A high-order embedded-boundary method based on smooth extension and RBFs for solving elliptic equations in multiply connected domains

Article

Mai-Duy, N. and Gu, Y. T.. 2023. "A high-order embedded-boundary method based on smooth extension and RBFs for solving elliptic equations in multiply connected domains." Engineering Analysis with Boundary Elements. 154, pp. 223-237. https://doi.org/10.1016/j.enganabound.2023.05.038
Article Title

A high-order embedded-boundary method based on smooth extension and RBFs for solving elliptic equations in multiply connected domains

ERA Journal ID3475
Article CategoryArticle
AuthorsMai-Duy, N. and Gu, Y. T.
Journal TitleEngineering Analysis with Boundary Elements
Journal Citation154, pp. 223-237
Number of Pages15
Year2023
PublisherElsevier
Place of PublicationUnited Kingdom
ISSN0955-7997
1873-197X
Digital Object Identifier (DOI)https://doi.org/10.1016/j.enganabound.2023.05.038
Web Address (URL)https://www.sciencedirect.com/science/article/pii/S0955799723002849
Abstract

This paper presents a new high-order embedded-/immersed-boundary method, based on point collocation, smooth extension of the solution and integrated radial basis functions (IRBFs), for solving the elliptic partial differential equation (PDE) defined in a domain with holes. The PDE is solved in the domain without holes, where the construction of the IRBF approximations is based on a fixed Cartesian grid and local five-point stencils, and the inner/immersed boundary conditions are included in the discretized equations. More importantly, nodal values of the second-, third- and fourth-order derivatives of the field variable are incorporated into the IRBF approximations, and the forcing term defined in the holes is constructed in a form that gives a globally smooth solution. These features enable the proposed scheme to achieve high level of sparseness of the system matrix, and high level of accuracy of the solution together. Numerical verification is carried out for problems with smooth and non-smooth inner boundaries. Highly accurate results are obtained using relatively coarse grids.

KeywordsEmbedded boundary; Smooth extension; Integrated radial basis function; Elliptic equation; Multiply connected domain; High-order discretization
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 2020490303. Numerical solution of differential and integral equations
401706. Numerical modelling and mechanical characterisation
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Byline AffiliationsSchool of Engineering
Queensland University of Technology
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A particle based model to simulate microscale morphological changes of plant tissues during drying
Karunasena, H. C. P., Senadeera, W., Brown, R. J. and Gu, Y. T.. 2014. "A particle based model to simulate microscale morphological changes of plant tissues during drying." Soft Matter. 10 (29), pp. 5249-5268. https://doi.org/10.1039/c4sm00526k
A mesh free model for plant tissue deformations during drying
Karunasena, H. C. P., Senadeera, W., Brown, R. J. and Gu, Y. T.. 2014. "A mesh free model for plant tissue deformations during drying." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 55 (EMAC2013), pp. C110-C137.
Numerical investigation of plant tissue porosity and its influence on cellular level shrinkage during drying
Karunasena, H. C. P., Gu, Y. T., Brown, R. J. and Senadeera, W.. 2015. "Numerical investigation of plant tissue porosity and its influence on cellular level shrinkage during drying." Biosystems Engineering. 132, pp. 71-87. https://doi.org/10.1016/j.biosystemseng.2015.02.002
Application of meshfree methods to numerically simulate microscale deformations of different plant food materials during drying
Karunasena, H. C. P., Brown, R. J., Gu, Y. T. and Senadeera, W.. 2015. "Application of meshfree methods to numerically simulate microscale deformations of different plant food materials during drying." Journal of Food Engineering. 146, pp. 209-226. https://doi.org/10.1016/j.jfoodeng.2014.09.011
Scanning electron microscopic study of microstructure of gala apples during hot air drying
Karunasena, H. C. P., Hesami, P., Senadeera, W., Gu, Y. T., Brown, R. J. and Oloyede, A.. 2014. "Scanning electron microscopic study of microstructure of gala apples during hot air drying." Drying Technology: an international journal. 32 (4), pp. 455-468. https://doi.org/10.1080/07373937.2013.837479
