DOI: 10.1016/s0955-7997(01)00092-3. Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson's equations

Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson's equations

10.1016/s0955-7997(01)00092-3

Crossref journal-article

Elsevier BV

Engineering Analysis with Boundary Elements (78)

Bibliography

Mai-Duy, N., & Tran-Cong, T. (2002). Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poissonâs equations. Engineering Analysis with Boundary Elements, 26(2), 133â156.

Authors 2

Nam Mai-Duy (first)
Thanh Tran-Cong (additional)

References 27 Referenced 52

{'key': '10.1016/S0955-7997(01)00092-3_BIB1', 'series-title': 'Neural networks: a comprehensive foundation', 'author': 'Haykin', 'year': '1999'} / Neural networks: a comprehensive foundation by Haykin (1999)
10.1002/cnm.1640100303 / Commun Numerical Meth Engng / Neural-network-based approximation for solving partial differential equations by Dissanayake (1994)
10.1016/0893-6080(94)90031-0 / Neural Networks / Neural network representation of finite element method by Takeuchi (1994)
10.1016/0898-1221(90)90270-T / Computers Math Applic / Multiquadrics — a scattered data approximation scheme with applications to computational fluid-dynamics-I. Surface approximations and partial derivative estimates by Kansa (1990)
10.1016/0898-1221(90)90271-K / Computers Math Applic / Multiquadrics — a scattered data approximation scheme with applications to computational fluid-dynamics-II. Solutions to parabolic, hyperbolic and elliptic partial differential equations by Kansa (1990)
{'issue': '1', 'key': '10.1016/S0955-7997(01)00092-3_BIB6', 'first-page': '146', 'article-title': 'Domain decomposition and local refinement for multiquadric approximations I: second-order equations in one-dimension', 'volume': '1', 'author': 'Dubal', 'year': '1994', 'journal-title': 'J Appl Sci Computation'} / J Appl Sci Computation / Domain decomposition and local refinement for multiquadric approximations I: second-order equations in one-dimension by Dubal (1994)
10.1016/S0096-3003(96)00109-9 / J Appl Sci Computation / Application of the multiquadric method for numerical solution of elliptic partial differential equations by Sharan (1997)
10.1002/(SICI)1097-0207(19980815)42:7<1263::AID-NME431>3.0.CO;2-I / Int J Numerical Meth Engng / A numerical method for heat transfer problems using collocation and radial basis functions by Zerroukat (1998)
Mai-Duy N, Tran-Cong T. Approximation of function and its derivatives using radial basis function networks. Submitted for publication.
10.1016/S0893-6080(00)00095-2 / Neural Networks / Numerical solution of differential equations using multiquadric radial basis function networks by Mai-Duy (2001)
10.1002/fld.165 / Int J Numerical Meth Fluids / Numerical solution of Navier–Stokes equations using multiquadric radial basis function networks by Mai-Duy (2001)
10.1137/0725069 / SIAM J Numerical Anal / An iterative procedure with interface relaxation for domain decomposition methods by Funaro (1988)
{'key': '10.1016/S0955-7997(01)00092-3_BIB13', 'series-title': 'Proceedings of First International Symposium on Domain Decomposition Methods for Partial Differential Equations', 'first-page': '129', 'article-title': 'An iterative procedure for domain decomposition methods: a finite element approach', 'author': 'Marini', 'year': '1988'} / Proceedings of First International Symposium on Domain Decomposition Methods for Partial Differential Equations / An iterative procedure for domain decomposition methods: a finite element approach by Marini (1988)
{'key': '10.1016/S0955-7997(01)00092-3_BIB14', 'series-title': 'Proceedings of Third International Symposium on Domain Decomposition Methods for Partial Differential Equations', 'first-page': '202', 'article-title': 'On the Schwarz alternating method III: a variant for nonoverlapping subdomains', 'author': 'Lions', 'year': '1990'} / Proceedings of Third International Symposium on Domain Decomposition Methods for Partial Differential Equations / On the Schwarz alternating method III: a variant for nonoverlapping subdomains by Lions (1990)
