Article
Computer Science, Interdisciplinary Applications
Erwan Deriaz
Summary: In this paper, a numerical method with 2pth-order accuracy for solving the d-dimensional Poisson equation is proposed in the Adaptive Mesh Refinement framework. Compact finite differences are used to provide high-order compact stencils suitable for the AMR framework. The method is compared to other existing methods and tested in extensive numerical experiments.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jannis Teunissen, Francesca Schiavello
Summary: A method is proposed for handling irregular domain boundaries in a geometric multigrid solver. The irregular boundary, defined by a level set function, can be subjected to Dirichlet boundary conditions. The implementation utilizes quadtree/octree grids with adaptive refinement, a cell-centered discretization, and pointwise smoothing. Boundary locations are determined at a subgrid resolution by carrying out line searches. Custom operator stencils that consider the interface are stored for grid blocks near the interface, while a standard second-order accurate discretization is used for grid blocks away from boundaries. The method's convergence properties, robustness, and computational cost are demonstrated through several test cases.
COMPUTER PHYSICS COMMUNICATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jeongho Kim, Chohong Min, Byungjoon Lee
Summary: Losasso et al. resolved the difficulty of T-junctions in Octree grids by introducing an ingenious Poisson solver with rectangular domains and Neumann boundary conditions. Empirical observation showed that the numerical solution is second order convergent and the numerical gradient is rigorously proved to be one and a half order convergent, known as super-convergence. This article extends the Poisson solver and its supporting proof from rectangular to irregular domains using the generalized Whitney decomposition and Heaviside treatment, demonstrating the continued existence of super-convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Xiaoqiang Yue, Kejia Pan, Jie Zhou, Zhifeng Weng, Shi Shu, Juan Tang
Summary: The article presents a MGRIT algorithm using FCF-relaxation with time-dependent time-grid propagators for approximating unsteady fractional Laplacian problems. It introduces a new temporal eigenvalue approximation property and a generalized two-level convergence theory to remove previous assumptions about unitary diagonalization, as well as includes numerical computations to confirm theoretical predictions and demonstrate the sharpness of convergence upper bound.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Giorgio Bornia, Andrea Chierici, Leonardo Chirco, Valentina Giovacchini, Sandro Manservisi
Summary: This paper presents a multigrid approach for solving elliptic equations over non-matching grids with domain decomposition methods. The algorithm searches for the global solution by projecting the residuals on the overlap region, and converges to the solution of the corresponding Lagrange multiplier problem. The method is reliable, easy to implement, and suitable for parallel computing and GPU clusters.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
Emily Bourne, Philippe Leleux, Katharina Kormann, Carola Kruse, Virginie Grandgirard, Yaman Guclu, Martin J. Kuhn, Ulrich Rude, Eric Sonnendrucker, Edoardo Zoni
Summary: This paper compares three finely tuned solvers for solving Poisson-like equations on complex geometries. The solvers are evaluated based on their solution accuracy, computational efficiency, and practical implementation aspects. The Spline FEM solver is shown to be the most accurate, the GMGPolar solver uses the least memory, and the Embedded Boundary solver is the fastest in most cases. All three solvers can handle realistic non-analytical geometries.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Konstantinos Agathos, Tim Dodwell, Eleni Chatzi, Stephane P. A. Bordas
Summary: An adapted deflation preconditioner is used to speed up the solution of linear systems resulting from the discretisation of fracture mechanics problems, and the performance is further improved by enriching the deflation space and combining it with a block-Jacobi preconditioner.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Kejia Pan, Hai-Wei Sun, Yuan Xu, Yufeng Xu
Summary: The paper extends the EXCMG method to solve spatial fractional diffusion equations, addressing both steady-state and time-dependent problems by handling dense and nonsymmetric linear systems, and introducing the Crank-Nicolson scheme to deal with the temporal derivative. The effectiveness of the method is demonstrated through numerical examples, showing superior performance compared to other multigrid methods for time-dependent SFDEs.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Computer Science, Hardware & Architecture
Jingshan Pan, Lei Xiao, Min Tian, Tao Liu, Yinglong Wang
Summary: In this paper, we propose swParaFEM, a highly efficient parallel finite element solver based on preconditioned conjugate gradient iteration algorithm, for simulating three-dimensional stress and strain. By utilizing a master-slave acceleration model, kernel aggregation optimization scheme, and memory access optimization, we achieve a speedup of 10.5x on SW26010-Pro processor and a strong scaling efficiency of 62.8% on 512 compute groups.
