메뉴 건너뛰기




Volumn 28, Issue 2, 2008, Pages 77-93

Improving the Ill-conditioning of the method of fundamental solutions for 2D laplace equation

Author keywords

Collocation method; Laplace equation; Method of fundamental solutions; Modified MFS (MMFS); Modified Trefftz method

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; INITIAL VALUE PROBLEMS; LAPLACE EQUATION; NUMERICAL METHODS; SOLUTIONS;

EID: 49149127660     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (50)

References (42)
  • 1
    • 0033334001 scopus 로고    scopus 로고
    • A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods
    • Atluri, S. N.; Kim, H. G.; Cho, J. Y. (1999): A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods. Computational Mechanics, vol. 24, pp. 348-372.
    • (1999) Computational Mechanics , vol.24 , pp. 348-372
    • Atluri, S.N.1    Kim, H.G.2    Cho, J.Y.3
  • 2
    • 0042964833 scopus 로고    scopus 로고
    • The meshless local Petrov-Galerkin (MLPG) method: A simple & less-costly alternative to the finite element and boundary element methods
    • Atluri, S. N.; Shen, S. (2002): The meshless local Petrov-Galerkin (MLPG) method: a simple & less-costly alternative to the finite element and boundary element methods. CMES: Computer Modeling in Engineering and Sciences, vol. 3, pp. 11-51.
    • (2002) CMES: Computer Modeling in Engineering and Sciences , vol.3 , pp. 11-51
    • Atluri, S.N.1    Shen, S.2
  • 3
    • 0022107918 scopus 로고
    • Fundamental solutions method for elliptic boundary value problems
    • Bogomolny, A. (1985): Fundamental solutions method for elliptic boundary value problems. SIAM Journal on Numerical Analysis, vol. 22, pp. 644-669.
    • (1985) SIAM Journal on Numerical Analysis , vol.22 , pp. 644-669
    • Bogomolny, A.1
  • 5
    • 33646130396 scopus 로고    scopus 로고
    • Some comments on the ill-conditioning of the method of fundamental solutions
    • Chen, C. S.; Cho, H. A.; Golberg, M. A. (2006): Some comments on the ill-conditioning of the method of fundamental solutions. Engineering Analysis with Boundary Elements, vol. 30, pp. 405-410.
    • (2006) Engineering Analysis with Boundary Elements , vol.30 , pp. 405-410
    • Chen, C.S.1    Cho, H.A.2    Golberg, M.A.3
  • 6
    • 0037206998 scopus 로고    scopus 로고
    • The boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function
    • Chen, J. T.; Chang, M. H.; Chen, K. H.; Lin, S. R. (2002): The boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function. Journal of Sound and Vibration, vol. 257, pp. 667-711.
    • (2002) Journal of Sound and Vibration , vol.257 , pp. 667-711
    • Chen, J.T.1    Chang, M.H.2    Chen, K.H.3    Lin, S.R.4
  • 7
    • 0036815548 scopus 로고    scopus 로고
    • Boundary collocation method for acoustic eigenanalysis of three-dimensional cavities using radial basis function
    • Chen, J. T.; Chang, M. H.; Chen, K. H.; Chen, I. L. (2002): Boundary collocation method for acoustic eigenanalysis of three-dimensional cavities using radial basis function. Computational Mechanics, vol. 29, pp. 392-408.
    • (2002) Computational Mechanics , vol.29 , pp. 392-408
    • Chen, J.T.1    Chang, M.H.2    Chen, K.H.3    Chen, I.L.4
  • 8
    • 34248149996 scopus 로고    scopus 로고
    • On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equations
    • Chen J. T.; Wu C. S.; Lee Y. T.; Chen K. H. (2007): On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equations. Computers and Mathematics with Applications 2007;53:851-879.
    • (2007) Computers and Mathematics with Applications 2007 , vol.53 , pp. 851-879
    • Chen, J.T.1    Wu, C.S.2    Lee, Y.T.3    Chen, K.H.4
  • 9
    • 0036467593 scopus 로고    scopus 로고
    • A meshless, integration-free, and boundary-only RBF technique
