Large Problems Research Articles

Phase-field lattice Boltzmann model with singular mobility for quasi-incompressible two-phase flows.

In this paper, a lattice Boltzmann for quasi-incompressible two-phase flows is proposed based on the Cahn-Hilliard phase-field theory, which can be viewed as an improved model of a previous one [Yang and Guo, Phys. Rev. E 93, 043303 (2016)2470-004510.1103/PhysRevE.93.043303]. The model is composed of two LBE's, one for the Cahn-Hilliard equation(CHE) with a singular mobility, and the other for the quasi-incompressible Navier-Stokes equations(qINSE). Particularly, the LBE for the CHE uses an equilibrium distribution function containing a free parameter associated with the gradient of chemical potential, such that the variable (and even zero) mobility can be handled. In addition, the LBE for the qINSE uses an equilibrium distribution function containing another free parameter associated with the local shear rate, such that the large viscosity ratio problems can be handled. Several tests are first carried out to test the capability of the proposed LBE for the CHE in capturing phase interface, and the results demonstrate that the proposed model outperforms the original LBE model in terms of accuracy and stability. Furthermore, by coupling the hydrodynamic equations, the tests of double-stationary droplets and droplets falling problems indicate that the proposed model can reduce numerical dissipation and produce physically acceptable results at large time scales. The results of droplets falling and phase separation of binary fluid problems show that the present model can handle two-phase flows with large viscosity ratio up to the magnitude of 10^{4}.

An implicit Updated Lagrangian Fragile Points Method with a support domain refinement scheme for solving large deformation problems

AbstractEngineering structures may undergo large deformations, but simulating is still challenging for existing numerical methods, for example, the element‐based methods struggle from the mesh distortion and the strong form particle‐based methods exhibit tensile instability. This article aims on presenting a novel numerical method for large deformation simulations, which is named the implicit Updated Lagrangian Fragile Points Method (ULFPM). The point‐based nature of the proposed method ensures immunity to mesh distortion, and its stability is guaranteed by its foundation on weak form formulations. For verifications, the proposed implicit ULFPM has been applied to several large deformation problems. For all the examples, the proposed method is able to provide reliable results with a good agreement with the reference results. Moreover, the implicit ULFPM performs better than the Finite Element Method to some extent for extremely large deformation problems. It is also discussed that the accuracy of the implicit ULFPM is improved significantly by using the support domain refinement scheme. The examples indicate that the proposed method can serve as a reliable tool for predicting the large deformations of structures in engineering practices.

Enhanced methods for the weight constrained shortest path problem

AbstractThe classic problem of constrained pathfinding is a well‐studied, yet challenging, network optimization problem with a broad range of applications in various areas such as communication and transportation. The weight constrained shortest path problem (WCSPP), the base form of constrained pathfinding with only one side constraint, aims to plan a cost‐optimum path with limited weight/resource usage. Given the bi‐criteria nature of the problem (i.e., dealing with the cost and weight of paths), methods addressing the WCSPP have some common properties with bi‐objective search. This article leverages the recent state‐of‐the‐art techniques in both constrained pathfinding and bi‐objective search and presents two new solution approaches to the WCSPP on the basis of A* search, both capable of solving hard WCSPP instances on very large graphs. We empirically evaluate the performance of our algorithms on a set of large and realistic problem instances and show their advantages over the state‐of‐the‐art algorithms in both time and space metrics. This article also investigates the importance of priority queues in constrained search with A*. We show with extensive experiments on both realistic and randomized graphs how bucket‐based queues without tie‐breaking can effectively improve the algorithmic performance of exhaustive A*‐based bi‐criteria searches.

An Accelerated Fixed-Point Algorithm Applied to Quadratic Convex Separable Knapsack Problems

In this article, we propose a root-finding algorithm for solving a quadratic convex separable knapsack problem, which is more straightforward than existing methods and competitive in practice. Besides, we also present an extension of the proposal, which improves its computational time, and then we incorporate the accelerated Anderson’s and Aitken’s fixed-point algorithms to obtain better results. The algorithm only performs function evaluations. We present partial convergence results of the algorithm. Moreover, we illustrate superior computational results in medium and large problems as well as the applicability of the algorithm with real-life applications to show their efficiency.