Numerical investigation of case hardening of plant tissue during drying and its influence on the cellular-level shrinkage
Karunasena, H. C. P., Gu, Y.T., Brown, R. J. and Senadeera, W.. 2015. "Numerical investigation of case hardening of plant tissue during drying and its influence on the cellular-level shrinkage." Drying Technology: an international journal. 33 (6), pp. 713-734. https://doi.org/10.1080/07373937.2014.982759
Strongly overdamped dissipative particle dynamics for fluid-solid systems
Phan-Thien, N., Mai-Duy, N., Khoo, B. C. and Duong-Hong, D.. 2016. "Strongly overdamped dissipative particle dynamics for fluid-solid systems." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 40 (13-14), pp. 6359-6375. https://doi.org/10.1016/j.apm.2016.01.051
A three-point coupled compact integrated RBF scheme for second-order differential problems
Tien, C. M. T., Thai-Quang, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2015. "A three-point coupled compact integrated RBF scheme for second-order differential problems." CMES Computer Modeling in Engineering and Sciences. 104 (6), pp. 425-469. https://doi.org/10.3970/cmes.2015.104.425
Stable integrated RBF calculation using preconditioning and high-order compact approximation for second-order PDEs
Tien, C. M. T., Mai-Duy, N., Ngo-Cong, D., Tran, C. D. and Tran-Cong, T.. 2015. "Stable integrated RBF calculation using preconditioning and high-order compact approximation for second-order PDEs." Witt, Peter (ed.) Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 2015. Melbourne, Victoria 07 - 09 Dec 2015 Australia.
Incompressible smoothed particle hydrodynamics-moving IRBFN method for viscous flow problems
Ngo-Cong, D., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2015. "Incompressible smoothed particle hydrodynamics-moving IRBFN method for viscous flow problems." Engineering Analysis with Boundary Elements. 59, pp. 172-186. https://doi.org/10.1016/j.enganabound.2015.06.006
High-order fully coupled scheme based on compact integrated RBF approximation for viscous flows in regular and irregular domains
Tien, C. M. T., Thai-Quang, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2015. "High-order fully coupled scheme based on compact integrated RBF approximation for viscous flows in regular and irregular domains." CMES Computer Modeling in Engineering and Sciences. 105 (4), pp. 301-340. https://doi.org/10.3970/cmes.2015.105.301
A high-order coupled compact integrated RBF approximation based domain decomposition algorithm for second-order differential problems
Tien, C. M. T., Pham-Sy, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2015. "A high-order coupled compact integrated RBF approximation based domain decomposition algorithm for second-order differential problems." CMES Computer Modeling in Engineering and Sciences. 104 (4), pp. 251-304. https://doi.org/10.3970/cmes.2015.104.251
Investigation of particles size effects in Dissipative Particle Dynamics (DPD) modelling of colloidal suspensions
Mai-Duy, N., Phan-Thien, N. and Khoo, B. C.. 2015. "Investigation of particles size effects in Dissipative Particle Dynamics (DPD) modelling of colloidal suspensions." Computer Physics Communications. 189, pp. 37-46. https://doi.org/10.1016/j.cpc.2014.12.003
Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution
Ngo-Cong, D., Mohammed, F. J., Strunin, D. V., Skvortsov, A. T., Mai-Duy, N. and Tran-Cong, T.. 2015. "Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution." Journal of Hydrology. 525, pp. 87-101. https://doi.org/10.1016/j.jhydrol.2015.03.038
A constitutive model for mechanical response characterization of pumpkin peel and flesh tissues under tensile and compressive loadings
Shirmohammadi, Maryam, Yarlagadda, Prasad K. D. V. and Gu, YuanTong. 2015. "A constitutive model for mechanical response characterization of pumpkin peel and flesh tissues under tensile and compressive loadings ." Journal of Food Science and Technology. 52 (8), pp. 4874-4884. https://doi.org/10.1007/s13197-014-1605-2
Comprehensive Contribution of Filament Thickness and Crosslinker Failure to the Rheological Property of F-actin Cytoskeleton