    • Chen, W.; Tanaka, M. (2002): A meshless, integration-free, and boundary-only RBF technique. Computers and Mathematics with Applications, vol. 43, pp. 379-391.
    • (2002) Computers and Mathematics with Applications , vol.43 , pp. 379-391
    • Chen, W.1    Tanaka, M.2
  • 12
    • 0032685674 scopus 로고    scopus 로고
    • Numerical studies on desingularized Cauchy's formula with applications to interior potential problems
    • Chuang, J. M. (1999): Numerical studies on desingularized Cauchy's formula with applications to interior potential problems. International Journal for Numerical Methods in Engineering, vol. 46, pp. 805-824.
    • (1999) International Journal for Numerical Methods in Engineering , vol.46 , pp. 805-824
    • Chuang, J.M.1
  • 13
    • 0032344733 scopus 로고    scopus 로고
    • The method of fundamental solutions for elliptic boundary value problems
    • Fairweather, G.; Karageorghis, A. (1998): The method of fundamental solutions for elliptic boundary value problems. Advances in Computational Mathematics, vol. 9, pp. 69-95.
    • (1998) Advances in Computational Mathematics , vol.9 , pp. 69-95
    • Fairweather, G.1    Karageorghis, A.2
  • 14
    • 15844386645 scopus 로고    scopus 로고
    • Analysis of the 2D Stokes flows by the nonsingular boundary integral equation method
    • Fan, C. M.; Young, D. L. (2002): Analysis of the 2D Stokes flows by the nonsingular boundary integral equation method. International Mathematical Journal, vol. 2, pp. 1199-1215.
    • (2002) International Mathematical Journal , vol.2 , pp. 1199-1215
    • Fan, C.M.1    Young, D.L.2
  • 17
    • 15544363903 scopus 로고    scopus 로고
    • The method of fundamental solution for solving multidimensional inverse heat conduction problems
    • Hon, Y. C.; Wei, T. (2005): The method of fundamental solution for solving multidimensional inverse heat conduction problems. CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 119-132.
    • (2005) CMES: Computer Modeling in Engineering & Sciences , vol.7 , pp. 119-132
    • Hon, Y.C.1    Wei, T.2
  • 18
    • 0032029312 scopus 로고    scopus 로고
    • Nonsingular direct formulation of boundary integral equations for potential flows
    • Hwang, W. S.; Huang, Y. Y. (1998): Nonsingular direct formulation of boundary integral equations for potential flows. International Journal for Numerical Methods in Fluids, vol. 26, pp. 627-635.
    • (1998) International Journal for Numerical Methods in Fluids , vol.26 , pp. 627-635
    • Hwang, W.S.1    Huang, Y.Y.2
  • 19
    • 33646091081 scopus 로고    scopus 로고
    • Boundary knot method based on geodesic distance for anisotropic problems
    • Jin, B.; Chen, W. (2006): Boundary knot method based on geodesic distance for anisotropic problems. Journal of Computational Physics, vol. 215, pp. 614-629.
    • (2006) Journal of Computational Physics , vol.215 , pp. 614-629
    • Jin, B.1    Chen, W.2
  • 21
    • 0032673969 scopus 로고    scopus 로고
    • Application of a direct Trefftz method with domain decomposition to 2D potential problems
    • Kita, E.; Kamiya, N.; Iio, T. (1999): Application of a direct Trefftz method with domain decomposition to 2D potential problems. Engineering Analysis with Boundary Elements, vol. 23, pp. 539-548.
    • (1999) Engineering Analysis with Boundary Elements , vol.23 , pp. 539-548
    • Kita, E.1    Kamiya, N.2    Iio, T.3
  • 22
    • 0003599931 scopus 로고
    • Irrotational flow about ship forms
    • No. 123, Iowa University
    • Landweber, L.; Macagno, M. (1969): Irrotational flow about ship forms. IIHR Report No. 123, Iowa University.
    • (1969) IIHR Report
    • Landweber, L.1    Macagno, M.2
  • 23
    • 0031277845 scopus 로고
    • On the accuracy of the desingularized boundary integral method in free surface flow problems