Pre-Numerical Tests for a New Conjugate Gradient Method

The performance of a new beta in conjugate gradient method is generally measured on its CPU time and the number of iterations using large scale problems without concerning the accuracy of the solution attained. The method is claimed to be the best when less CPU time is used in comparison with the other classical beta. However, the accuracy of the solution gained compared to the exact solution of the function has never been tested as part of the performance measurement. Our previous research has already proven that our new beta perform well in both speed and number of iterations used. Therefore, in this research, we will accommodate this with alternative numerical test on the new beta in assessing the accuracy of the gained solution. This is to further ensure the efficiency of the new beta. Assessment was done with four other classical conjugate gradient methods on fourteen small scale problems. Results attained were promising to be tested for more tests in real functional problems.

Uncertainties in measuring precipitation hinders precise evaluation of loss of diversity in biomes and ecotones

Assessing changes in the distribution of biological communities that share a climate (biomes) is essential for estimating their vulnerability to climate change. We use CMIP6 climate models to calculate biome changes as featuring in classifications such as Holdridge’s Life Zones (climate envelopes). We found that transitional zones between biomes (known as ecotones) are expected to decline under all climate change scenarios, but also that model consensus remains low. Accurate assessments of diversity loss are limited to certain areas of the globe, while model consensus is still poor for half of the planet. We identify where there are robust estimates of changes in biomes and ecotones, and where consensus is lacking. We argue that caution should be exercised in measuring biodiversity loss in the latter, but that greater confidence can be placed in the former. We find that shortcomings in the life zone classification are related to inter-model variability, which ultimately depends on a larger problem, namely the accurate estimation of precipitation compared to CRU. Application of the methodology to other climate classifications confirms the findings.

An Improved Alternating Direction Method of Multipliers for Matrix Completion

Abstract Matrix completion is widely used in information science fields such as machine learning and image processing. The alternating direction method of multipliers (ADMM), due to its ability to utilize the separable structure of the objective function, has become an extremely popular approach for solving this problem. But its subproblems can be computationally demanding. In order to improve computational e ciency, for large scale matrix completion problems, this paper proposes an improved ADMM by using convex combination technique. Under certain assumptions, the global convergence of the new algorithm is proved. Finally, we demonstrate the performance of the proposed algorithms via numerical experiments.

Compressive Sensing Enhanced Multilevel Characteristic Basis Function Method for Analyzing Electrically Large Scattering Problems

Compressive Sensing Enhanced Multilevel Characteristic Basis Function Method for Analyzing Electrically Large Scattering Problems

Enabling Delay-Guaranteed Congestion Control With One-Bit Feedback in Cellular Networks

Unexpected large packet delays are often observed in cellular networks due to huge network queuing caused by excessive traffic coming into the network. To deal with the large queue problem, many congestion control algorithms try to find out how much traffic the network can accommodate, either by measuring network performance or by directly providing explicit information. However, due to the nature of the control in which queue growth should be observed or the necessity to modify the overall network architecture, existing algorithms are experiencing difficulties in keeping queues within a strict bound. In this paper, we propose a novel congestion control algorithm based on simple feedback, ECLAT which can provide bounded queuing delay using only one-bit signaling already available in traditional network architecture. To do so, a base station or a router running ECLAT 1) calculates how many packets each flow should transmit and 2) analyzes when congestion feedback needs to be forwarded to adjust the flow’s packet transmission to the desired rate. Our extensive experiments in our testbed demonstrate that ECLAT achieves strict queuing delay bounds, even in the dynamic cellular network environment.

Improved cooperative Ant Colony Optimization for the solution of binary combinatorial optimization applications

AbstractBinary combinatorial optimization plays a crucial role in various scientific and engineering fields. While deterministic approaches have traditionally been used to solve these problems, stochastic methods, particularly metaheuristics, have gained popularity in recent years for efficiently handling large problem instances. Ant Colony Optimization (ACO) is among the most successful metaheuristics and is frequently employed in non‐binary combinatorial problems due to its adaptability. Although for binary combinatorial problems ACO can suffer from issues such as rapid convergence to local minima, its eminently parallel structure means that it can be exploited to solve large and complex problems also in this field. In order to provide a versatile ACO implementation that achieves competitive results across a wide range of binary combinatorial optimization problems, we introduce a parallel multicolony strategy with an improved cooperation scheme to maintain search diversity. We evaluate our proposal (Binary Parallel Cooperative ACO, BiPCACO) using a comprehensive benchmark framework, showcasing its performance and, most importantly, its flexibility as a successful all‐purpose solver for binary combinatorial problems.