JOURNAL OF SUPERCOMPUTING
(2023)
Article
Mathematics, Applied
Kejia Pan, Dongdong He, Zhilin Li
Summary: In this paper, a new high order compact immersed interface method is proposed for solving interface problems with discontinuous solutions and fluxes, along with an augmented method developed for elliptic interface problems with discontinuous coefficients. These methods demonstrate good performance in various examples and have the feature of computed normal derivative being nearly third order accurate.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Victor P. DeCaria, Cory D. Hauck, Ming Tse P. Laiu
Summary: The study introduces a new iterative solver for implicit discretizations of a simplified Boltzmann-Poisson system, eliminating the need for nesting and requiring only one transport sweep per iteration. It improves efficiency and is numerically compared against a recently developed nested iterative solver.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Jin Wen, Shan-Shan Wang, Zhuan-Xia Liu
Summary: In this paper, the inversion of inner boundary data for the Poisson equation in a doubly connected domain is studied using a fast Fourier ultraspherical spectral solver. The solver relies on truncated Fourier series expansion and employs an ultraspherical spectral method to solve the differential equations of the Fourier coefficients. Tikhonov regularization is applied to the ill-conditioned linear system obtained from the seriously ill-posed problem, and the regularization parameters are selected using the generalized cross-validation (GCV) criterion. The accuracy and efficiency of the proposed method are demonstrated through numerical results in different regions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Geochemistry & Geophysics
Jiawen Li, Zhen Guan, Jianwen Wang, Li-Ye Xiao, Qing Huo Liu
Summary: An efficient 2-D electromagnetic full-wave inversion method based on the hybrid spectral-element spectral-integral forward solver is proposed. The method combines the spectral element method, integral equation method, and conjugate gradient method to achieve the inversion of relative permittivity and conductivity values.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2022)
Article
Engineering, Ocean
Yunxing Zhang, Shan Ma, Kangping Liao, Wenyang Duan
Summary: In this study, a two-dimensional Geometric Multigrid (GMG) model is developed for the Poisson equation with interface on a Structured Adaptive Mesh Refinement (SAMR) grid. Special attention is given to flux conservation on the coarse-fine interface, and the Galerkin Coarse grid Approximation (GCA) method is used to enhance robustness and efficiency. The model shows 2nd-order accuracy and acceptable efficiency even with density ratios reaching 104, with comparison of point and line relaxation iterations for performance improvement.
APPLIED OCEAN RESEARCH
(2021)
Article
Computer Science, Interdisciplinary Applications
Kairui Bao, Wen Yao, Xiaoya Zhang, Wei Peng, Yu Li
Summary: This paper proposes a physics and data co-driven surrogate modeling method for temperature field prediction on irregular geometric domains. By adapting Bezier curves and body-fitted coordinate mapping to handle irregular geometry, and combining physics-driven CNN surrogate and data-driven surrogate models, an end-to-end surrogate model from geometric parameters to temperature field prediction is established. Numerical results demonstrate significant improvement in accuracy prediction and reduced training time compared to other CNN methods.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Computer Science, Software Engineering
Ran Luo, Weiwei Xu, Huamin Wang, Kun Zhou, Yin Yang
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
(2018)
Article
Computer Science, Software Engineering
Weiwei Xu, Haifeng Yang, Yin Yang, Yiduo Wang, Kun Zhou
COMPUTER AIDED GEOMETRIC DESIGN
(2018)
Article
Computer Science, Software Engineering
Haiming Zhao, Xiaogang Jin, Xiaojian Huang, Menglei Chai, Kun Zhou
IEEE COMPUTER GRAPHICS AND APPLICATIONS
(2018)
Article
Computer Science, Artificial Intelligence
Chen Li, Kun Zhou, Hsiang-Tao Wu, Stephen Lin
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2019)
Editorial Material
Computer Science, Software Engineering
Xin Tong, Kun Zhou
IEEE COMPUTER GRAPHICS AND APPLICATIONS
(2019)
Article
Computer Science, Software Engineering
Lijuan Liu, Youyi Zheng, Di Tang, Yi Yuan, Changjie Fan, Kun Zhou
ACM TRANSACTIONS ON GRAPHICS
(2019)
Article
Computer Science, Software Engineering
Lingchen Yang, Zefeng Shi, Youyi Zheng, Kun Zhou
ACM TRANSACTIONS ON GRAPHICS
(2019)
Article
Engineering, Multidisciplinary
Kun Zhou, Xiao Jiang, Tat Leung Chan
APPLIED MATHEMATICAL MODELLING
(2020)
Article
Computer Science, Interdisciplinary Applications
Kun Zhou, S. Balachandar
Summary: The study investigates the application and performance of the immersed boundary method in simulating rigid particulate flows, introducing new findings such as the solution to a least-squares error problem and the optimal choice of Lagrangian volume-weight. It also highlights the importance of high-resolution grids and small time steps for obtaining high-precision simulation results.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mechanics
Zhanhong Wan, Kun Zhou, Wei Yang, Zhenjiang You, Ke Sun
FLUID DYNAMICS RESEARCH
(2019)
Proceedings Paper
Computer Science, Theory & Methods
Meng Zhang, Pan Wu, Hongzhi Wu, Yanlin Weng, Youyi Zheng, Kun Zhou
SIGGRAPH ASIA'18: SIGGRAPH ASIA 2018 TECHNICAL PAPERS
(2018)
Proceedings Paper
Computer Science, Theory & Methods
Jiahao Geng, Tianjia Shao, Youyi Zheng, Yanlin Weng, Kun Zhou
SIGGRAPH ASIA'18: SIGGRAPH ASIA 2018 TECHNICAL PAPERS
(2018)
Article
Computer Science, Software Engineering
Y. Wang, B. Liu, K. Zhou, Y. Tong
COMPUTER GRAPHICS FORUM
(2018)
Review
Nanoscience & Nanotechnology
Kun Zhou, Ke Sun, Xiao Jiang, Shaojie Liu, Zhu He, Zhou Ding
JOURNAL OF NANOTECHNOLOGY
(2018)
Article
Nanoscience & Nanotechnology
Xiao Jiang, Kun Zhou, Ming Xiao, Ke Sun, Yu Wang
JOURNAL OF NANOTECHNOLOGY
(2018)