    • Lalli, F. (1991): On the accuracy of the desingularized boundary integral method in free surface flow problems. International Journal for Numerical Methods in Fluids, vol. 25, pp. 1163-1184.
    • (1991) International Journal for Numerical Methods in Fluids , vol.25 , pp. 1163-1184
    • Lalli, F.1
  • 25
    • 35348966933 scopus 로고    scopus 로고
    • A modified Trefftz method for two-dimensional Laplace equation considering the domain's characteristic length
    • Liu, C.-S. (2007a): A modified Trefftz method for two-dimensional Laplace equation considering the domain's characteristic length. CMES: Computer Modeling in Engineering & Sciences, vol. 21, pp. 53-65.
    • (2007) CMES: Computer Modeling in Engineering & Sciences , vol.21 , pp. 53-65
    • Liu, C.-S.1
  • 26
    • 34250180604 scopus 로고    scopus 로고
    • A meshless regularized integral equation method for Laplace equation in arbitrary interior or exterior plane domains
    • Liu, C.-S. (2007b): A meshless regularized integral equation method for Laplace equation in arbitrary interior or exterior plane domains. CMES: Computer Modeling in Engineering Sc Sciences, vol. 19, pp. 99-109.
    • (2007) CMES: Computer Modeling in Engineering Sc Sciences , vol.19 , pp. 99-109
    • Liu, C.-S.1
  • 27
    • 34250207387 scopus 로고    scopus 로고
    • A MRIEM for solving the Laplace equation in the doubly-connected domain
    • Liu, C.-S. (2007c): A MRIEM for solving the Laplace equation in the doubly-connected domain. CMES: Computer Modeling in Engineering & Sciences, vol. 19, pp. 145-161.
    • (2007) CMES: Computer Modeling in Engineering & Sciences , vol.19 , pp. 145-161
    • Liu, C.-S.1
  • 28
    • 34547764810 scopus 로고    scopus 로고
    • A highly accurate solver for the mixed-boundary potential problem and singular problem in arbitrary plane domain
    • Liu, C.-S. (2007d): A highly accurate solver for the mixed-boundary potential problem and singular problem in arbitrary plane domain. CMES: Computer Modeling in Engineering & Sciences, vol. 20, pp. 111-122.
    • (2007) CMES: Computer Modeling in Engineering & Sciences , vol.20 , pp. 111-122
    • Liu, C.-S.1
  • 29
    • 34547777321 scopus 로고    scopus 로고
    • An effectively modified direct Trefftz method for 2D potential problems considering the domain's characteristic length
    • Liu, C.-S. (2007e): An effectively modified direct Trefftz method for 2D potential problems considering the domain's characteristic length. Engineering Analysis with Boundary Elements, vol. 31, pp. 983-993.
    • (2007) Engineering Analysis with Boundary Elements , vol.31 , pp. 983-993
    • Liu, C.-S.1
  • 30
    • 38049156326 scopus 로고    scopus 로고
    • A highly accurate collocation Trefftz method for solving the Laplace equation in the doubly connected domains
    • Liu, C.-S. (2008): A highly accurate collocation Trefftz method for solving the Laplace equation in the doubly connected domains. Numerical Methods for Partial Differential Equations, vol. 24, pp. 179-192.
    • (2008) Numerical Methods for Partial Differential Equations , vol.24 , pp. 179-192
    • Liu, C.-S.1
  • 31
    • 0036860667 scopus 로고    scopus 로고
    • Method of fundamental solutions: Singular value decomposition analysis
    • Ramachandran, P. A. (2002): Method of fundamental solutions: singular value decomposition analysis. Communications in Numerical Methods in Engineering, vol. 18, pp. 789-801.
    • (2002) Communications in Numerical Methods in Engineering , vol.18 , pp. 789-801
    • Ramachandran, P.A.1
  • 32
    • 0242340540 scopus 로고    scopus 로고
    • Multipole fast algorithm for the least-squares approach of the method of fundamental solutions for three-dimensional harmonic problems