Li, Tong, Liu, Ling, Hu, Dean, Oloyede, Adekunle, Xiao, Yin, Yarlagadda, Prasad and Gu, YuanTong. 2015. "Comprehensive Contribution of Filament Thickness and Crosslinker Failure to the Rheological Property of F-actin Cytoskeleton." Cellular and Molecular Bioengineering. 8 (2), pp. 278-284. https://doi.org/10.1007/s12195-015-0382-y
Parallel control-volume method based on compact local integrated RBFs for the solution of fluid flow problems
Pham-Sy, N., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2014. "Parallel control-volume method based on compact local integrated RBFs for the solution of fluid flow problems." CMES Computer Modeling in Engineering and Sciences. 100 (5), pp. 363-397. https://doi.org/10.3970/cmes.2014.100.363
Trans-scale Granular Modelling of Cytoskeleton: a Mini-Review
Li, Tong, Yarlagadda, Prasad K. D. V., Oloyede, Adekunle, Thibbotuwawa, Namal and Gu, YuanTong. 2015. "Trans-scale Granular Modelling of Cytoskeleton: a Mini-Review." Molecular and Cellular Biomechanics. 12 (1), pp. 17-35. https://doi.org/10.3970/mcb.2015.012.017
A spring model for suspended particles in dissipative particle dynamics
Phan-Thien, N., Mai-Duy, N. and Khoo, B. C.. 2014. "A spring model for suspended particles in dissipative particle dynamics." Journal of Rheology. 58 (4), pp. 839-867. https://doi.org/10.1122/1.4874679
Exponential-time differencing schemes for low-mass DPD systems
Phan-Thien, N., Mai-Duy, N., Pan, D. and Khoo, B.C.. 2014. "Exponential-time differencing schemes for low-mass DPD systems." Computer Physics Communications. 185 (1), pp. 229-235. https://doi.org/10.1016/j.cpc.2013.09.022
A fully coupled scheme for viscous flows in regular and irregular domains using compact integrated RBF approximation
Tien, C. M. T., Thai-Quang, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2014. "A fully coupled scheme for viscous flows in regular and irregular domains using compact integrated RBF approximation." Applied Mechanics and Materials. 553, pp. 138-143. https://doi.org/10.4028/www.scientific.net/AMM.553.138
Tensile properties of Si nanowires with faulted stacking layers
Zhan, Haifei, Gu, Yuantong, Yan, Cheng and Yarlagadda, Prasad K. D. V.. 2014. "Tensile properties of Si nanowires with faulted stacking layers." Science of Advanced Materials. 6 (7), pp. 1489-1492. https://doi.org/10.1166/sam.2014.1800
Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method
Mohammed, F. J., Ngo-Cong, D., Strunin, D. V., Mai-Duy, N. and Tran-Cong, T.. 2014. "Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 38 (14), pp. 3672-3691. https://doi.org/10.1016/j.apm.2013.12.007
Dissipative particle dynamics modeling of low Reynolds number incompressible flows
Mai-Duy, N., Pan, D., Phan-Thien, N. and Khoo, B. C.. 2013. "Dissipative particle dynamics modeling of low Reynolds number incompressible flows." Journal of Rheology. 57 (2), pp. 585-604. https://doi.org/10.1122/1.4789444
Numerical investigations on the compressibility of a DPD fluid
Pan, Dingyi, Phan-Thien, Nhan, Mai-Duy, Nam and Khoo, Boo Cheong. 2013. "Numerical investigations on the compressibility of a DPD fluid." Journal of Computational Physics. 242, pp. 196-210. https://doi.org/10.1016/j.jcp.2013.02.013
Molecular investigation of the mechanical properties of single actin filaments based on vibration analyses
Li, Tong, Gu, Y. T., Oloyede, Adekunle and Yarlagadda, Prasad K. D. V.. 2014. "Molecular investigation of the mechanical properties of single actin filaments based on vibration analyses." Computer Methods in Biomechanics and Biomedical Engineering: Imaging and Visualization. 17 (6), pp. 616-622. https://doi.org/10.1080/10255842.2012.706279
A compact five-point stencil based on integrated RBFs for 2D second-order differential problems
Mai-Duy, N. and Tran-Cong, T.. 2013. "A compact five-point stencil based on integrated RBFs for 2D second-order differential problems." Journal of Computational Physics. 235, pp. 302-321. https://doi.org/10.1016/j.jcp.2012.10.048
Modelling of solid bodies in dissipative particle dynamics
Mai-Duy, N., Phan-Thien, N., Khoo, B. C. and Tran-Cong, T.. 2013. "Modelling of solid bodies in dissipative particle dynamics." Bischoff, M., Onate, E., Owen, D. R. J., Ramm, E. and Wriggers, P. (ed.) 3rd International Conference on Particle-based Methods Fundamentals and Applications (Particles 2013): Particle-Based Methods III: Fundamentals and Applications. Stuttgart, Germany 18 - 20 Sep 2013 Barcelona, Spain.
ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows
An-Vo, D.-A., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2013. "ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 37 (7), pp. 5184-5203. https://doi.org/10.1016/j.apm.2012.10.034
A direct forcing immersed boundary method employed with compact integrated RBF approximations for heat transfer and fluid flow problems
Thai-Quang, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2013. "A direct forcing immersed boundary method employed with compact integrated RBF approximations for heat transfer and fluid flow problems." CMES Computer Modeling in Engineering and Sciences. 96 (1), pp. 49-90. https://doi.org/10.3970/cmes.2013.096.049
Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination detection based parallel algorithm
Pham-Sy, N., Tran, C.-D., Hoang-Trieu, T.-T., Mai-Duy, N. and Tran-Cong, T.. 2013. "Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination detection based parallel algorithm." CMES Computer Modeling in Engineering and Sciences. 92 (1), pp. 1-31. https://doi.org/10.3970/cmes.2013.092.001
A finite-volume method based on compact local integrated radial basis function approximations for second-order differential problems
Hoang-Trieu, T.-T., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2013. "A finite-volume method based on compact local integrated radial basis function approximations for second-order differential problems." CMES Computer Modeling in Engineering and Sciences. 91 (6), pp. 485-516. https://doi.org/10.3970/cmes.2013.091.485
A numerical scheme based on compact integrated-RBFs and Adams-Bashforth/Crank-Nicolson algorithms for diffusion and unsteady fluid flow problems
Thai-Quang, N., Le-Cao, K., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2013. "A numerical scheme based on compact integrated-RBFs and Adams-Bashforth/Crank-Nicolson algorithms for diffusion and unsteady fluid flow problems." Engineering Analysis with Boundary Elements. 37 (12), pp. 1653-1667. https://doi.org/10.1016/j.enganabound.2013.09.011
How to increase the accuracy of analysis and reduce the computational time in ANSYS in the case of deformation study of orthopedic bone plates
Malekani, Javad, Yarlagadda, Prasad K. D. V., Schmutz, Beat, Gu, YuanTong and Schuetz, Michael. 2014. "How to increase the accuracy of analysis and reduce the computational time in ANSYS in the case of deformation study of orthopedic bone plates." 3rd International Conference on Materials and Products Manufacturing Technology (ICMPMT 2013). China 25 - 26 Sep 2013 Scientific.Net. https://doi.org/10.4028/www.scientific.net/AMR.834-836.1592
Bending properties of Ag nanowires with pre-existing surface defects
Zhan, H. F., Gu, Y. T., Yan, C. and Yarlagadda, P. K. D. V.. 2014. "Bending properties of Ag nanowires with pre-existing surface defects." Computational Materials Science. 81, pp. 45-51. https://doi.org/10.1016/j.commatsci.2013.05.032
A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation
Mai-Duy, N., Thai-Quang, N., Hoang-Trieu, T.-T. and Tran-Cong, T.. 2014. "A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 38 (4), pp. 1495-1510. https://doi.org/10.1016/j.apm.2013.08.017
Simulation of Newtonian-fluid flows with C2-continuous two-node integrated-RBF elements
An-Vo, D.-A., Mai-Duy, N. and Tran-Cong, T.. 2010. "Simulation of Newtonian-fluid flows with C2-continuous two-node integrated-RBF elements." Structural Longevity. 4 (1), pp. 39-45. https://doi.org/10.3970/sl.2010.004.039
Compact local stencils employed with integrated RBFs for fourth-order differential problems
Hoang-Trieu, T.-T., Mai-Duy, N. and Tran-Cong, T.. 2011. "Compact local stencils employed with integrated RBFs for fourth-order differential problems." Structural Longevity. 6 (2), pp. 93-107. https://doi.org/10.3970/sl.2011.006.093
A numerical study of integrated radial-basis-functions for the pressure-velocity formulation
Thai-Quang, Nha, Mai-Duy, Nam and Tran-Cong, Thanh. 2012. "A numerical study of integrated radial-basis-functions for the pressure-velocity formulation." 7th ICCES Special Symposium on Meshless & Other Novel Computational Methods (ICCES MM 2011). Zonguldak, Turkey 06 - 10 Sep 2011 USA.