10.1093/imanum/16.1.75 / SIAM J Numerical Anal / A parallel iterative nonoverlapping domain decomposition procedure for elliptic problems by Yang (1996)
10.1016/S0955-7997(98)00071-X / Engng Anal Boundary Elem / A fast convergent iterative boundary element method on PVM cluster by Mai-Duy (1998)
{'key': '10.1016/S0955-7997(01)00092-3_BIB17', 'series-title': 'Numerical Analysis 1987 Proceedings', 'first-page': '223', 'article-title': 'Radial basis function approximations to polynomial', 'author': 'Powell', 'year': '1987'} / Numerical Analysis 1987 Proceedings / Radial basis function approximations to polynomial by Powell (1987)
10.1016/S0893-6080(96)00091-3 / Neural Networks / Function emulation using radial basis function networks by Chakravarthy (1997)
{'key': '10.1016/S0955-7997(01)00092-3_BIB19', 'series-title': 'Boundary element techniques: theory and applications in engineering', 'author': 'Brebbia', 'year': '1984'} / Boundary element techniques: theory and applications in engineering by Brebbia (1984)
{'key': '10.1016/S0955-7997(01)00092-3_BIB20', 'series-title': 'Boundary element methods in engineering sciences', 'author': 'Banerjee', 'year': '1981'} / Boundary element methods in engineering sciences by Banerjee (1981)
{'key': '10.1016/S0955-7997(01)00092-3_BIB21', 'series-title': 'The dual reciprocity boundary element method', 'author': 'Partridge', 'year': '1992'} / The dual reciprocity boundary element method by Partridge (1992)
{'key': '10.1016/S0955-7997(01)00092-3_BIB22', 'series-title': 'The multiple reciprocity boundary element method', 'author': 'Nowak', 'year': '1994'} / The multiple reciprocity boundary element method by Nowak (1994)
{'key': '10.1016/S0955-7997(01)00092-3_BIB23', 'series-title': 'On the numerical evaluation of finite part integrals involving an algebraic singularity (report WISK 179)', 'author': 'Kutt', 'year': '1975'} / On the numerical evaluation of finite part integrals involving an algebraic singularity (report WISK 179) by Kutt (1975)
{'key': '10.1016/S0955-7997(01)00092-3_BIB24', 'series-title': 'Quadrature formulae for finite part integrals (report WISK 178)', 'author': 'Kutt', 'year': '1975'} / Quadrature formulae for finite part integrals (report WISK 178) by Kutt (1975)
10.1016/0168-874X(94)90017-5 / Finite Elem Anal Des / Boundary element analysis and design in seepage problems using dual integral formulation by Chen (1994)
{'key': '10.1016/S0955-7997(01)00092-3_BIB26', 'series-title': 'Boundary element method', 'author': 'Chen', 'year': '1992'} / Boundary element method by Chen (1992)
{'key': '10.1016/S0955-7997(01)00092-3_BIB27', 'series-title': 'Singular integrals in boundary element methods', 'first-page': '85', 'article-title': 'Formulation and numerical treatment of boundary integral equations with hypersingular kernels', 'author': 'Guiggiani', 'year': '1998'} / Singular integrals in boundary element methods / Formulation and numerical treatment of boundary integral equations with hypersingular kernels by Guiggiani (1998)

Dates

Type	When
Created	23 years ago (July 25, 2002, 5:43 a.m.)
Deposited	6 years, 3 months ago (April 28, 2019, 8:50 p.m.)
Indexed	3 months, 2 weeks ago (May 2, 2025, 3:24 p.m.)
Issued	23 years, 6 months ago (Feb. 1, 2002)
Published	23 years, 6 months ago (Feb. 1, 2002)
Published Print	23 years, 6 months ago (Feb. 1, 2002)

Funders 0

None

BibTeX

@article{Mai_Duy_2002, title={Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson’s equations}, volume={26}, ISSN={0955-7997}, url={http://dx.doi.org/10.1016/s0955-7997(01)00092-3}, DOI={10.1016/s0955-7997(01)00092-3}, number={2}, journal={Engineering Analysis with Boundary Elements}, publisher={Elsevier BV}, author={Mai-Duy, Nam and Tran-Cong, Thanh}, year={2002}, month=feb, pages={133–156} }

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