Relaxation Method Research Articles

Investigating the numerical stability of dynamic relaxation methods with automatic load-increment schemes to improve snap-back prediction

Investigating the numerical stability of dynamic relaxation methods with automatic load-increment schemes to improve snap-back prediction

Nonlinear Isogeometric Analyses of Instabilities in Thin Elastic Shells Exhibiting Combined Bending and Stretching

Abstract Thin structures like shells are highly susceptible to mechanical instabilities. They can undergo large nonlinear elastic deformations while exhibiting combined bending and stretching modes of deformation. Here, we propose a new displacement-based finite element (FE) formulation based on the isogeometric discretization of Koiter’s nonlinear shell theory and use of the method of dynamic relaxation (DR) to solve equilibrium configurations of problems involving fine-scale and hierarchical wrinkling and buckling. No imperfection seeding is required to trigger instabilities. The use of the NURBS basis provides a rotation-free, conforming, higher-order spatial continuity such that curvatures and membrane strains can be computed directly from interpolating the position vectors of the control points using spatial finite differences. The pseudo-dissipative FE dynamical system is updated through explicit time integration and made scalable for parallel computing using a message passing interface (MPI). The proposed FE method is successfully benchmarked against several numerical and experimental results.

Optimized Schwarz Waveform Relaxation Methods for the Telegrapher Equation

Optimized Schwarz Waveform Relaxation Methods for the Telegrapher Equation

A Lagrangian relaxation approach for algae-based biofuel supply chain network design under uncertainty and pricing issue.

Biofuel has gained significant attention as a potential source to meet fuel demands instead of fossil fuel. The price of biofuel and alternative fuel have a considerable impact on biofuel demand. Thus, it is important to design a biofuel supply chain network that incorporates the biofuel price into an elastic demand. More precisely, a variable demand, including customer importance level (to the environment), biofuel price, and substituted fuel price, is considered in this research. Furthermore, this research presents a bi-objective mixed-integer quadratic formulation that aims to maximize the total profit of the supply chain and carbon absorption in harvesting areas. The problem is solved by the ε-constraint and lagrangian relaxation methods due to its complexity. Moreover, substituted fuel price uncertainty is addressed by two-stage stochastic programming. Finally, a real case study utilizing the data envelopment analysis approach is applied to assess the efficiency and currency of the addressed model. Several consequences are illustrated in the case study, such as rich areas for exporting algae, suggesting hub locations for biofuel production, etc.

Integrated energy microgrids participating in voltage regulation ancillary services: An improved ADMM based distributed optimization approach

AbstractThe integrated energy microgrid (IEM) has good potential for both active and reactive power regulation, which are gradually becoming critical resources for participating in power system ancillary services. This paper constructs a distributed optimization model for the IEMs participating in voltage regulation ancillary services by considering multiple physical network constraints. To reduce computational complexity, the DistFlow power flow model and the second‐order cone relaxation method are introduced to transform the optimization model into a second‐order cone programming problem. Moreover, an improved accelerated consensus alternating direction method of multipliers algorithm is proposed to accelerate distributed optimization solutions of the model while protecting user privacy. Finally, the proposed optimization model and solution method are tested in the modified IEEE‐33 node test case to verify their effectiveness and feasibility.

Modeling the effect of external load variations on single, serie and parallel connected microbial fuel cells

This paper presents a microbial fuel cell (MFC) model designed to analyze the effect of the external load on MFC performance. The model takes into account the voltage and the chemical oxygen demand (COD) dependence on the external load. The value of the model parameters were calibrated by means of the voltage relaxation method tests using a controlled load current. Laboratory measurements and MATLAB Simulink model computations were used to validate the proposed model. The tests results demonstrated that the proposed model accurately predicts the voltage and COD evolution during the batch cycle of the MFC. The root mean square error (RMSE) was used to assess the fitting goodness of the model. The RMSE of COD and voltage generation was in all the cases lower than 4%, predicting accurately the behaviour of single MFC as well as MFC connected in series or parallel.