RBF computation of multiscale elliptic problems [Keynote paper]
An-Vo, D.-A., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2012. "RBF computation of multiscale elliptic problems [Keynote paper]." Atluri, S. N., Vusanovic, I. and Sarler, B. (ed.) 8th ICCES Special Symposium on Meshless & Other Novel Computational Methods (ICCES MM 2012). Budva, Montenegro 02 - 06 Sep 2012 Montenegro.
Discretisation of the velocity-pressure formulation with integrated radial-basis-function networks
Thai-Quang, N., Le-Cao, K., Mai-Duy, N. and Tran-Cong, T.. 2011. "Discretisation of the velocity-pressure formulation with integrated radial-basis-function networks." Structural Longevity. 6 (2), pp. 77-91. https://doi.org/10.3970/sl.2011.006.077
A numerical study of strongly overdamped dissipative particle dynamics (DPD) systems
Mai-Duy, N., Phan-Thien, N. and Khoo, B. C.. 2013. "A numerical study of strongly overdamped dissipative particle dynamics (DPD) systems." Journal of Computational Physics. 245, pp. 150-159. https://doi.org/10.1016/j.jcp.2013.03.013
Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method
Tran, Canh-Dung, Mai-Duy, Nam and Tran-Cong, Thanh. 2012. "Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method." Eberhardsteiner, J., Böhm, H. J. and Rammerstorfer, F. G. (ed.) 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012). Vienna, Austria Vienna, Austria.
Numerical solution of Fokker-Planck equation using the integral radial basis function networks
Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2012. "Numerical solution of Fokker-Planck equation using the integral radial basis function networks." Pimenta, P. M. and Campello, E. M. B. (ed.) 10th World Congress on Computational Mechanics (WCCM 2012). Sao Paulo, Brazil 08 - 13 Jul 2012 Sao Paulo, Brazil. https://doi.org/10.5151/10.5151/meceng-wccm2012-19433
Modeling strain localisation in a segmented bar by a C2-continuous two-node integrated-RBF element formulation
An-Vo, D.-A., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2012. "Modeling strain localisation in a segmented bar by a C2-continuous two-node integrated-RBF element formulation." Brebbia, C. A. and Poljak, D. (ed.) 34th International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2012). Split, Croatia 25 - 27 Jun 2012 United Kingdom. https://doi.org/10.2495/BE120011
Development of parallel algorithm for boundary value problems using compact local integrated RBFN and domain decomposition
Pham-Sy, N., Hoang-Trieu, T.-T., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2012. "Development of parallel algorithm for boundary value problems using compact local integrated RBFN and domain decomposition." Gu, Y. T. and Saha, Suvash C. (ed.) 4th International Conference on Computational Methods (ICCM 2012). Gold Coast, Australia 25 - 28 Nov 2012 Brisbane, Australia.
A high-order compact integrated-RBF scheme for time-dependent problems
Thai-Quang, N., Le-Cao, K., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2012. "A high-order compact integrated-RBF scheme for time-dependent problems." Gu, Y. T. and Saha, Suvash C. (ed.) 4th International Conference on Computational Methods (ICCM 2012). Gold Coast, Australia 25 - 28 Nov 2012 Brisbane, Australia.
Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems
Hoang-Trieu, T.-T., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2012. "Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems." Gu, Y. T. and Saha, Suvash C. (ed.) 4th International Conference on Computational Methods (ICCM 2012). Gold Coast, Australia 25 - 28 Nov 2012 Brisbane, Australia.
