Article
Mathematics, Applied
Xing Zhang, Xiaoyu Jiang, Zhaolin Jiang, Heejung Byun
Summary: This paper implements matrix order-reduction algorithms to solve the CUPL-Toeplitz linear system. Firstly, order-reduction algorithms for the multiplication of real skew-circulant matrix or complex circulant matrix and vector are described. Secondly, based on two fast approaches [1] by splitting the CUPL-Toeplitz matrix into a Toeplitz matrix subtracting a low-rank matrix, new fast Toeplitz solvers are proposed to reduce the amount of calculation. Finally, numerical experiments are conducted to demonstrate the performance of the proposed algorithms.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Computer Science, Information Systems
Lu Zhang, Lei Chen, Xiao Song
Summary: The paper presents a fast numerical method for solving the nonlinear space fractional complex Ginzburg-Landau equations, utilizing a circulant preconditioner and fast Fourier transform to solve the linear system, resulting in computational superiority. Numerical examples are conducted to demonstrate the advantage of the method.
Article
Cell Biology
Aiye Wang, Zhuoqun Zhang, Siqi Wang, An Pan, Caiwen Ma, Baoli Yao
Summary: This paper introduces a method called ADMM-FPM which utilizes the concept of alternating direction method of multipliers to solve the phase retrieval problem in Fourier ptychographic microscopy (FPM). Compared to existing algorithms, ADMM-FPM shows better stability and robustness under noisy conditions.
Article
Mathematics, Applied
Jianjun Zhang, James G. Nagy
Summary: This study focuses on color image restoration as an ill-posed problem that requires regularization. By formulating the problem as a constrained minimization problem and proposing an effective alternating direction method of multipliers, the paper demonstrates that the proposed method is feasible and much more effective for color image restoration.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Automation & Control Systems
Yinan Li, Ruili Wang, Yuqiang Fang, Meng Sun, Zhangkai Luo
Summary: This article proposes a variable splitting based convolutive NMF algorithm to address the issues of low convergence rates, difficulty in reaching optimal solutions, and sparse results. Experimental results demonstrate the superiority of the proposed algorithm in terms of efficiency, optimal solutions, and sparsity.
IEEE TRANSACTIONS ON CYBERNETICS
(2022)
Article
Mathematics, Applied
Di Gan, Guo-Feng Zhang
Summary: In this paper, the alternating direction implicit (ADI) finite difference method and preconditioned Krylov subspace method are combined to solve high-dimensional spatial fractional diffusion equations with variable diffusion coefficients. The unconditional stability and convergence rate of the ADI finite difference method are proven under certain conditions on the diffusion coefficients. A circulant approximate inverse preconditioner is established to accelerate the Krylov subspace method for the linear system in each spatial direction. Matrix-free algorithms and fast Fourier transforms (FFT) are used to speed up the solution of linear systems. Numerical experiments demonstrate the effectiveness of the ADI method and the preconditioner.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
V. N. Chugunov
Summary: A full description is provided for the corresponding relationship of pairs of symmetric Toeplitz matrices whose squares are identical.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
(2022)
Article
Computer Science, Artificial Intelligence
Zhang-Lei Shi, Xiao Peng Li, Chi-Sing Leung, Hing Cheung So
Summary: This study introduces an algorithm for portfolio optimization that explicitly controls the cardinality of the portfolio through a non-convex optimization problem. Results on real-world datasets demonstrate the superiority of the proposed algorithm over several existing algorithms.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Mathematics
Mu-Zheng Zhu, Ya-E Qi, Guo-Feng Zhang
Summary: The paper presents efficient preconditioners based on circulant and skew-circulant approximations to accelerate the convergence of Krylov subspace methods for discretized linear systems of spatial fractional diffusion equations. Numerical experiments show that the new preconditioners can significantly speed up the convergence of CGNR and BiCGSTAB. Results also indicate that there is minimal difference in acceleration effects between the circulant and skew-circulant approximation-based preconditioners for the problems considered.
LINEAR & MULTILINEAR ALGEBRA
(2021)
Article
Mathematics
Zhangquan Wang, Shanshan Huo, Xinlong Xiong, Ke Wang, Banteng Liu
Summary: This paper proposes an adaptive parameter selection method based on the ADMM, which decomposes a convex model-fitting problem into a set of sub-problems that can be executed in parallel. The effectiveness of the algorithm is verified through experiments on eight classification datasets, showing improved speed of data processing and increased parallelism.
Article
Operations Research & Management Science
Sedi Bartz, Ruben Campoy, Hung M. Phan
Summary: This paper proposes and studies an adaptive version of ADMM for the case where the objective function is the sum of a strongly convex function and a weakly convex function. By combining generalized notions of convexity and penalty parameters with the convexity constants of the functions, we prove convergence of the algorithm under natural assumptions.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Jing Wu, Xian-Ming Gu, Yong-Liang Zhao, Yu-Yun Huang, Bruno Carpentieri
Summary: This note presents a new structured perturbation analysis method for Toeplitz inversion, which improves the existing upper bounds proposed by Wu et al. and Feng et al. It also provides practical issues and numerical experiments to support the theoretical findings.
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
(2023)
Article
Mechanics
James I. Petrie, M. Reza Hirmand, Katerina D. Papoulia
Summary: A method for quasistatic cohesive fracture using the ADMM algorithm is introduced, which demonstrates good iteration performance and computational efficiency. The algorithm is capable of handling larger-scale problems and shows insensitivity to numerical parameters. It is effective in dealing with close spaced minima in complicated microstructures.
ENGINEERING FRACTURE MECHANICS
(2022)
Review
Mathematics, Applied
Yao-Yuan Cai, Hai-Wei Sun, Sik-Chung Tam
Summary: This paper investigates a numerical method for solving the multi-dimensional spatial fractional Allen-Cahn equations. After semi-discretizing the equations, a system of nonlinear ordinary differential equations with a Toeplitz structure is obtained. The author proposes a two-level Strang splitting method by splitting the Toeplitz matrix into a circulant matrix and a skew-circulant matrix to reduce computational complexity. This method unconditionally preserves the discrete maximum principle and achieves second-order convergence. Numerical experiments are conducted to validate the proposed theories.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Electrical & Electronic
Yufeng Liu, Zhibin Zhu, Shuo Wang, Ruwen Zhao, Benxin Zhang
Summary: In this article, a new cost function is established based on the contraction integral equation (CIE) model and hybrid regularization technique. The new cost function effectively reduces the nonlinearity of the 3-D inverse scattering problems (ISPs) and alleviates the illposedness. The inversion algorithm accuracy is verified through experiments on synthetic and experimental data.
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES
(2023)
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)