Thirty-five years of personalized promotion. The contribution of medicine in the workplace

Abstract Issue/problem Occupational medicine has always had the task of identifying and solving problems caused by exposure to occupational risks and improving the health conditions of workers. This traditional prevention task can be advantageously associated with promotional activities to reduce the incidence of non-communicable diseases. Description of the problem Since the end of the 1980s we have conducted health promotion interventions in the workplace, integrated into the company’s occupational prevention plan. The results, discussed internationally, have allowed the improvement of projects such as the one presented here, aimed at the prevention of cardiovascular and metabolic risks. Results Workers carry out a clinical check integrated with blood chemistry tests, actigraphic measurement of physical activity and sleep, bioimpedance measurement and plicometry, to objectify the data of interest. Furthermore, they keep a food diary and answer questionnaires on lifestyle, stress, and sleep. They receive personalized non-pharmacological treatment aimed at making salutogenic changes to diet, sleep, physical activity, and relaxation methods. They are monitored monthly and carry out a follow-up after six months. The pilot study, conducted on 20 healthcare workers with previously undiagnosed metabolic problems, indicates a significant improvement in abdominal circumference, systolic blood pressure and sleep duration in the third month. Workers report a high level of satisfaction with the initiative, a lower level of occupational stress and a higher quality of sleep. Lessons Accumulated experience demonstrates that projects of this type are feasible, sustainable, and advantageous and can be applied to companies of all sizes, regardless of the quantity of resources available. Key messages • Health promotion in the workplace can contribute to the reduction of chronic non-communicable diseases. • The active participation of workers in health promotion activities contributes to improving job engagement and satisfaction derived from work.

Proton ARC based LATTICE radiation therapy: feasibility study, energy layer optimization and LET optimization

Objective.LATTICE, a spatially fractionated radiation therapy (SFRT) modality, is a 3D generalization of GRID and delivers highly modulated peak-valley spatial dose distribution to tumor targets, characterized by peak-to-valley dose ratio (PVDR). Proton LATTICE is highly desirable, because of the potential synergy of the benefit from protons compared to photons, and the benefit from LATTICE compared to GRID. Proton LATTICE using standard proton RT via intensity modulated proton therapy (IMPT) (with a few beam angles) can be problematic with poor target dose coverage and high dose spill to organs-at-risk (OAR). This work will develop novel proton LATTICE method via proton ARC (with many beam angles) to overcome these challenges in target coverage and OAR sparing, with optimized delivery efficiency via energy layer optimization and optimized biological dose distribution via linear energy transfer (LET) optimization, to enable the clinical use of proton LATTICE.Approach.ARC based proton LATTICE is formulated and solved with energy layer optimization, during which plan quality and delivery efficiency are jointly optimized. In particular, the number of energy jumps (NEJ) is explicitly modelled and minimized during plan optimization for improving delivery efficiency, while target dose conformality and OAR dose objectives are optimized. The plan deliverability is ensured by considering the minimum-monitor-unit (MMU) constraint, and the plan robustness is accounted for using robust optimization. The biological dose is optimized via LET optimization. The optimization solution algorithm utilizes iterative convex relaxation method to handle the dose-volume constraint and the MMU constraint, with spot-weight optimization subproblems solved by proximal descent method.Main results.ARC based proton LATTCE substantially improved plan quality from IMPT based proton LATTICE, such as (1) improved conformity index (CI) from 0.47 to 0.81 for the valley target dose and from 0.62 to 0.97 for the peak target dose, (2) reduced esophagus dose from 0.68 Gy to 0.44 Gy (a 12% reduction with respect to 2 Gy valley prescription dose) and (3) improved PVDR from 4.15 to 4.28 in the lung case. Moreover, energy layer optimization improved plan delivery efficiency for ARC based proton LATTICE, such as (1) reduced NEJ from 71 to 56 and (2) reduction of energy layer switching time by 65% and plan delivery time by 52% in the lung case. The biological target and OAR dose distributions were further enhanced via LET optimization. On the other hand, proton ARC LATTCE also substantially improved plan quality from VMAT LATTICE, such as (1) improved CI from 0.45 to 0.81 for the valley target dose and from 0.63 to 0.97 for the peak target dose, (2) reduced esophagus dose from 0.59 Gy to 0.38 Gy (a 10.5% reduction with respect to 2 Gy valley prescription dose) and (3) improved PVDR from 3.88 to 4.28 in the lung case.Significance.The feasibility of high-plan-quality proton LATTICE is demonstrated via proton ARC with substantially improved target dose coverage and OAR sparing compared to IMPT, while the plan delivery efficiency for ARC based proton LATTICE can be optimized using energy layer optimization.

