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| 1 | A novel numerical method for infinite domain potential problems显示文摘The infinite domain potential problems arise in many branches of scientific and engineering fields, which by now still pose a great challenge to scientific computing community.This study proposes a novel meshless singular boundary method (SBM) to solve infinite domain potential problems.The SBM is mathematically simple, easy-to-program, meshless and integration-free.To guar-antee the uniqueness of numerical solutions, this article adds a constant term into the SBM approximate representation.The effi-ciency and accuracy of the proposed technique are tested to the three infinite domain potential problems. | CHEN Wen FU ZhuoJia | 2010 | Chinese Science Bulletin2010，55，16： | 9 |
| 2 | A localized Fourier collocation method for 2D and 3D elliptic partial differential equations:Theory and MATLAB code显示文摘A localized Fourier collocation method is proposed for solving certain types of elliptic boundary value problems.The method first discretizes the entire domain into a set of overlapping small subdomains,and then in each of the subdomains,the unknown functions and their derivatives are approximated using the pseudo-spectral Fourier collocation method.The key idea of the present method is to combine the merits of the quick convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique to yield a new framework that may be suitable for large-scale simulations.The present method can be viewed as a competitive alternative for solving numerically large-scale boundary value problems with complex-shape geometries.Preliminary numerical experiments involving Poisson,Helmholtz,and modified-Helmholtz equations in both two and three dimensions are presented to demonstrate the accuracy and efficiency of the proposed method. | Yan Gu Zhuojia Fu Mikhail V.Golub | 2022 | International Journal of Mechanical System Dynamics2022，2，4： | 2 |
| 3 | Recursive Schemes for Scattered Data Interpolation via Bivariate Continued Fractions显示文摘In the paper,firstly,based on new non-tensor-product-typed partially inverse divided differences algorithms in a recursive form,scattered data interpolating schemes are constructed via bivariate continued fractions with odd and even nodes,respectively.And equivalent identities are also obtained between interpolated functions and bivariate continued fractions.Secondly,by means of three-term recurrence relations for continued fractions,the characterization theorem is presented to study on the degrees of the numerators and denominators of the interpolating continued fractions.Thirdly,some numerical examples show it feasible for the novel recursive schemes.Meanwhile,compared with the degrees of the numerators and denominators of bivariate Thiele-typed interpolating continued fractions,those of the new bivariate interpolating continued fractions are much low,respectively,due to the reduction of redundant interpolating nodes.Finally,the operation count for the rational function interpolation is smaller than that for radial basis function interpolation. | Jiang QIAN Fan WANG Zhuojia FU Yunbiao WU | 2016 | Journal of Mathematical Research with Applications2016，36，5： | 2 |
| 4 | Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory显示文摘A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation.Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations.Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies.The advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed. | Yan Gu Chia-Ming Fan Zhuojia Fu | 2021 | Advances in Applied Mathematics and Mechanics2021，13，6： | 2 |
| 5 | Boundary knot method for heat conduction in nonlinear funetionally graded material显示文摘 | Fu Zhuojia Chen Wen Qin Qinghua | 2011 | Engineering Analysis with Boundary Elements2011，35，5： | 1 |
| 6 | Boundary knot method for heat conduction in nonlinear functionally graded material 显示文摘 | FU Zhuojia CHEN Wen QIN Qinghua | 2011 | Engineering Analysis with Bound- ary Elements2011，35，5： | 1 |
| 7 | Winkler plate bending problems by a truly boundary-only boundary particle method显示文摘 | Zhuojia Fu Wen Chen Wei Yang | 2009 | Computational Mechanics2009，，6： | 1 |
| 8 | Isogeometric Boundary Element Analysis for 2D Transient Heat Conduction Problem with Radial Integration Method显示文摘This paper presents an isogeometric boundary element method(IGABEM)for transient heat conduction analysis.The Non-Uniform Rational B-spline(NURBS)basis functions,which are used to construct the geometry of the structures,are employed to discretize the physical unknowns in the boundary integral formulations of the governing equations.Bezier extraction technique is employed to accelerate the evaluation of NURBS basis functions.We adopt a radial integration method to address the additional domain integrals.The numerical examples demonstrate the advantage of IGABEM in dimension reduction and the seamless connection between CAD and numerical analysis. | Leilei Chen Kunpeng Li Xuan Peng Haojie Lian Xiao Lin Zhuojia Fu | 2021 | Computer Modeling in Engineering & Sciences2021，，1： | 1 |
