Splitting Algorithm Research Articles

Modeling the flexural rigidity of spunlace nonwoven fabrics

Nonwoven fabrics, especially spunlace varieties, find application across diverse fields. This study presents an analytical model that utilizes the energy method, factoring in bending and torsion strain energies. This model is integrated with the dynamic recursive splitting (DYRES) algorithm to predict the flexural rigidity by estimating fiber-to-fiber contacts within spunlace nonwoven fabrics. The input parameters for this proposed model encompass the number of bending couples, the bending stiffness of fibers, and the orientation characteristics of spunlace nonwoven fabrics. To validate the predictive capability of the model, six samples with varying fiber types, basis weights, and thicknesses were fabricated. A comparison between experimental and theoretical values reveals a consistent trend but with overestimated values in both the machine direction (MD) and cross-machine direction (CD). Through the utilization of two coefficients (0.7854 and 0.7823) to refine the presented model, an average relative error of 4.22% and 8.92% was achieved for the MD and CD directions, respectively. This research proposes a theory that utilizes fewer parameters compared to other studies in the field of nonwoven textiles. The proposed approach offers a more convenient and accessible method for obtaining these parameters, as well as determining the bending stiffness of the fabric. Moreover, advanced and more suitable techniques, including knot theory and image processing, have been employed to obtain accurate parameter measurements. This work is believed to lay the foundation for future investigations into the mechanical behavior of nonwoven fabrics.

Integrating factor techniques applied to the Schrödinger-like equations. Comparison with Split-Step methods

The nonlinear Schrödinger and the Schrödinger–Newton equations model many phenomena in various fields. Here, we perform an extensive numerical comparison between splitting methods (often employed to numerically solve these equations) and the integrating factor technique, also called Lawson method. Indeed, the latter is known to perform very well for the nonlinear Schrödinger equation, but has not been thoroughly investigated for the Schrödinger–Newton equation. Comparisons are made in one and two spatial dimensions, exploring different boundary conditions and parameters values. We show that for the short range potential of the nonlinear Schrödinger equation, the integrating factor technique performs better than splitting algorithms, while, for the long range potential of the Schrödinger–Newton equation, it depends on the particular system considered.

A cooperative resilience-oriented planning framework for integrated distribution energy systems and multi-carrier energy microgrids considering energy trading

Integrated distribution systems (IDSs) and multi-carrier energy microgrids (MCEMs) can play a crucial role in enhancing distribution energy systems’ overall efficiency and flexibility. By cascading energy usage and cooperating through energy trading, IDSs and MCEMs can reduce overall system costs and provide more flexibility for system operators. Adding resilience to the planning problem of IDSs can reduce planning costs in the long term, as proactive preparedness is key to coping with high-impact rare (HR) events. Adding resilience to the planning problem of IDSs can reduce the planning costs in the long term since proactive preparedness is a key necessity to cope with high-impact rare (HR) events. This paper proposes a resilience-oriented stochastic tri-level and two-stage cooperative expansion planning of IDSs and MCEMs, considering energy trading between IDSs and MCEMs. The first stage comprises two levels; the first level minimizes the investment and operation costs of IDSs and MCEMs, while the second level desires to maximize the energy exchange profit for MCEMs and thus reduce the overall costs. The second stage includes the third level problem involving two objective functions: resilience cost minimization and resilience index (RI) maximization. The multi-objective problem in the second stage is converted into a single-objective problem using the min–max regret method. The DC and AC configurations for the power distribution system (PDS) and power microgrids (PMGs) are studied to identify the optimal configuration of these networks in the expansion planning problem. A new framework is proposed based on an aggregator-agent splitting solution using the aggregator coupling coordinator unit (ACC) responsible for coordinating IDNs and MCEMs. The studied large-scale complex optimization problem is efficiently solved computationally by introducing a combined adaptive dynamic programming (ADP) and linearized alternating direction method of multipliers with parallel splitting (LADMMPSAP) algorithm. Three cases are studied to demonstrate the effectiveness of the proposed model and method. The results depict that MCEMs help reduce expansion planning costs and improve the system’s resilience. Adding resilience to the expansion planning problem enhances the resilience of the whole system and simultaneously reduces the costs by 2.7%. The expansion planning costs for the AC and DC configuration are close, and the AC is the optimal choice in all case studies. By increasing the planning horizon from 5 to 10 years, DC will be the optimal solution since network reinforcement costs and power losses are significantly lower.