    • Saavedra, I.; Power, H. (2003): Multipole fast algorithm for the least-squares approach of the method of fundamental solutions for three-dimensional harmonic problems. Numerical Methods for Partial Differential Equations, vol. 19, pp. 828-845.
    • (2003) Numerical Methods for Partial Differential Equations , vol.19 , pp. 828-845
    • Saavedra, I.1    Power, H.2
  • 33
    • 0041950033 scopus 로고    scopus 로고
    • Some aspects of the method of fundamental solutions for certain harmonic problems
    • Smyrlis, Y. S.; Karageorghis, A. (2001): Some aspects of the method of fundamental solutions for certain harmonic problems. Journal of Scientific Computing, vol. 16, pp. 341-371.
    • (2001) Journal of Scientific Computing , vol.16 , pp. 341-371
    • Smyrlis, Y.S.1    Karageorghis, A.2
  • 34
    • 8344281356 scopus 로고    scopus 로고
    • Some aspects of the method of fundamental solutions for certain biharmonic problems
    • Smyrlis, Y. S.; Karageorghis, A. (2003): Some aspects of the method of fundamental solutions for certain biharmonic problems. CMES: Computer Modeling in Engineering and Sciences, vol. 4, pp. 535-550.
    • (2003) CMES: Computer Modeling in Engineering and Sciences , vol.4 , pp. 535-550
    • Smyrlis, Y.S.1    Karageorghis, A.2
  • 37
    • 0032586187 scopus 로고    scopus 로고
    • A solution method for two-dimensional potential flow about bodies with smooth surfaces by direct use of the boundary integral equation
    • Young, S. A. (1999): A solution method for two-dimensional potential flow about bodies with smooth surfaces by direct use of the boundary integral equation. Communications in Numerical Methods in Engineering, vol. 15, pp. 469-478.
    • (1999) Communications in Numerical Methods in Engineering , vol.15 , pp. 469-478
    • Young, S.A.1
  • 38
    • 20344402529 scopus 로고    scopus 로고
    • Novel meshless method for solving the potential problems with arbitrary domain
    • Young, D. L.; Chen, K. H.; Lee, C. W. (2005): Novel meshless method for solving the potential problems with arbitrary domain. Journal of Computational Physics, vol. 209, pp. 290-321.
    • (2005) Journal of Computational Physics , vol.209 , pp. 290-321
    • Young, D.L.1    Chen, K.H.2    Lee, C.W.3
  • 39
    • 34250213281 scopus 로고    scopus 로고
    • A modified method of fundamental solutions with source on the boundary for solving Laplace equations with circular and arbitrary domains
    • Young, D. L.; Chen, K. H.; Chen, J. T.; Kao, J. H. (2007): A modified method of fundamental solutions with source on the boundary for solving Laplace equations with circular and arbitrary domains. CMES: Computer Modeling in Engineering & Sciences, vol. 19, pp. 197-222.
    • (2007) CMES: Computer Modeling in Engineering & Sciences , vol.19 , pp. 197-222
    • Young, D.L.1    Chen, K.H.2    Chen, J.T.3    Kao, J.H.4
  • 40
    • 15544379149 scopus 로고    scopus 로고
    • Method of fundamental solutions for scattering problems of electromagnetic waves
    • Young, D. L.; Ruan J. W. (2005): Method of fundamental solutions for scattering problems of electromagnetic waves. CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 223-232.
    • (2005) CMES: Computer Modeling in Engineering & Sciences , vol.7 , pp. 223-232
    • Young, D.L.1    Ruan, J.W.2
  • 41
    • 33749837530 scopus 로고    scopus 로고
    • The method of fundamental solutions for eigenfrequencies of plate vibrations
    • Young, D. L.; Tsai, C. C.; Lin, Y. C.; Chen, C. S. (2006): The method of fundamental solutions for eigenfrequencies of plate vibrations. CMC: Computers, Materials & Continua, vol. 4, pp. 1-10.
    • (2006) CMC: Computers, Materials & Continua , vol.4 , pp. 1-10
    • Young, D.L.1    Tsai, C.C.2    Lin, Y.C.3    Chen, C.S.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.