Close Search Advanced
Journals
Resources
About Us
Open Access

A Dual-Level Method of Fundamental Solutions in Conjunction with Kernel-Independent Fast Multipole Method for Large-Scale Isotropic Heat Conduction Problems

A Dual-Level Method of Fundamental Solutions in Conjunction with Kernel-Independent Fast Multipole Method for Large-Scale Isotropic Heat Conduction Problems
Preview
Add to basket

Year:    2019

Author:    Junpu Li, Zhuojia Fu, Wen Chen, Xiaoting Liu

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 501–517

Abstract

A dual-level method of fundamental solutions in conjunction with kernel- independent fast multipole method is proposed in this study. The competitive attributes of the method are that it inherits high accuracy of the method of fundamental solutions, yet avoids producing the resulting ill-conditioned linear system of equations. In contrast to the method of fundamental solutions, the proposed method places two sets of source nodes on the fictitious boundary and physical boundary, respectively, and then combines the fundamental solutions generated by these two sets of source nodes as the modified fundamental solutions of the Laplace equation. This strategy improves significantly the stability of the method of fundamental solutions. In addition, the method is accelerated by the kernel-independent fast multipole method, which reduces the asymptotic complexity of the method to $\mathcal{O}(N)$ from $\mathcal{O}({N}^{2})$. Numerical experiments show that the method can simulate successfully the large-scale heat conduction problems via a single laptop with up to 250000 degrees of freedom.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0148

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 501–517

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Dual-level method of fundamental solutions isotropic heat conduction problems ill-conditioning range restricted GMRES method kernel-independent fast multipole method.

Author Details

Junpu Li

Zhuojia Fu

Wen Chen

Xiaoting Liu

  1. Local non-singular knot method for large-scale computation of acoustic problems in complicated geometries

    Yue, Xingxing | Wang, Fajie | Li, Po-Wei | Fan, Chia-Ming

    Computers & Mathematics with Applications, Vol. 84 (2021), Iss. P.128

    https://doi.org/10.1016/j.camwa.2020.12.014 [Citations: 13]

  2. A novel B-spline method to analyze convection-diffusion-reaction problems in anisotropic inhomogeneous medium

    Reutskiy, Sergiy | Zhang, Yuhui | Lin, Ji | Lu, Jun | Xu, Haifeng | He, Yongjun

    Engineering Analysis with Boundary Elements, Vol. 118 (2020), Iss. P.216

    https://doi.org/10.1016/j.enganabound.2020.06.013 [Citations: 5]

  3. A Numerical Method for Filtering the Noise in the Heat Conduction Problem

    Sun, Yao | Wei, Xiaoliang | Zhuang, Zibo | Luan, Tian

    Mathematics, Vol. 7 (2019), Iss. 6 P.502

    https://doi.org/10.3390/math7060502 [Citations: 2]

  4. A spatial–temporal GFDM with an additional condition for transient heat conduction analysis of FGMs

    Qu, Wenzhen | He, Hua

    Applied Mathematics Letters, Vol. 110 (2020), Iss. P.106579

    https://doi.org/10.1016/j.aml.2020.106579 [Citations: 67]

  5. A cubic B-spline semi-analytical algorithm for simulation of 3D steady-state convection-diffusion-reaction problems

    Lin, Ji | Reutskiy, Sergiy

    Applied Mathematics and Computation, Vol. 371 (2020), Iss. P.124944

    https://doi.org/10.1016/j.amc.2019.124944 [Citations: 13]

  6. A localized spatiotemporal particle collocation method for long-time transient homogeneous diffusion analysis

    Li, Junpu | Zhang, Lan | Qin, Qinghua | Wang, Fei

    International Journal of Heat and Mass Transfer, Vol. 192 (2022), Iss. P.122893

    https://doi.org/10.1016/j.ijheatmasstransfer.2022.122893 [Citations: 2]

  7. A modified multilevel algorithm for large-scale scientific and engineering computing

    Li, Junpu | Chen, Wen | Qin, Qing-Hua | Fu, Zhuojia

    Computers & Mathematics with Applications, Vol. 77 (2019), Iss. 8 P.2061

    https://doi.org/10.1016/j.camwa.2018.12.012 [Citations: 33]

  8. A regularized method of moments for three-dimensional time-harmonic electromagnetic scattering

    Li, Junpu | Zhang, Lan | Qin, Qing-Hua

    Applied Mathematics Letters, Vol. 112 (2021), Iss. P.106746

    https://doi.org/10.1016/j.aml.2020.106746 [Citations: 43]