Improving BFS measurement accuracy of BOTDR based on Cauchy proximal splitting

A novel approach based on the Cauchy proximal splitting (CPS) algorithm is proposed to improve Brillouin frequency shift (BFS) measurement accuracy in Brillouin optical time domain reflectometry system. The CPS algorithm utilizes proximal splitting to handle the data and the penalty function based on Cauchy distribution to accurately estimate the target signal to promote sparsity, achieving significant improvement in signal-to-noise ratio (SNR). Experimental results confirm that with a SNR increase of 12.7 dB, an increase in BFS measurement accuracy from 4.78 MHz to 0.43 MHz is achieved over a 10.3 km sensing fiber. The denoising effects of the CPS, wavelet denoising (WD) and non-local mean (NLM) algorithms are further compared, demonstrating that the CPS algorithm has the lowest root mean square error (0.43 MHz) and no deterioration in spatial resolution rather than the WD and NLM algorithms does.

Two-step inertial forward–reflected–anchored–backward splitting algorithm for solving monotone inclusion problems

The main purpose of this paper is to propose and study a two-step inertial anchored version of the forward–reflected–backward splitting algorithm of Malitsky and Tam in a real Hilbert space. Our proposed algorithm converges strongly to a zero of the sum of a set-valued maximal monotone operator and a single-valued monotone Lipschitz continuous operator. It involves only one forward evaluation of the single-valued operator and one backward evaluation of the set-valued operator at each iteration; a feature that is absent in many other available strongly convergent splitting methods in the literature. Finally, we perform numerical experiments involving image restoration problem and compare our algorithm with known related strongly convergent splitting algorithms in the literature.

MGDUN: An interpretable network for multi-contrast MRI image super-resolution reconstruction

Magnetic resonance imaging (MRI) Super-Resolution (SR) aims to obtain high resolution (HR) images with more detailed information for precise diagnosis and quantitative image analysis. Deep unfolding networks outperform general MRI SR reconstruction methods by providing better performance and improved interpretability, which enhance the trustworthiness required in clinical practice. Additionally, current SR reconstruction techniques often rely on a single contrast or a simple multi-contrast fusion mechanism, ignoring the complex relationships between different contrasts. To address these issues, in this paper, we propose a Model-Guided multi-contrast interpretable Deep Unfolding Network (MGDUN) for medical image SR reconstruction, which explicitly incorporates the well-studied multi-contrast MRI observation model into an unfolding iterative network. Specifically, we manually design an objective function for MGDUN that can be iteratively computed by the half-quadratic splitting algorithm. The iterative MGDUN algorithm is unfolded into a special model-guided deep unfolding network that explicitly takes into account both the multi-contrast relationship matrix and the MRI observation matrix during the end-to-end optimization process. Extensive experimental results on the multi-contrast IXI dataset and the BraTs 2019 dataset demonstrate the superiority of our proposed model, with PSNR reaching 37.3366 and 35.9690 respectively. Our proposed MGDUN provides a promising solution for multi-contrast MR image super-resolution reconstruction. Code is available at https://github.com/yggame/MGDUN.

A particle refinement technique with dynamic splitting and coalescing pattern for fluid-structure interaction problem

With the increasing demand of large scale computation, multi-resolution particle methods have been paid much attention by many researchers. In multi-resolution method, high resolution is applied in local area to reduce the whole computational costs and maintain the local accuracy. However, there are still many challenges in the stability and accuracy of multi-resolution particle methods. In this research, an efficient variable particle size (VSP) multi-resolution method, using particle splitting and coalescing techniques, is developed in moving semi-implicit particle (MPS) method. Particles split or coalesce in dynamic five steps to avoid particle overlap and clustering. The mixed splitting mechanism by combining hexagonal splitting pattern and pair splitting pattern are proposed in the five-step splitting algorithm. Pair splitting and coalescing techniques with variable particle size are proposed to strictly ensure the conservation of mass and momentum and avoid particle clustering. To solve the non-linear fluid-structure interaction problem, the VSP algorithm is introduced in MPS-DEM method. The numerical results are compared with the analytical solutions and experimental results. It shows that the proposed VSP algorithm cannot only maintain the local accuracy, but also improve the computational efficiency by avoiding unnecessary chain operations between particle splitting and coalescing.

Unconditionally energy-stable linear convex splitting algorithm for the L2 quasicrystals

Quasicrystals have extensive applications in material sciences. In this article, we develop an unconditional energy-dissipation-preserving, temporally second-order accurate, and linear method for solving a L2-gradient flow-based quasicrystal model. A truncated technique is introduced to regularize the nonlinear terms so that their second derivative is upper bounded. Based on the idea of the convex splitting method, we split free energy into the difference between two convex functionals. The convexity provides an appropriate choice of linear stabilization parameter. A linear and temporally second-order accurate algorithm is constructed utilizing the implicit-explicit Runge–Kutta method. In each time step, we can analytically prove that the proposed scheme satisfies the energy dissipation law. The Fourier spectral method is used to perform spatial discretization. Through numerical experiments, the accuracy, energy stability, and capability of the proposed method for quasicrystals are verified.