A Relaxation Scheme for the Simulation of Two‐Phase Flows With Inaccessible Pore Volume in Polymer Flooding

ABSTRACTThe simulation of polymer injection in a reservoir is of paramount importance in enhanced oil recovery. Despite decades of research, the computation of polymer flows in porous media remains a challenging task. The main difficulty lies in the necessity to take into account the effect of inaccessible pore volumes (IPV), for which standard closure laws give rise to a weakly hyperbolic or even non‐hyperbolic system. In the latter case, exponential instabilities may appear at the continuous level, which must be addressed at the discrete level so as to prevent a premature stop of the numerical simulations. The notion of IPV was introduced by engineers in order to account for the following observation: when a polymer solution is injected into an initial core saturated with water, the breakthrough of the polymer at the exit occurs before that of the water in which it is injected. It seems that due to their large size, the polymer molecules cannot insinuate themselves into all pores as well as water. Having less volume to flood, the polymer molecules see their speed increased, hence the ad hoc acceleration factor associated with the polymer. In this work, we propose a relaxation method that guarantees some practical robustness for all IPV laws. This is achieved by replacing the original system by a relaxation model which is always hyperbolic. The designed relaxation model involves two parameters which enable us not only to adjust the correct amount of numerical dissipation, but also to ensure positivity for some critical quantities such as water saturation and polymer concentration. Extensive numerical tests are performed in order to compare the relaxation scheme to the more classical upwind scheme for several IPV laws.

Numerical simulation of shale gas reservoir based on ILU-GMRES method

ABSTRACT The numerical simulation of shale gas reservoirs requires transforming mathematical models into large linear equation systems, and solving large linear equation systems requires a lot of time. A novel ILU-GMRES method for solving large linear equations is presented, which treats the sub matrix discretized at nodes as the basic elements of the coefficient matrix. By combining the incomplete LU decomposition method (ILU) with the generalized minimum residue method (GMRES), the discretized large linear equations are iteratively solved. A comparison was made between the new method and other methods for calculating the actual shale gas reservoir model. The results reveal that the new method has a faster calculation speed in solving linear equation systems. The calculation time of the novel ILU-GMRES method is 1029s, the calculation time of the generalized minimum residual method (GMRES) method is 2709s, the calculation time of the Gauss–Seidel method (GS) is 3786s, and the calculation time of the successive over relaxation method (SOR) method is 3386s, the calculation time of the preprocessing conjugate gradient method (PCG) is 3115s. The calculation speed of the novel method is almost 2.6 times faster than the GMRES method, the novel method is more effective in the numerical simulation of shale gas.

Blending neural operators and relaxation methods in PDE numerical solvers

Blending neural operators and relaxation methods in PDE numerical solvers

Development of three-dimensional forward modeling method for the magnetometric resistivity (MMR) method

We have developed a 3-D forward modeling method for the magnetometric resistivity (MMR) technique, specially focusing on the marine MMR method, which utilizes a vertical bipole source and seafloor receivers to measure magnetic field variations. The bipole source generates an artificial electric current between two electrodes: one on the sea surface and another on the seafloor. When computing the electric potential using the relaxation method, while conserving electric current, singularities arise at the electrode locations. To address this issue, we introduce two electrical resistivity structures to mitigate the effects of these singularities and to obtain magnetic field anomalies caused by arbitrary 3-D electrical resistivity anomalies beneath the seafloor. By determining the sign of the magnetic field anomaly, we can infer whether the electrical resistivity of the anomalous body is more conductive or more resistive compared to the surrounding oceanic crust. Furthermore, we demonstrate that increasing the number of bipole sources is more effective in exploring anomalous bodies than increasing the number of receivers.Graphical abstract

Optimal operation of three-phase unbalanced active distribution system based on semidefinite relaxation and convex-concave procedure

The three-phase distribution optimal power flow (D-OPF) problem has attracted much attention in recent years due to practical requirements for managing distributed energy resources and multi-energy customers in unbalanced active distribution systems. To deal with the strong nonconvexity of the three-phase OPF problem, this paper develops the semidefinite programming (SDP) formulation of three-phase OPF problems considering the mutual coupling in multi-phase networks. Instead of directly dropping the rank-one constraints, a sequential convex optimization algorithm based on the convex-concave procedure (CCP) is proposed for recovering a feasible and optimal solution of three-phase power flow. The proposed iterative algorithm not only has high computational efficiency but also guarantees the optimality when the semidefinite relaxation or second-order cone relaxation method is inexact. Case studies on various IEEE testing distribution systems verify that the proposed algorithm recovers the feasible and optimal power flow solution. It also exhibits a relatively low number of iterations and short solving time in large-scale IEEE testing systems.