High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady convection-diffusion equations
Thai-Quang, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2012. "High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady convection-diffusion equations." CMES Computer Modeling in Engineering and Sciences. 89 (3), pp. 189-220. https://doi.org/10.3970/cmes.2012.089.189
RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients
An-Vo, D.-A., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2012. "RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients." CMES Computer Modeling in Engineering and Sciences. 89 (4), pp. 303-359. https://doi.org/10.3970/cmes.2012.089.303
Local Moving Least Square - One-Dimensional IRBFN Technique: Part II- Unsteady Incompressible Viscous Flows
Ngo-Cong, D., Mai-Duy, N., Karunasena, W. and Tran-Cong, T.. 2012. "Local Moving Least Square - One-Dimensional IRBFN Technique: Part II- Unsteady Incompressible Viscous Flows ." CMES Computer Modeling in Engineering and Sciences. 83 (3), pp. 311-351. https://doi.org/10.3970/cmes.2012.083.311
Local Moving Least Square - One-Dimensional IRBFN Technique: Part I - Natural Convection Flows in Concentric and Eccentric Annuli
Ngo-Cong, D., Mai-Duy, N., Karunasena, W. and Tran-Cong, T.. 2012. "Local Moving Least Square - One-Dimensional IRBFN Technique: Part I - Natural Convection Flows in Concentric and Eccentric Annuli ." CMES Computer Modeling in Engineering and Sciences. 83 (3), pp. 275-310. https://doi.org/10.3970/cmes.2012.083.275
A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows
Tran, C.-D., Mai-Duy, N., Le-Cao, K. and Tran-Cong, T.. 2012. "A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows." CMES Computer Modeling in Engineering and Sciences. 85 (6), pp. 499-519. https://doi.org/10.3970/cmes.2012.085.499
Studies on bending limitations for the optimal fit of orthopaedic bone plates
Malekani, J., Schmutz, B., Gudimetla, P., Gu, Y., Schuetz, M. and Yarlagadda, Prasad. 2013. "Studies on bending limitations for the optimal fit of orthopaedic bone plates." 2nd International Conference on Materials and Products Manufacturing Technology (ICMPMT 2012). 22 - 23 Sep 2012 Switzerland. https://doi.org/10.4028/www.scientific.net/AMR.602-604.1181
A high-order compact local integrated-RBF scheme for steady-state incompressible viscous flows in the primitive variables
Thai-Quang, N., Le-Cao, K., Mai-Duy, N. and Tran-Cong, T.. 2012. "A high-order compact local integrated-RBF scheme for steady-state incompressible viscous flows in the primitive variables." CMES Computer Modeling in Engineering and Sciences. 84 (6), pp. 528-557. https://doi.org/10.3970/cmes.2012.084.528
A numerical procedure based on 1D-IRBFN and local MLS-1D-IRBFN methods for fluid-structure interaction analysis
Ngo-Cong, D., Mai-Duy, N., Karunasena, W. and Tran-Cong, T.. 2012. "A numerical procedure based on 1D-IRBFN and local MLS-1D-IRBFN methods for fluid-structure interaction analysis." CMES Computer Modeling in Engineering and Sciences. 83 (5), pp. 459-498. https://doi.org/10.3970/cmes.2012.083.459
Local moving least square-one-dimensional integrated radial basis function networks technique for incompressible viscous flows
Ngo-Cong, D., Mai-Duy, N., Karunasena, W. and Tran-Cong, T.. 2012. "Local moving least square-one-dimensional integrated radial basis function networks technique for incompressible viscous flows." International Journal for Numerical Methods in Fluids. 70 (11), pp. 1443-1474. https://doi.org/10.1002/fld.3640
Several compact local stencils based on integrated RBFs for fourth-order ODEs and PDEs
Hoang-Trieu, T.-T., Mai-Duy, N. and Tran-Cong, T.. 2012. "Several compact local stencils based on integrated RBFs for fourth-order ODEs and PDEs." CMES Computer Modeling in Engineering and Sciences. 84 (2), pp. 171-203. https://doi.org/10.3970/cmes.2012.084.171
Simulation of viscous and viscoelastic flows using a RBF-Galerkin approach
Ho-Minh, D., Mai-Duy, N. and Tran-Cong, T.. 2012. "Simulation of viscous and viscoelastic flows using a RBF-Galerkin approach." Australian Journal of Mechanical Engineering. 9 (2), pp. 101-112. https://doi.org/10.7158/M10-719.2012.9.2
Moving least square: one dimensional integrated radial basis function networks for time dependent problems
Ngo-Cong, D., Mai-Duy, N., Karunasena, W. and Tran-Cong, T.. 2011. "Moving least square: one dimensional integrated radial basis function networks for time dependent problems." Brebbia, C. A. and Popov, V. (ed.) 33rd International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2011). New Forest, United Kingdom 28 - 30 Jun 2011 Southampton, UK. https://doi.org/10.2495/BE110271
