Close Search Advanced
Journals
Resources
About Us
Open Access

Fast Solution of Three-Dimensional Modified Helmholtz Equations by the Method of Fundamental Solutions

Fast Solution of Three-Dimensional Modified Helmholtz Equations by the Method of Fundamental Solutions
Preview
Add to basket

Year:    2016

Communications in Computational Physics, Vol. 20 (2016), Iss. 2 : pp. 512–533

Abstract

This paper describes an application of the recently developed sparse scheme of the method of fundamental solutions (MFS) for the simulation of three-dimensional modified Helmholtz problems. The solution to the given problems is approximated by a two-step strategy which consists of evaluating the particular solution and the homogeneous solution. The homogeneous solution is approximated by the traditional MFS. The original dense system of the MFS formulation is condensed into a sparse system based on the exponential decay of the fundamental solutions. Hence, the homogeneous solution can be efficiently obtained. The method of particular solutions with polyharmonic spline radial basis functions and the localized method of approximate particular solutions in combination with the Gaussian radial basis function are employed to approximate the particular solution. Three numerical examples including a near singular problem are presented to show the simplicity and effectiveness of this approach.

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/cicp.060915.301215a

Communications in Computational Physics, Vol. 20 (2016), Iss. 2 : pp. 512–533

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:   

  1. A Novel Meshfree Approach with a Radial Polynomial for Solving Nonhomogeneous Partial Differential Equations

    Ku, Cheng-Yu | Xiao, Jing-En | Liu, Chih-Yu

    Mathematics, Vol. 8 (2020), Iss. 2 P.270

    https://doi.org/10.3390/math8020270 [Citations: 1]

  2. A backward-forward Lie-group shooting method for nonhomogeneous multi-dimensional backward heat conduction problems under a long time span

    Chen, Yung-Wei

    International Journal of Heat and Mass Transfer, Vol. 133 (2019), Iss. P.226

    https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.103 [Citations: 4]

  3. Diffusion toward non-overlapping partially reactive spherical traps: Fresh insights onto classic problems

    Grebenkov, Denis S.

    The Journal of Chemical Physics, Vol. 152 (2020), Iss. 24

    https://doi.org/10.1063/5.0012719 [Citations: 25]

  4. A new approach to solve the anti-plane crack problems by the method of fundamental solutions

    Jiang, Quan | Zhou, Zhidong | Yang, Fengpeng

    Engineering Analysis with Boundary Elements, Vol. 135 (2022), Iss. P.284

    https://doi.org/10.1016/j.enganabound.2021.12.003 [Citations: 2]

  5. A homogenization function technique to solve the 3D inverse Cauchy problem of elliptic type equations in a closed walled shell

    Liu, Chein-Shan | Zhang, Yaoming | Wang, Fajie

    Inverse Problems in Science and Engineering, Vol. 29 (2021), Iss. 7 P.944

    https://doi.org/10.1080/17415977.2020.1814284 [Citations: 2]

  6. A novel Trefftz method of the inverse Cauchy problem for 3D modified Helmholtz equation

    Liu, Chein-Shan | Qu, Wenzhen | Chen, Wen | Lin, Ji

    Inverse Problems in Science and Engineering, Vol. 25 (2017), Iss. 9 P.1278

    https://doi.org/10.1080/17415977.2016.1247449 [Citations: 13]

  7. Meshless Method for Analysis of Permeable Breakwaters in the Proximity of A Vertical Wall

    Chioukh, Nadji | Ouazzane, Karim | Yüksel, Yalçın | Hamoudi, Benameur | Çevik, Esin

    China Ocean Engineering, Vol. 33 (2019), Iss. 2 P.148

    https://doi.org/10.1007/s13344-019-0015-7 [Citations: 8]

  8. A quasi-reversibility regularization method for a Cauchy problem of the modified Helmholtz-type equation

    Yang, Hong | Yang, Yanqi

    Boundary Value Problems, Vol. 2019 (2019), Iss. 1

    https://doi.org/10.1186/s13661-019-1142-z [Citations: 2]

  9. Pseudo and anisotropic MFS for Laplace equation and optimal sources using maximal projection method with a substitution function

    Liu, Chein-Shan | Kuo, Chung-Lun

    Engineering Analysis with Boundary Elements, Vol. 158 (2024), Iss. P.313

    https://doi.org/10.1016/j.enganabound.2023.11.005 [Citations: 1]

  10. Maximizing the projection/minimizing the mass gap to choose optimal source points in the MFS for 2D and 3D Laplace equations

    Liu, Chein-Shan | Kuo, Chung-Lun

    Engineering Analysis with Boundary Elements, Vol. 164 (2024), Iss. P.105674

    https://doi.org/10.1016/j.enganabound.2024.04.013 [Citations: 0]

  11. Stress analysis of anti-plane finite elastic solids with hole by the method of fundamental solutions using conformal mapping technique

    Yuan, Xiaoguang | Jiang, Quan | Zhou, Zhidong | Yang, Fengpeng

    Archive of Applied Mechanics, Vol. 92 (2022), Iss. 6 P.1823

    https://doi.org/10.1007/s00419-022-02150-0 [Citations: 1]

  12. On solving free surface problems in layered soil using the method of fundamental solutions

    Xiao, Jing-En | Ku, Cheng-Yu | Liu, Chih-Yu | Fan, Chia-Ming | Yeih, Weichung

    Engineering Analysis with Boundary Elements, Vol. 83 (2017), Iss. P.96

    https://doi.org/10.1016/j.enganabound.2017.07.011 [Citations: 17]