A novel homological approach for the comprehensive study of nonstoichiometric oxide with exceptional oxygen mobility

Actual work devoted to the development of a novel homological approach for describing the kinetic properties of grossly nonstoichiometric oxides ABO3-δ with perovskite structure. The approach consists in considering such oxides having different oxygen stoichiometry 3-δ as chemical homologues involved in the same oxygen exchange reaction and forming a continuous series in δ. The proposed approach is considered using the oxide with exceptional oxygen mobility Ba0·5Sr0·5Co0·8Fe0·2O3-δ (BSCF). The kinetic properties of BSCF were studied by new method of the oxygen partial pressure relaxation. The equilibrium properties of BSCF were reported earlier and obtained by original technique of the quasi-equilibrium oxygen release. The power law dependence of the kinetic parameters on the equilibrium oxygen partial pressure is considered as the consequence of linear free energy relationship similar to the Brønsted-Evans-Polanyi relation.

A Relaxed Tseng’s Method-based Algorithm for Solving Split Variational Inequalities with Multiple Output Sets

In this paper, the split variational inequality problem with multiple output sets is considered in a more general framework of reflexive Banach spaces. We introduce a relaxed Tseng extragradient method for approximating the solution of this problem when the cost operators are pseudomonotone and non-Lipschitz. Moreover, our proposed algorithm employs the inertial technique and a new self-adaptive step size to guarantee high rate of convergence. Strong convergence of the algorithm is proved in this case without the need for the sequential weak continuity condition. Finally, some numerical experiments are given to show the applicability of our proposed algorithm.

Energy Efficiency Maximization for Multi-UAV-IRS-Assisted Marine Vehicle Systems

Mobile edge computing is envisioned as a prospective technology for supporting time-sensitive and computation-intensive applications in marine vehicle systems. However, the offloading performance is highly impacted by the poor wireless channel. Recently, an Unmanned Aerial Vehicle (UAV) equipped with an Intelligent Reflecting Surface (IRS), i.e., UIRS, has drawn attention due to its capability to control wireless signals so as to improve the data rate. In this paper, we consider a multi-UIRS-assisted marine vehicle system where UIRSs are deployed to assist in the computation offloading of Unmanned Surface Vehicles (USVs). To improve energy efficiency, the optimization problem of the association relationships, computation resources of USVs, multi-UIRS phase shifts, and multi-UIRS trajectories is formulated. To solve the mixed-integer nonlinear programming problem, we decompose it into two layers and propose an integrated convex optimization and deep reinforcement learning algorithm to attain the near-optimal solution. Specifically, the inner layer solves the discrete variables by using the convex optimization based on Dinkelbach and relaxation methods, and the outer layer optimizes the continuous variables based on the Multi-Agent Twin Delayed Deep Deterministic Policy Gradient (MATD3). The numerical results demonstrate that the proposed algorithm can effectively improve the energy efficiency of the multi-UIRS-assisted marine vehicle system in comparison with the benchmarks.

An embedded differential evolution approach to adaptive covariance inflation with the ensemble Kalman filter