A Perturbation Framework for Convex Minimization and Monotone Inclusion Problems with Nonlinear Compositions

We introduce a framework based on Rockafellar’s perturbation theory to analyze and solve general nonsmooth convex minimization and monotone inclusion problems involving nonlinearly composed functions as well as linear compositions. Such problems have been investigated only from a primal perspective and only for nonlinear compositions of smooth functions in finite-dimensional spaces in the absence of linear compositions. In the context of Banach spaces, the proposed perturbation analysis serves as a foundation for the construction of a dual problem and of a maximally monotone Kuhn–Tucker operator, which is decomposable as the sum of simpler monotone operators. In the Hilbertian setting, this decomposition leads to a block-iterative primal-dual algorithm that fully splits all the components of the problem and appears to be the first proximal splitting algorithm for handling nonlinear composite problems. Various applications are discussed. Funding: The work of L. M. Briceño-Arias was supported by Agencia Nacional de Investigación y Desarrollo-Chile [Grant Fondo Nacional de Desarrollo Científico y Tecnológico 1190871, Grant Centro de Modelamiento Matemático ACE210010, Grant Centro de Modelamiento Matemático FB210005, and basal Funds for Centers of Excellence], and the work of P. L. Combettes was supported by the National Science Foundation [Grant DMS-1818946].

New accelerated splitting algorithm for monotone inclusion problems

ABSTRACT Forward-reflected-backward splitting algorithm with inertial extrapolation of two inertial effects to find a zero of the sum of a maximal monotone and a Lipschitz continuous monotone operator is studied in this paper. The incorporation of two inertial effects on the extrapolation step is to further improve the convergence speed of the forward-reflected-backward splitting algorithm with one inertial effect extrapolation already proposed in the literature. The parameter of the second inertial effect of our proposed algorithm is chosen to be non-positive. Weak, strong, and linear convergence results are obtained under standard conditions in Hilbert spaces. Preliminary numerical illustrations show that our proposed algorithm is competitive with other related algorithms in the literature.

FedEHR: A Federated Learning Approach towards the Prediction of Heart Diseases in IoT-Based Electronic Health Records.

In contemporary healthcare, the prediction and identification of cardiac diseases is crucial. By leveraging the capabilities of Internet of Things (IoT)-enabled devices and Electronic Health Records (EHRs), the healthcare sector can largely benefit to improve patient outcomes by increasing the accuracy of disease prediction. However, protecting data privacy is essential to promote participation and adhere to rules. The suggested methodology combines EHRs with IoT-generated health data to predict heart disease. For its capacity to manage high-dimensional data and choose pertinent features, a soft-margin L1-regularised Support Vector Machine (sSVM) classifier is used. The large-scale sSVM problem is successfully solved using the cluster primal-dual splitting algorithm, which improves computational complexity and scalability. The integration of federated learning provides a cooperative predictive analytics methodology that upholds data privacy. The use of a federated learning framework in this study, with a focus on peer-to-peer applications, is crucial for enabling collaborative predictive modeling while protecting the confidentiality of each participant's private medical information.

Influence of specimen size on granite fracture characteristics and acoustic emission phenomena under mode I loading conditions

The rock mode I fracture characteristics and the size effect are of great significance in understanding the crack initiation, nucleation, propagation, and characterizing the fracture toughness of rocks which is essential for predicting the behavior of rock masses and designing underground structures. In this paper, three-point bending fracture experiments were carried out using single-edge notched beam specimens of different sizes. The fracture characteristics of the entire loading stage, including the post peak stage, were analyzed using digital image correlation (DIC) technology and acoustic emission (AE) technology. Specifically, the calculation of the b value uses the Fisher optimal split and global search algorithm (FGS) method. The results show that both the Fracture process zone (FPZ) length and fracture toughness of granite are size-dependent parameters, and the FPZ length growth rate increases with increasing load level. The failure mode of the source during fracture is mainly tensile failure, and the proportion of tensile failure tends to increase with the increase of specimen size. The temporal b value, average AF value and RA value show corresponding stage changes with time, and the minimum b value, minimum AF value and maximum RA value can characterize the maximum of macroscopic growth rate.