Replay with Feedback: How does the performance of HPC system impact user submission behavior?

High Performance Computing (HPC) is a key infrastructure to solve large scale scientific problems, from weather to quantum simulations. Scheduling jobs in HPC infrastructures is complex due to their scale, the different behaviors of their users, and the multiple objectives, from performance to ecological impact. Schedulers are evaluated on data center simulations, due to the complexity and cost of evaluating them in-situ. One key element for this evaluation is the behavioral model of users. Most studies are limited to replaying past workload of existing data centers. This reduces the realism of performance evaluation in cases where the scheduler and the hardware infrastructure are not exactly the same. Any such change would potentially impact the behavior of the users.In this article we introduce a novel model “Replay with Feedback” accounting for the impact of HPC system performances on user submission behavior in simulations. Instead of keeping the original timestamps of job submissions, we exhibit and use the relationships between each user jobs. We propose an open-source implementation of this model along with an extensive and reproducible set of experiments to assess the impact of the scheduler and infrastructure changes. We also provide new metrics adapted to the flexibility of user submission behaviors. Results show that using this model, we advance towards more realistic simulations of schedulers in HPC systems.

Study on dynamic response of cushion layer-reinforced concrete slab under rockfall impact based on smoothed particle hydrodynamics and finite-element method coupling

Abstract In the rockfall prevention and control project, the reinforced concrete (RC) slab and sand (gravel soil) soil cushion layer are commonly used to form the protection structure, thereby resisting the rockfall impact. Considering that the oversized deformation of the cushion layer under impact load using the finite element simulation cannot converge, this article establishes a numerical calculation model using smoothed particle hydrodynamics–finite-element method coupling (SPH–FEM). First, the standard Lagrange finite-element mesh is established for the whole model using ABAQUS, and then the finite-element mesh of the soil cushion layer is converted to SPH particle at the initial moment of the calculation, and finally the calculation results are solved and outputted. The results indicate that, compared with the results of the outdoor rockfall impact test, the relative errors of the rockfall impact force and the displacement of the RC slab are within 10%, which proves the rationality of the coupling algorithm; moreover, in terms of the numerical simulation, the SPH–FEM coupling algorithm is more practical than the finite element for reproducing the mobility of the rockfall impacting the sand and soil particles. In addition, at an impact speed of less than 12 m·s−1, the cushion layer is able to absorb more than 85% of the impact energy, which effectively ensures that the RC slab is in an elastic working state under small impact energy and does not undergo destructive damage under large impact energy; the peak impact force of the rockfall is approximately linear with the velocity, and the simulated value of the peak impact force is basically the same as that of the theoretical value of Hertz theory; the numerical simulation is good for reproducing the damage process of the RC slab in accordance with the actual situation. The SPH–FEM coupling algorithm is more justified than the FEM in simulating the large deformation problem, and it can provide a new calculation method for the design and calculation of the rockfall protection structure.

Piecewise linear approximation for MILP leveraging piecewise convexity to improve performance

To realize adaptive operation planning with MILP unit commitment, piecewise-linear approximations of the functions that describe the operating behavior of devices in the energy system have to be computed. We present an algorithm to compute a piecewise-linear approximation of a multi-variate non-linear function. The algorithm splits the domain into two regions and approximates each region with a set of hyperplanes that can be translated to a convex set of constraints in MILP. The main advantage of this “piecewise-convex approximation” (PwCA) compared to more general piecewise-linear approximation with simplices is that the MILP representation of PwCA requires only one auxiliary binary variable. For this reason, PwCA yields significantly faster solving times in large MILP problems where the MILP representation of certain functions has to be replicated many times, such as in unit commitment. To quantify the impact on solving time, we compare the performance using PwCA with the performance of simplex approximation with logarithmic formulation and show that PwCA outperforms the latter by a big margin. For this reason, we conclude that PwCA will be a useful tool to set up and solve large MILP problems such as arise in unit commitment and similar engineering optimization problems.