ABSTRACT The limited ensemble sizes and the neglected model errors in ensemble-based Data Assimilation (DA) usually lead to underestimation of the error variance, and covariance inflation ‘inflates’ the covariance of a forecast or analysis ensemble by some positive factor in each assimilation cycle. In practice, the value of the inflation factor is often set by trial and error. Thus, a variety of adaptive covariance inflation (ACI) algorithms have been proposed to improve assimilation performance by adjusting the optimal parameters. Most of these used traditional optimization algorithms, such as gradient methods and relaxation methods. However, Evolutionary Algorithms(EAs), which encompass a range of population-based stochastic search techniques widely used in various engineering optimization problems, are rarely seen in DA. In this study, we developed a new framework for adaptive inflation factors, introducing differential evolution (DE) algorithm into local ensemble Transform Kalman filter (LETKF) that can explore the most suitable/optimal inflation factors online. A ‘micro-DE’ based data assimilation method can obtain better assimilation results step by step without taking a much longer time. The feasibility and effectiveness of the algorithm is demonstrated in an idealized Lorenz-96 model with simulated observations. Under both perfect and imperfect-model scenarios, it is found that the ‘micro-DE’LETKF method is capable of outperforming the original LETKF with a considerable lower computational cost. The adaptive inflation factor is optimally updated at each assimilation cycle either around the upper bound or around the lower bound, which means that only an adaptive factor helps mitigate the ensemble collapse due to a lack of spread. However, the further study will consider the application of the methodology to more complex atmospheric models.

Mercury-probe measurement of electron mobility in β-Ga2O3 using junction moderated dielectric relaxation

We demonstrate the junction-moderated dielectric relaxation method to measure the in-plane electron mobility in β-Ga2O3 epitaxial layers. Unlike the Hall technique and channel mobility measurement in field-effect transistors, this method does not require the deposition of permanent metal contacts. Rather, it measures the bias voltage and frequency dependence of the equivalent capacitance of the Mercury/β-Ga2O3/Mercury structure consisting of a Schottky contact, a quasi-neutral thin film semiconductor, and an Ohmic contact connected in series. The intrinsic dielectric relaxation of the bulk β-Ga2O3 semiconductor typically occurs at ∼1012 s−1, but when moderated by the Mercury/β-Ga2O3 Schottky junction, it manifests itself as an inflection in the capacitance-frequency characteristics at a much lower frequency of ∼106 s−1 within the range of most capacitance measuring instruments. Using carrier density and layer thickness determined from capacitance-voltage measurement, we extract the electron mobility of β-Ga2O3 from the junction-moderated dielectric relaxation frequency.

A distribution-free-based approach for stochastic food closed-loop supply chain

ABSTRACT Resource scarcity has driven growing interest in circular economy (CE). Closed-loop supply chain (CLSC) with returnable transport items (RTIs) in the food industry is an important component of CE. However, existing works on food CLSC with RTIs have not simultaneously considered the perishability, facility location, and uncertain demand under limited information. Therefore, this work addresses a new food CLSC optimisation problem. We first propose a non-linear chance-constrained programming model. It is then transformed into a mixed-integer linear programming model via using the distribution-free (DF) method and sample average approximation (SAA) method, respectively. An illustrative example reveals that the DF method needs only 10.50% of the computation time of the SAA method. To address large-scale problems, an improved Lagrangian relaxation (LR) method is developed. To address the computational challenge in large-scale problems, an improved Lagrangian relaxation (LR) algorithm is developed. Results show that CPLEX achieves a gap of 75.57%, while the LR surpasses it by finding near-optimal solutions with a gap of 1.22%, using only 31.82% of the computation time required by CPLEX. For this work, the main insights are summarised: (1) extending product shelf life can reduce the total cost; and (2) to alleviate uncertain demand and production risks, production capacity and product inventory capacity can be appropriately expanded, but excessive investment may not improve returns.

Multi-helix buckling of a slender compression rod constrained by a cylinder

As early as the mid-18th century, Euler proposed a critical load formula for compression rods with multiple half-sine wave modes. However, a critical load formula for compression rods constrained by cylinders with multi-helix buckling modes has not yet been proposed. In this paper, a mechanical model of multi-helix buckling of a slender compression constrained by a cylinder is established. Utilizing the dynamic relaxation method, a finite element solution strategy is presented. Its notable advantage lies in its capability to compute stable configurations of multiple helical buckling, effectively addressing challenges such as contact identification and convergence issues during computation. Furthermore, parameter analysis quantifies the influence of length, diameter, and annular gap on the critical load, while also analyzes the shear force, bending moment, and contact force after buckling. This paper presents formulas for the critical load of multi-helix buckling and the length of the multi-helix buckling modes, which is suitable for various length, diameter, and annular space gap conditions, and partially validates these results against finite element analysis.