One Approach to Numerical Modeling of the Heat and Mass Transfers of Two-Phase Fluids in Fractured-Porous Reservoirs

The work is devoted to numerical modeling of the processes of heat and mass transfer of a two-phase fluid in the environment of a production well, which is necessary for monitoring the development of fractured-porous reservoirs. This work proposes an efficient approach to constructing a solution to the problem. To solve the problem, a model of the “double medium” type is used, where the pore part of the reservoir is considered as the first medium, and the system of natural fractures is considered as the second medium. For the resulting mathematical model, the difference schemes with time weights are constructed based on the algorithm of splitting by physical processes, which ensure the correctness and consistency of fluxes in the fracture system and the pore reservoir. In the numerical solution, the approximations of differential operators obtained in the framework of the finite difference method are used. For the parallel implementation of the developed numerical approach, the domain decomposition method and the matrix sweep algorithm are chosen. The program implementation is made using the MPI standard. Computational experiments are carried out, the results of which confirm the effectiveness of the developed numerical algorithm and its parallel implementation. In numerical experiments, the distributions of pressure and temperature near an operating production well are obtained, on the basis of which it is possible to adjust the operation of wells in order to increase production.

SwPTS: an efficient parallel Thomas split algorithm for tridiagonal systems on Sunway manycore processors

swPTS: an efficient parallel Thomas split algorithm for tridiagonal systems on Sunway manycore processors

Identification of geothermal potential based on land surface temperature derived from remotely sensed data.

With the continuous development of thermal infrared remote sensing technology and the maturation of remote sensing inversion algorithms based on surface temperatures, identifying high-temperature anomalous areas by inverting surface temperatures has become an crucial approach to finding geothermal potential areas. The eastern region of Longyang in western Yunnan Province is renowned for geothermal resources, though the distribution area of geothermal potential remains unknown. Therefore, this study used Landsat-8 TIRS data and four surface temperature inversion algorithms, namely, mono-window algorithm, single-channel algorithm, Du split window algorithm (SWD), and Jiménez-Muñoz split window algorithm (SWJ), to explore the astern region of Longyang. The inversion results were compared with Moderate Resolution Imaging Spectroradiometer Land Surface Temperature (MODIS LST) results for analysis and cross-validation to select the optimal algorithm. A multi-view remote sensing temperature anomaly information extraction method was adopted. Moreover, the overall threshold method, the fracture structure buffer method, and the joint analysis of diurnal temporal data were combined for the reduction of the thermal anomaly area as well as for comprehensively defining the geothermal prospective area in the study area. The results demonstrated that the mono-window algorithm had the highest accuracy with a Pearson coefficient of 0.77, which is more suitable for the surface temperature inversion in Longyang area. Furthermore, three geothermal anomalies (A, B, and C) were identified in the study area, with larger thermal anomaly in A and C, but a smaller one in B. All three areas had hot spring points verified, with A and C exhibiting more significant development potential. The research results provide a reliable methodological basis for the development of geothermal resources in the region.

Sliced optimal transport on the sphere

Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport on the line. More precisely, sliced optimal transport is the concatenation of the well-known Radon transform and the cumulative density transform, which analytically yields the solutions of the reduced transport problems. Inspired by this concept, we propose two adaptions for optimal transport on the 2-sphere. Firstly, as counterpart to the Radon transform, we introduce the vertical slice transform, which integrates along all circles orthogonal to a given direction. Secondly, we introduce a semicircle transform, which integrates along all half great circles with an appropriate weight function. Both transforms are generalized to arbitrary measures on the sphere. While the vertical slice transform can be combined with optimal transport on the interval and leads to a sliced Wasserstein distance restricted to even probability measures, the semicircle transform is related to optimal transport on the circle and results in a different sliced Wasserstein distance for arbitrary probability measures. The applicability of both novel sliced optimal transport concepts on the sphere is demonstrated by proof-of-concept examples dealing with the interpolation and classification of spherical probability measures. The numerical implementation relies on the singular value decompositions of both transforms and fast Fourier techniques. For the inversion with respect to probability measures, we propose the minimization of an entropy-regularized Kullback–Leibler divergence, which can be numerically realized using a primal-dual proximal splitting algorithm.

Fast Compressed Sensing of 3D Radial T1 Mapping with Different Sparse and Low-Rank Models.