IRBFN-based multiscale solution of a model 1D elliptic equation
An-Vo, D.-A., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2011. "IRBFN-based multiscale solution of a model 1D elliptic equation." Brebbia, C. A. and Popov, V. (ed.) 33rd International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2011). New Forest, United Kingdom 28 - 30 Jun 2011 Southampton, United Kingdom. https://doi.org/10.2495/BE110211
Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian grids
Le-Cao, K., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2011. "Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian grids." Computers and Fluids. 44 (1), pp. 32-42. https://doi.org/10.1016/j.compfluid.2010.11.027
An integrated RBFN-based macro-micro multi-scale method for computation of visco-elastic fluid flows
Tran, C.-D., An-Vo, D.-A., Mai-Duy, N. and Tran-Cong, T.. 2011. "An integrated RBFN-based macro-micro multi-scale method for computation of visco-elastic fluid flows." CMES Computer Modeling in Engineering and Sciences. 82 (2), pp. 137-162. https://doi.org/10.3970/cmes.2011.082.137
Compact local approximations employed with integrated RBFs for second-order elliptic differential equations
Mai-Duy, Nam and Tran-Cong, Thanh. 2011. "Compact local approximations employed with integrated RBFs for second-order elliptic differential equations." Yang, Yeong-Bin, Leu, Liang-Jenq and Chen, Chuin-Shan David (ed.) 3rd International Symposium on Computational Mechanics (ISCM III) and 2nd Symposium on Computational Structural Engineering (CSE II). Taipei, Taiwan 05 - 07 Dec 2011 Taiwan.
A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems
Mai-Duy, N. and Tran-Cong, T.. 2011. "A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems." Teh, Kian, Davies, Ian and Howard, Ian (ed.) 6th Australasian Congress on Applied Mechanics (ACAM 6). Perth, Western Australia 12 - 15 Dec 2010 Perth, Western Australia. Taylor & Francis. https://doi.org/10.1080/14484846.2011.11464606
A numerical technique based on integrated RBFs for the system evolution in molecular dynamics
Mai-Duy, N., Tran-Cong, T. and Phan-Thien, N.. 2011. "A numerical technique based on integrated RBFs for the system evolution in molecular dynamics." CMES Computer Modeling in Engineering and Sciences. 79 (4), pp. 223-236. https://doi.org/10.3970/cmes.2011.079.223
High-order upwind methods based on C2-continuous two-node integrated-RBF elements for viscous flows
An-Vo, D. A., Mai-Duy, N. and Tran-Cong, T.. 2011. "High-order upwind methods based on C2-continuous two-node integrated-RBF elements for viscous flows." CMES Computer Modeling in Engineering and Sciences. 80 (2), pp. 141-177. https://doi.org/10.3970/cmes.2011.080.141
A C2-continuous control-volume technique based on cartesian grids and two-node integrated-RBF elements for second-order elliptic problems
An-Vo, D. A., Mai-Duy, N. and Tran-Cong, T.. 2011. "A C2-continuous control-volume technique based on cartesian grids and two-node integrated-RBF elements for second-order elliptic problems." CMES Computer Modeling in Engineering and Sciences. 72 (4), pp. 299-334. https://doi.org/10.3970/cmes.2011.072.299
Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations
Nguyen-Van, H., Mai-Duy, N., Karunasena, W. and Tran-Cong, T.. 2011. "Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations." Computers and Structures. 89 (7-8), pp. 612-625. https://doi.org/10.1016/j.compstruc.2011.01.005
Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method
Ngo-Cong, D., Mai-Duy, N., Karunasena, W. and Tran-Cong, T.. 2011. "Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method." Computers and Structures. 89 (1-2), pp. 1-13. https://doi.org/10.1016/j.compstruc.2010.07.012
A high-order upwind control-volume method based on integrated RBFs for fluid-flow problems
Mai-Duy, N. and Tran-Cong, T.. 2011. "A high-order upwind control-volume method based on integrated RBFs for fluid-flow problems." International Journal for Numerical Methods in Fluids. 67 (12), pp. 1973-1992. https://doi.org/10.1002/fld.2477
Analysis of piezoelectric solids with an efficient node-based element
Nguyen-Van, H., Mai-Duy, N. and Tran-Cong, T.. 2008. "Analysis of piezoelectric solids with an efficient node-based element." Schrefler, B. A. and Perego, U. (ed.) 8th World Congress on Computational Mechanics (WCCM8), and 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008). Venice, Italy 30 Jun - 04 Jul 2008 Barcelona, Spain.