| 9 | A Modified Formulation of Singular Boundary Method for Exterior Acoustics显示文摘This paper proposes amodified formulation of the singular boundarymethod(SBM)by introducing the combined Helmholtz integral equation formulation(CHIEF)and the self-regularization technique to exterior acoustics.In the SBM,the concept of the origin intensity factor(OIF)is introduced to avoid the singularities of the fundamental solutions.The SBM belongs to the meshless boundary collocation methods.The additional use of the CHIEF scheme and the self-regularization technique in the SBM guarantees the unique solution of the exterior acoustics accurately and efficiently.Consequently,by using the SBM coupled with the CHIEF scheme and the self-regularization technique,the accuracy of the numerical solution can be improved,especially near the corresponding internal characteristic frequencies.Several numerical examples of two-dimensional and threedimensional benchmark examples about exterior acoustics are used to verify the effectiveness and accuracy of the proposed method.The proposed numerical results are compared with the analytical solutions and the solutions obtained by the other numerical methods. | Yi Wu Zhuojia Fu Jian Min | 2023 | Computer Modeling in Engineering & Sciences2023，，4： | 0 |
| 10 | A Truly Boundary-Only Meshfree Method Applied to Kirchhoff Plate Bending Problems显示文摘The boundary particle method(BPM)is a truly boundary-only collocation scheme,whose basis function is the high-order nonsingular general solution or singular fundamental solution,based on the recursive composite multiple reciprocity method(RC-MRM).The RC-MRM employs the high-order composite differential operator to solve a much wider variety of inhomogeneous problems with boundary-only collocation nodes while significantly reducing computational cost via a recursive algorithm.In this study,we simulate the Kirchhoff plate bending problems by the BPM based on the RC-MRM.Numerical results show that this approach produces accurate solutions of plates subjected to various loadings with boundary-only discretization. | Zhuojia Fu Wen Chen | 2009 | Advances in Applied Mathematics and Mechanics2009，1，3： | 0 |
| 11 | Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials显示文摘The localized method of fundamental solutions(LMFS)is a relatively new meshless boundary collocation method.In the LMFS,the global MFS approxima-tion which is expensive to evaluate is replaced by local MFS formulation defined in a set of overlapping subdomains.The LMFS algorithm therefore converts differential equations into sparse rather than dense matrices which are much cheaper to calcu-late.This paper makes thefirst attempt to apply the LMFS,in conjunction with a domain-decomposition technique,for the numerical solution of steady-state heat con-duction problems in two-dimensional(2D)anisotropic layered materials.Here,the layered material is decomposed into several subdomains along the layer-layer inter-faces,and in each of the subdomains,the solution is approximated by using the LMFS expansion.On the subdomain interface,compatibility of temperatures and heatfluxes are imposed.Preliminary numerical experiments illustrate that the proposed domain-decomposition LMFS algorithm is accurate,stable and computationally efficient for the numerical solution of large-scale multi-layered materials. | Shuainan Liu Zhuojia Fu Yan Gu | 2022 | Advances in Applied Mathematics and Mechanics2022，14，3： | 0 |
| 12 | Recent Advances and Emerging Applications of the Singular Boundary Method for Large-Scale and High-Frequency Computational Acoustics显示文摘With the rapid development of computer technology,numerical simulation has become the third scientific research tool besides theoretical analysis and experi-mental research.As the core of numerical simulation,constructing efficient,accurate and stable numerical methods to simulate complex scientific and engineering prob-lems has become a key issue in computational mechanics.The article outlines the ap-plication of singular boundary method to the large-scale and high-frequency acoustic problems.In practical application,the key issue is to construct efficient and accurate numerical methodology to calculate the large-scale and high-frequency soundfield.This article focuses on the following two research areas.They are how to discretize partial differential equations into more appropriate linear equations,and how to solve linear equations more efficiently.The bottle neck problems encountered in the compu-tational acoustics are used as the technical routes,i.e.,efficient solution of dense linear system composed of ill-conditioned matrix and stable simulation of wave propagation at low sampling frequencies.The article reviews recent advances in emerging appli-cations of the singular boundary method for computational acoustics.This collection can provide a reference for simulating other more complex wave propagation. | Junpu Li Zhuojia Fu Yan Gu Qing-Hua Qin | 2022 | Advances in Applied Mathematics and Mechanics2022，14，2： | 0 |
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