Knowledge of the relative performance of the well-known sparse and low-rank compressed sensing models with 3D radial quantitative magnetic resonance imaging acquisitions is limited. We use 3D radial T1 relaxation time mapping data to compare the total variation, low-rank, and Huber penalty function approaches to regularization to provide insights into the relative performance of these image reconstruction models. Simulation and ex vivo specimen data were used to determine the best compressed sensing model as measured by normalized root mean squared error and structural similarity index. The large-scale compressed sensing models were solved by combining a GPU implementation of a preconditioned primal-dual proximal splitting algorithm to provide high-quality T1 maps within a feasible computation time. The model combining spatial total variation and locally low-rank regularization yielded the best performance, followed closely by the model combining spatial and contrast dimension total variation. Computation times ranged from 2 to 113 min, with the low-rank approaches taking the most time. The differences between the compressed sensing models are not necessarily large, but the overall performance is heavily dependent on the imaged object.

Numerical approximation with the splitting algorithm to a solution of the modified regularized long wave equation

In this article, a Lie-Totter splitting algorithm, which is highly reliable, flexible and convenient, is proposed along with the collocation finite element method to approximate solutions of the modified regular long wave equation. For this article, quintic B-spline approximation functions are used in the implementation of collocation methods. Four numerical examples including a single solitary wave, the interaction of two- three solitary waves, and a Maxwellian initial condition are presented to test the closeness of the solutions obtained by the proposed algorithm to the exact solutions. The solutions produced are compared with those in some studies with the same parameters that exist in the literature. The fact that the present algorithm produces results as intended is a proof of how useful, accurate and reliable it is. It can be stated that this fact will be very useful the application of the presented technique for other partial differential equations, with the thought that it may lead the reader to obtain superior results from this study.

Tikhonov regularized iterative methods for nonlinear problems

ABSTRACT We consider the monotone inclusion problems in real Hilbert spaces. Proximal splitting algorithms are very popular technique to solve it and generally achieve weak convergence under mild assumptions. Researchers assume the strong conditions like strong convexity or strong monotonicity on the considered operators to prove strong convergence of the algorithms. Mann iteration method and normal S-iteration method are popular methods to solve fixed point problems. We propose a new common fixed point algorithm based on normal S-iteration method using Tikhonov regularization to find common fixed point of non-expansive operators and prove strong convergence of the generated sequence to the set of common fixed points without assuming strong convexity and strong monotonicity. Based on proposed fixed point algorithm, we propose a forward–backward-type algorithm and a Douglas–Rachford algorithm in connection with Tikhonov regularization to find the solution of monotone inclusion problems. Further, we consider the complexly structured monotone inclusion problems which are very popular these days. We also propose a strongly convergent forward–backward-type primal–dual algorithm and a Douglas–Rachford-type primal–dual algorithm to solve the monotone inclusion problems. Finally, we conduct a numerical experiment to solve image deblurring problems.

Probabilistic dual hesitant fuzzy MAGDM method based on generalized extended power average operator and its application to online teaching platform supplier selection

Probabilistic dual hesitation fuzzy set (PDHFS) is a new tool used to enhance fuzzy and imprecise information in a changing and complex decision-making environment. Compared with the existing fuzzy sets, PDHFS is more suitable for identifying uncertain evaluation data in complex and realistic decision-making situations. The extended power average (EPA) and generalized power average (GPA) operators provide more information for the information aggregation process, reflecting the mutual support among all aggregation values. To solve the evaluation problems related to decision analysis involving extremely complex information, especially in the case of extreme data in the consideration of decision problems. In this paper, the generalized extended power average (GEPA) operator is proposed in the PDHF environment. This research has the following four important contributions. First, we propose a probability splitting algorithm of normalizing PDHFE, and give some new basic operations, score function, distance measures and aggregation operators. Second, to better integrate the advantages of EPA and GPA operators, we developed the GEPA operator, weighted form (WGEPA) and ordered form (GEPOWA). Meanwhile, by adjusting the parameter in three types of operators, we can find that many existing operators are special forms of the three types of operators. Third, extended the three types of operators to the PDHF environment, the PDHFGEPA, PDHFWGEPA, PDHFGEPOWA operators and some special aggregation operators are obtained, and studied their valuable properties in detail. Finally, taking the application of PDHFWGEPA operator as an example, a new multi-attribute group decision-making (MAGDM) technique is developed and used to solve the problem of online teaching platform supplier selection (OTPSS). Through parameter sensitivity analysis, the flexibility and stability of MAGDM technique are illustrated, and compared with some existing decision-making methods, the effectiveness of MAGDM method is proved. In addition, this technique also provides some theoretical references for dealing with other complex MAGDM problems, and provides a new operator for the extension of GEPA operator in other fuzzy environments. The biggest advantage of several operators is that they can pay full attention to the special role of extreme data in decision-making.