  9. A robust kernel-based solver for variable-order time fractional PDEs under 2D/3D irregular domains

    Fu, Zhuo-Jia | Reutskiy, Sergiy | Sun, Hong-Guang | Ma, Ji | Khan, Mushtaq Ahmad

    Applied Mathematics Letters, Vol. 94 (2019), Iss. P.105

    https://doi.org/10.1016/j.aml.2019.02.025 [Citations: 66]

  10. An efficient boundary collocation scheme for transient thermal analysis in large-size-ratio functionally graded materials under heat source load

    Xi, Qiang | Fu, Zhuo-Jia | Rabczuk, Timon

    Computational Mechanics, Vol. 64 (2019), Iss. 5 P.1221

    https://doi.org/10.1007/s00466-019-01701-7 [Citations: 34]

  11. An efficient meshless boundary point interpolation method for acoustic radiation and scattering

    Chen, Linchong | Li, Xiaolin

    Computers & Structures, Vol. 229 (2020), Iss. P.106182

    https://doi.org/10.1016/j.compstruc.2019.106182 [Citations: 13]

  12. The rapid assessment for three-dimensional potential model of large-scale particle system by a modified multilevel fast multipole algorithm

    Li, Junpu | Gu, Yan | Qin, Qing-Hua | Zhang, Lan

    Computers & Mathematics with Applications, Vol. 89 (2021), Iss. P.127

    https://doi.org/10.1016/j.camwa.2021.03.003 [Citations: 35]

  13. High-precision calculation of electromagnetic scattering by the Burton-Miller type regularized method of moments

    Li, Junpu | Zhang, Lan

    Engineering Analysis with Boundary Elements, Vol. 133 (2021), Iss. P.177

    https://doi.org/10.1016/j.enganabound.2021.09.001 [Citations: 18]

  14. A meshless radial basis function based method for modeling dual-phase-lag heat transfer in irregular domains

    Lin, Ji | Yu, Hao | Reutskiy, Sergiy | Wang, Yuan

    Computers & Mathematics with Applications, Vol. 85 (2021), Iss. P.1

    https://doi.org/10.1016/j.camwa.2020.12.018 [Citations: 4]

  15. A Modified Formulation of Singular Boundary Method for Exterior Acoustics

    Wu, Yi | Fu, Zhuojia | Min, Jian

    Computer Modeling in Engineering & Sciences, Vol. 135 (2023), Iss. 1 P.377

    https://doi.org/10.32604/cmes.2022.023205 [Citations: 0]

  16. A regularized fast multipole method of moments for rapid calculation of three-dimensional time-harmonic electromagnetic scattering from complex targets

    Li, Junpu | Zhang, Lan | Qin, Qinghua

    Engineering Analysis with Boundary Elements, Vol. 142 (2022), Iss. P.28

    https://doi.org/10.1016/j.enganabound.2022.06.001 [Citations: 14]

  17. An improved boundary point interpolation method for exterior acoustic radiation problem

    Chen, Linchong | Li, Xiaolin

    Engineering Analysis with Boundary Elements, Vol. 103 (2019), Iss. P.11

    https://doi.org/10.1016/j.enganabound.2019.02.002 [Citations: 10]

  18. Augmented moving least squares approximation using fundamental solutions

    Wang, Fajie | Qu, Wenzhen | Li, Xiaolin

    Engineering Analysis with Boundary Elements, Vol. 115 (2020), Iss. P.10

    https://doi.org/10.1016/j.enganabound.2020.03.003 [Citations: 10]

  19. The MAPS with polynomial basis functions for solving axisymmetric time-fractional equations

    Xi, Qiang | Chen, C.S. | Fu, Zhuojia | Comino, Eva

    Computers & Mathematics with Applications, Vol. 88 (2021), Iss. P.78

    https://doi.org/10.1016/j.camwa.2019.11.014 [Citations: 5]

  20. A Coupled FE-Meshfree Triangular Element for Acoustic Radiation Problems

    Li, Wei | Zhang, Qifan | Gui, Qiang | Chai, Yingbin

    International Journal of Computational Methods, Vol. 18 (2021), Iss. 03 P.2041002

    https://doi.org/10.1142/S0219876220410029 [Citations: 57]

  21. A semi-analytical boundary collocation solver for the inverse Cauchy problems in heat conduction under 3D FGMs with heat source