Robust Positioning Estimation for Underwater Acoustics Targets with Use of Multi-Particle Swarm Optimization

With the extensive application of sensor technology in scientific ocean research, ocean resource exploration, underwater engineering construction, and other fields, underwater target positioning technology has become an important support for the ocean field. This paper proposes a robust positioning algorithm that combines the disadvantages of distributed estimation and particle swarm optimization, which can solve the large localization error problem caused by uncertainties in underwater acoustic communication and sampling processes. Considering the presence of ranging anomalies and sampling packet loss in underwater acoustic measurements, a weighted coupling filling method is used to correct the outliers in an underwater acoustic ranging signal. Based on the mapping model from the element array to the underwater acoustic responder, an unconstrained optimization algorithm for one-time localization estimation of underwater acoustic targets was established. Based on the one-time localization estimation results of underwater acoustic targets, an improved multi-particle swarm optimization estimation based on interactive search is proposed, which improves the accuracy of underwater target localization. The numerical results show that the positioning accuracy of the proposed algorithm can be effectively enhanced in cases of distance measurement errors and azimuth measurement errors. Compared with the positioning error before optimization, the positioning error can be reduced after optimization. Additionally, the experiment was carried out in the underwater environment of Hangzhou Qiandao Lake, which verified the positioning performance of the proposed algorithm.

Solving Resource Allocation Problem in Wifi Network by Dantzig-Wolfe Decomposition Algorithm

Online advertising and advancements is a recent trend in marketing technology, in this context we consider a new form of contract which allows advertisers to specify in the Wifi system. Based on the structure of the system, we have to organize and manage resource allocation such that the guaranteed display is satisfied. We introduce a new mathematical model and develop an optimization framework that aims to optimize “fairness” of allocation each campaign over its targeted location. Because of large scale problem, the Dantzig-Wolfe decomposition is proposed for solving it. Dantzig-Wolfe decomposition is a technique for dealing with large scale linear programming and modified to solve linear integer programming, nonlinear programming. Especially, it is used mostly in linear programming when its size is very large, and its structure is appropriate. The technique has been successfully applied in a variety of contexts. In this paper, we introduce a new model of a resource allocation problem in Wifi network and represent Dantzig-Wolfe decomposition for solving this problem by dividing the number of advertisement impressions when users access the Wifi network. The numerical simulation shows the efficiency of our proposed method.

A hydro-mechanical coupled contact method for two-phase geotechnical large deformation problems within the SNS-PFEM framework

This paper proposes a novel numerical algorithm to solve frictional contact problems in two-phase porous media, accounting for the large deformation and interface fluid flow, within the framework of the Stable Node-based Smoothed Particle Finite Element Method (SNS-PFEM). The proposed approach builds on our previous work that was only designed for single-phase large deformation contact problems. Within this work, the hydro-mechanical coupling system is discretized using equal-order interpolation, with a polynomial pressure projection method to eliminate the pore pressure instability. Surface-to-surface discretization is then applied to formulate the contact constraint of the two-phase porous medium. Using the dual Lagrange multiplier approach, a coordinate transformation is introduced to enforce the contact constraint of the solid phase. This transformation is subsequently utilized to develop a new interface fluid element, which serves as a tool to model the fluid exchange behaviour between porous media and contact gaps. Different from existing interface fluid elements, the proposed element is constructed based on the contact algorithm, thereby enabling it to handle non-conforming interfaces and tackle challenges associated with large sliding problems. Furthermore, the proposed method can maintain a well-conditioned system matrix throughout the computation process. These distinctive attributes significantly enhance the flexibility of numerical modelling. Finally, the accuracy and performance of our method are verified through four numerical examples. The results show that the proposed method can effectively simulate various geotechnical problems, including multi-layer soil consolidation, fluid-soil-structure interaction, and geological interface-controlled slope failure.

