Article
Mathematics, Applied
Bo Song, Jing-Yi Wang, Yao-Lin Jiang
Summary: This paper presents a new parallel-in-time algorithm for time-periodic problems based on the classical PP-PC algorithm and the Krylov subspace method. The algorithm uses a new propagator derived by the Krylov subspace as the coarse propagator, which leads to faster convergence compared to the classical PP-PC algorithm.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Jun Li, Yao-Lin Jiang
Summary: In this paper, we study the parareal algorithm for linear switched systems based on two coarse time subinterval divisions: the algorithm based on the original switching time subinterval and the algorithm based on a new time subinterval division. These algorithms efficiently compute systems with high-frequency oscillatory and discontinuous input, and convergence analysis is provided for both algorithms.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Jun Li, Yaolin Jiang
Summary: In this paper, a new accelerated waveform relaxation method is proposed based on a time-parallel algorithm to solve general systems of ordinary differential equations. The method decouples or linearizes large-scale complex systems into simpler subsystems that can be computed in parallel in each iteration. To accelerate the computation, a time-parallel approach using the Parareal algorithm is applied to solve the subsystems. Convergence analysis, speedup analysis, and numerical experiments are provided to verify the effectiveness of the proposed algorithms.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Automation & Control Systems
Yiheng Wei, Yuquan Chen, Xuan Zhao, Jinde Cao
Summary: This study proposes a framework for processing gradient algorithms based on the nabla fractional-order system theory. The gradient algorithm is transformed into a nabla fractional-order dynamic system, and it is designed using control theory and analyzed using the Lyapunov theory, which improves the performance of the algorithm. Three types of algorithms are built in this study, and a comprehensive simulation study is conducted to verify the correctness, usefulness, and practicality of the framework.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Mathematics, Applied
Laura Grigori, Sever A. Hirstoaga, Julien Salomon
Summary: In this paper, a new strategy for solving highly oscillatory two-dimensional Vlasov-Poisson systems is introduced using a specific version of the parareal algorithm. The novelty lies in the use of reduced models, obtained from the two-scale convergence theory, for coarse solving. These reduced models approximate the original Vlasov-Poisson model at a low computational cost by avoiding high oscillations. Both models are numerically solved in a particle-in-cell framework. The strategy is illustrated with numerical experiments on a charged beam in a focusing channel under the influence of a rapidly oscillating external electric field. An efficiency analysis of the parareal algorithm in terms of speedup is provided based on computing times.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Yuan Cao, Shuai Su
Summary: This paper proposes two gradient descent based fractional methods for systems with outliers. The conventional fractional gradient descent (FGD) algorithm assumes the fractional derivative is a scalar, resulting in slow convergence rates, especially for ill-conditioned matrix systems. The proposed algorithms in this paper have several advantages: (1) unbiased estimates; (2) faster convergence rates; (3) enrichment of the FGD estimation framework. Simulation examples demonstrate the effectiveness of the proposed algorithms.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Ren-Hao Zhang, Yao-Lin Jiang, Jun Li, Bo Song
Summary: This paper presents a parallel implementation algorithm with parameterized propagators for solving linear parametric differential equations over a wide range of parameters. By transforming the initial value problem into nonparametric ODEs based on Taylor series, the general parameterized fine and coarse propagators for the parallel implementation algorithm are constructed in each time subinterval. Furthermore, a coarse propagator based on the waveform relaxation method is proposed to accelerate the convergence of the algorithm. Convergence analysis of the algorithm with these propagators is presented and illustrated with two numerical experiments.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2023)
Article
Mathematics, Applied
Mohamed Kamel Riahi
Summary: This paper presents a new algorithm for parallel in time numerical simulation, which solves the problem algebraically and using an adapted Bi-Conjugate gradient stabilized method. The proposed algorithm, PiTSBiCG, shows great potential in stabilizing the parallel resolution for a variety of problems and outperforms the standard parareal method.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Mahsa Fozuni Shirjini, Amin Nikanjam, Mahdi Aliyari Shoorehdeli
Summary: In this study, the stability and convergence of the Bat Algorithm (BA) were theoretically analyzed and then validated through extensive simulations. The results confirmed the theoretical predictions regarding the proposed updating relations.
ENGINEERING WITH COMPUTERS
(2021)
Article
Computer Science, Artificial Intelligence
Prasanjit Chakraborty, Sushmita Sharma, Apu Kumar Saha
Summary: This paper analyzes the convergence behavior of the Butterfly Optimization Algorithm (BOA) by developing a Markov chain model. It mathematically proves the global convergence of BOA based on the analysis using the Markov chain model and the global convergence theorem. The impact of other factors on the convergence rate of BOA is experimentally demonstrated, and a comparison with other state-of-the-art algorithms is conducted. The effects of sensory modality and power exponent on the performance of BOA are also studied.
Article
Computer Science, Artificial Intelligence
Zhong-kai Feng, Jie-feng Duan, Wen-jing Niu, Zhi-qiang Jiang, Yi Liu
Summary: This study proposes an enhanced sine cosine algorithm (ESCA) to improve the performance of the Sine Cosine Algorithm (SCA) in multivariable optimization problems. ESCA incorporates several modified strategies to enhance its search range, global exploration, population diversity, and solution quality. Experimental results demonstrate that ESCA outperforms traditional methods in terms of solution efficiency and convergence rate for multivariable parameter optimization problems. The feasibility of ESCA in practical applications is further confirmed through engineering optimization problems, where ESCA produces high-quality solutions with better objective values.
APPLIED SOFT COMPUTING
(2022)
Article
Engineering, Multidisciplinary
Kim Jie Koh, Fehmi Cirak
Summary: Efficient representation of random fields on geometrically complex domains is crucial for Bayesian modelling in engineering and machine learning. The SPDE representation enables scalable statistical finite element analysis and Gaussian process regression on such domains, allowing modeling of anisotropic and non-stationary random fields.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Automation & Control Systems
Qian Liu, Senping Tian
Summary: This research focuses on the analysis of iterative learning control for linear fractional-order singular systems. The design of iterative learning control algorithm for tracking the desired output trajectory is proposed. The P-type algorithm is developed for linear fractional-order singular systems, and the PD alpha-type algorithm is presented for systems with time-delay. The convergence of the algorithms is thoroughly analyzed, and their efficiency is verified through simulation illustration.
INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS
(2022)
Article
Multidisciplinary Sciences
Qi Xiong, Jincheng She, Jinkun Xiong
Summary: This paper introduces a modified Pelican Optimization Algorithm (FPPOA) for accurate and fast parameter identification, which is a key issue in chaotic control and synchronization. The algorithm improves optimization speed and avoids local optima by incorporating a chaotic sequence and Pareto distribution. In simulation experiments, the FPPOA outperforms three traditional swarm intelligence optimization algorithms, and achieves parameter identification with error rates within a 1% range.
Article
Automation & Control Systems
Qian Liu, Zhaojing Wu, Senping Tian
Summary: This research discusses the issue of iterative learning control for fractional differential nonlinear singular systems. The PD alpha iterative learning control algorithm is proposed to track the desired trajectory. Analysis on iterative learning control for such systems with time delay and interference is considered, and sufficient conditions for convergence are thoroughly analyzed. Simulation illustrations are provided to demonstrate the validity and efficiency of the algorithm.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2022)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)