    Xi, Qiang | Fu, Zhuojia | Alves, Carlos | Ji, Hongli

    Numerical Heat Transfer, Part B: Fundamentals, Vol. 76 (2019), Iss. 5 P.311

    https://doi.org/10.1080/10407790.2019.1665386 [Citations: 7]

  22. Moving pseudo-boundary method of fundamental solutions for nonlinear potential problems

    Grabski, Jakub Krzysztof | Karageorghis, Andreas

    Engineering Analysis with Boundary Elements, Vol. 105 (2019), Iss. P.78

    https://doi.org/10.1016/j.enganabound.2019.04.009 [Citations: 10]

  23. Two-dimensional FM-IBEM solution to the broadband scattering of elastic waves in a fluid-saturated poroelastic half-space

    Liu, Zhongxian | He, Chenrui | Wang, Hailiang | Shuaijie, Sun

    Engineering Analysis with Boundary Elements, Vol. 104 (2019), Iss. P.300

    https://doi.org/10.1016/j.enganabound.2019.03.027 [Citations: 16]

  24. A hybrid meshless method for the solution of the second order hyperbolic telegraph equation in two space dimensions

    Zhou, Yunxu | Qu, Wenzhen | Gu, Yan | Gao, Hongwei

    Engineering Analysis with Boundary Elements, Vol. 115 (2020), Iss. P.21

    https://doi.org/10.1016/j.enganabound.2020.02.015 [Citations: 21]

  25. Numerical solution of scalar wave equation by the modified radial integration boundary element method

    Najarzadeh, L. | Movahedian, B. | Azhari, M.

    Engineering Analysis with Boundary Elements, Vol. 105 (2019), Iss. P.267

    https://doi.org/10.1016/j.enganabound.2019.04.027 [Citations: 14]

  26. Application of the Fast Multipole Method to Optimization of the Boundary Element Method of Solving the Helmholtz Equation

    Sivak, S. A. | Royak, M. E. | Stupakov, I. M.

    Journal of Applied and Industrial Mathematics, Vol. 15 (2021), Iss. 3 P.490

    https://doi.org/10.1134/S199047892103011X [Citations: 0]

  27. A regularized approach evaluating origin intensity factor of singular boundary method for Helmholtz equation with high wavenumbers

    Li, Junpu | Fu, Zhuojia | Chen, Wen | Qin, Qing-Hua

    Engineering Analysis with Boundary Elements, Vol. 101 (2019), Iss. P.165

    https://doi.org/10.1016/j.enganabound.2019.01.008 [Citations: 12]

  28. Estimation of Tumor Characteristics in a Skin Tissue by a Meshless Collocation Solver

    Fu, Zhuo-Jia | Chu, Wen-Hui | Yang, Min | Li, Po-Wei | Fan, Chia-Ming

    International Journal of Computational Methods, Vol. 18 (2021), Iss. 03 P.2041009

    https://doi.org/10.1142/S0219876220410091 [Citations: 6]

  29. A meshless numerical method for time harmonic quasi-periodic scattering problem

    Luan, Tian | Sun, Yao | Zhuang, Zibo

    Engineering Analysis with Boundary Elements, Vol. 104 (2019), Iss. P.320

    https://doi.org/10.1016/j.enganabound.2019.03.034 [Citations: 2]

  30. An accurate meshless collocation technique for solving two-dimensional hyperbolic telegraph equations in arbitrary domains

    Lin, Ji | Chen, Fen | Zhang, Yuhui | Lu, Jun

    Engineering Analysis with Boundary Elements, Vol. 108 (2019), Iss. P.372

    https://doi.org/10.1016/j.enganabound.2019.08.012 [Citations: 25]

  31. Dispersion error reduction for interior acoustic problems using the radial point interpolation meshless method with plane wave enrichment functions

    Gui, Qiang | Zhang, Yang | Chai, Yingbin | You, Xiangyu | Li, Wei

    Engineering Analysis with Boundary Elements, Vol. 143 (2022), Iss. P.428

    https://doi.org/10.1016/j.enganabound.2022.07.001 [Citations: 13]

  32. A regularized approach evaluating the near-boundary and boundary solutions for three-dimensional Helmholtz equation with wideband wavenumbers

    Li, Junpu | Chen, Wen | Fu, Zhuojia | Qin, Qing-Hua

    Applied Mathematics Letters, Vol. 91 (2019), Iss. P.55

    https://doi.org/10.1016/j.aml.2018.11.027 [Citations: 37]