placement (VMP). In this study, we consider a network-aware variant of the problem where the objective is to partition a virtual request so as to minimize the total amount of inter-cluster traffic. This problem is equivalent to the (k, v)-balanced partitioning problem, an NP-complete problem. To handle the inherent complexity of this problem, we develop a spectral clustering-based partitioning scheme that produces good solutions in a reasonable amount of time. Our solution consists of several components: (a) spectral clustering, (b) a Constrained k-means partitioning algorithm that ensures that capacity limits for clusters are met, and for which we present a polynomial-time greedy algorithm, and (c) a greedy refinement algorithm using simulated annealing to further improve the clustering solution. Simulation results indicate that our algorithm outperforms existing partitioning schemes in terms of inter-cluster traffic minimization.

Spatiotemporal Local-Remote Senor Fusion (ST-LRSF) for Cooperative Vehicle Positioning.

Vehicle positioning plays an important role in the design of protocols, algorithms, and applications in the intelligent transport systems. In this paper, we present a new framework of spatiotemporal local-remote sensor fusion (ST-LRSF) that cooperatively improves the accuracy of absolute vehicle positioning based on two state estimates of a vehicle in the vicinity: a local sensing estimate, measured by the on-board exteroceptive sensors, and a remote sensing estimate, received from neighbor vehicles via vehicle-to-everything communications. Given both estimates of vehicle state, the ST-LRSF scheme identifies the set of vehicles in the vicinity, determines the reference vehicle state, proposes a spatiotemporal dissimilarity metric between two reference vehicle states, and presents a greedy algorithm to compute a minimal weighted matching (MWM) between them. Given the outcome of MWM, the theoretical position uncertainty of the proposed refinement algorithm is proven to be inversely proportional to the square root of matching size. To further reduce the positioning uncertainty, we also develop an extended Kalman filter model with the refined position of ST-LRSF as one of the measurement inputs. The numerical results demonstrate that the proposed ST-LRSF framework can achieve high positioning accuracy for many different scenarios of cooperative vehicle positioning.

Decomposing and Cluster Refinement Design Method for Application-Specific Network-on-Chips

Along with higher and higher integration of intellectual properties (IPs) on a single chip, traditional bus-based system-on-chips (SoC) meets several design difficulties (such as low scalability, high power consumption, packet latency and clock tree problem). As a promising solution, network-on-chips (NoC) has been proposed and widely studied. In this work, a novel algorithm for NoC topology synthesis, which is decomposing and cluster refinement (DCR) algorithm, has been proposed to minimize the total power consumption of application-specific NoC. This algorithm is composed of two stages: decomposing with cluster generation, and cluster refinement. For partitioning and cluster generation, an initial low-power solution for NoC topology is generated. For cluster refinement, the clustering is optimized by performing floorplan to further reduce power consumption. Meanwhile, a good tradeoff between power consumption and CPU time can be achieved. Experimental results show that the proposed method outperforms the existing work.