Time-dependent behavior of reinforcement rock unit anchored by energy-absorbing bolt for large deformation control in tunneling

The energy-absorbing bolt is designed to counteract both burst-prone and squeezing rock conditions in rock excavation. In this paper, the mechanical contribution of energy-absorbing bolts installed systematically around tunnels excavated in rock masses was investigated based on the assumptions of the reinforced rock unit (RRU) model. The time-dependent behavior of rock with a large deformation problem was simulated using a Nishihara model, while that of an energy-absorbing bolt was simplified by a rheological model connecting a Hookean elastic element and a Saint-Venant element in series. The mechanical model of RRU anchored by an energy-absorbing bolt was established by connecting the rock mass model and the energy-absorbing bolt model in a parallel combination. The closed-form solution presented the time-dependent behavior of RRU under an instantaneously applied tension stress and an linearly increasing load, respectively. The results showed the reinforcement could reduce the time-dependent deformation of the reinforced region of tunnels significantly. A preliminary estimate of NPR-bolt reinforcement for large-deformation controls in the Muzhailing tunnel was carried out using the proposed model. The results showed that the NPR cables could have critical effects in controlling the large deformation of the tunnel.

A gradient descent akin method for constrained optimization: algorithms and applications

We present a ‘gradient descent akin’ method (GDAM) for constrained optimization problem, i.e. the search direction is computed using a linear combination of the negative and normalized objective and constraint gradient. We give fundamental theoretical guarantees on the global convergence of the method. This work focuses on the algorithms and applications of GDAM. We present computational algorithms that adapt common strategies for the gradient descent method. We demonstrate the potential of the method using two engineering applications, shape optimization and sensor network localization. When practically implemented, GDAM is robust and very competitive in solving the considered large and challenging optimization problems.

Towards High-Performance Linear Potential Flow BEM Solver with Low-Rank Compressions

The interaction of water waves with floating bodies can be modeled with linear potential flow theory and numerically solved with the boundary element method (BEM). This method requires the construction of dense matrices and the resolution of the corresponding linear systems. The cost of this method in terms of time and memory grows at least quadratically with the size of the mesh, and the resolution of large problems (such as large farms of wave energy converters) can, thus, be very costly. Approximating some blocks of the matrix with data-sparse matrices can limit this cost. While matrix compression with low-rank blocks has become a standard tool in the larger BEM community, the present paper provides its first application (to our knowledge) to linear potential flows. In this paper, we assess how efficiently low-rank blocks can approximate interaction matrices between distant meshes when using the Green function of linear potential flow. Due to the complexity of this Green function, a theoretical study is difficult, and numerical experiments are used to test the approximation method. Typical results on large arrays of floating bodies show that 99% of the accuracy can be reached with 10% of the coefficients of the matrix.

Dollo-CDP: a polynomial-time algorithm for the clade-constrained large Dollo parsimony problem

The last decade of phylogenetics has seen the development of many methods that leverage constraints plus dynamic programming. The goal of this algorithmic technique is to produce a phylogeny that is optimal with respect to some objective function and that lies within a constrained version of tree space. The popular species tree estimation method ASTRAL, for example, returns a tree that (1) maximizes the quartet score computed with respect to the input gene trees and that (2) draws its branches (bipartitions) from the input constraint set. This technique has yet to be used for parsimony problems where the input are binary characters, sometimes with missing values. Here, we introduce the clade-constrained character parsimony problem and present an algorithm that solves this problem for the Dollo criterion score in O(|Sigma |^{3.726}(n+k) + |Sigma |^{1.726}nk) time, where n is the number of leaves, k is the number of characters, and Sigma is the set of clades used as constraints. Dollo parsimony, which requires traits/mutations to be gained at most once but allows them to be lost any number of times, is widely used for tumor phylogenetics as well as species phylogenetics, for example analyses of low-homoplasy retroelement insertions across the vertebrate tree of life. This motivated us to implement our algorithm in a software package, called Dollo-CDP, and evaluate its utility for analyzing retroelement insertion presence / absence patterns for bats, birds, toothed whales as well as simulated data. Our results show that Dollo-CDP can improve upon heuristic search from a single starting tree, often recovering a better scoring tree. Moreover, Dollo-CDP scales to data sets with much larger numbers of taxa than branch-and-bound while still having an optimality guarantee, albeit a more restricted one. Lastly, we show that our algorithm for Dollo parsimony can easily be adapted to Camin-Sokal parsimony but not Fitch parsimony.