An IRBFN cartesian grid method based on displacement-stress formulation for 2D elasticity problems
Le, P., Mai-Duy, N., Tran-Cong, T. and Baker, G.. 2008. "An IRBFN cartesian grid method based on displacement-stress formulation for 2D elasticity problems." Schrefler, B. A. and Perego, U. (ed.) 8th World Congress on Computational Mechanics (WCCM8), and 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008). Venice, Italy 30 Jun - 04 Jul 2008 Barcelona, Spain.
Solving 2D biharmonic equations by the Galerkin approach using integrated radial basis function networks
Mai-Duy, N. and Tran-Cong, T.. 2008. "Solving 2D biharmonic equations by the Galerkin approach using integrated radial basis function networks." Vigo-Aguiar, J., Khanal, H., Garcia Guirao, I. J., Oharu, S. and Venturino, E. (ed.) 8th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE-2008). Murcia, Spain 13 - 17 Jun 2008 Murcia, Spain.
RBF interpolation of boundary values in the BEM for heat transfer problems
Mai-Duy, Nam and Tran-Cong, Thanh. 2003. "RBF interpolation of boundary values in the BEM for heat transfer problems." International Journal of Numerical Methods for Heat and Fluid Flow. 13 (5/6), pp. 611-632. https://doi.org/10.1108/09615530310482472
An efficient indirect RBFN-based method for numerical solution of PDEs
Mai-Duy, Nam and Tran-Cong, Thanh. 2005. "An efficient indirect RBFN-based method for numerical solution of PDEs." Numerical Methods for Partial Differential Equations. 21 (4), pp. 770-790. https://doi.org/10.1002/num.20062
Solving high-order partial differential equations with indirect radial basis function networks
Mai-Duy, N. and Tanner, R. I.. 2005. "Solving high-order partial differential equations with indirect radial basis function networks." International Journal for Numerical Methods in Engineering. 63 (11), pp. 1636-1654. https://doi.org/10.1002/nme.1332
Solving high order ordinary differential equations with radial basis function networks
Mai-Duy, Nam. 2005. "Solving high order ordinary differential equations with radial basis function networks." International Journal for Numerical Methods in Engineering. 62 (6), pp. 824-852. https://doi.org/10.1002/nme.1220
Computing non-Newtonian fluid flow with radial basis function networks
Mai-Duy, N. and Tanner, R. I.. 2005. "Computing non-Newtonian fluid flow with radial basis function networks." International Journal for Numerical Methods in Fluids. 48 (12), pp. 1309-1336. https://doi.org/10.1002/fld.977
An effective RBFN-boundary integral approach for the analysis of natural convection flow
Mai-Duy, Nam and Tran-Cong, Thanh. 2004. "An effective RBFN-boundary integral approach for the analysis of natural convection flow." International Journal for Numerical Methods in Fluids. 46 (5), pp. 545-568. https://doi.org/10.1002/fld.769
Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks
Mai-Duy, Nam and Tran-Cong, Thanh. 2001. "Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks." International Journal for Numerical Methods in Fluids. 37 (1), pp. 65-86. https://doi.org/10.1002/fld.165
Numerical solution of differential equations using multiquadric radial basis function networks
Mai-Duy, Nam and Tran-Cong, Thanh. 2001. "Numerical solution of differential equations using multiquadric radial basis function networks." Neural Networks. 14 (2), pp. 185-199. https://doi.org/10.1016/S0893-6080(00)00095-2
Approximation of function and its derivatives using radial basis function networks
Mai-Duy, Nam and Tran-Cong, Thanh. 2003. "Approximation of function and its derivatives using radial basis function networks." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 27 (3), pp. 197-220. https://doi.org/10.1016/S0307-904X(02)00101-4
A new meshless RBF-based method for unsteady fluid flow analysis
Mai-Duy, N., Mai-Cao, L. and Tran-Cong, T.. 2006. "A new meshless RBF-based method for unsteady fluid flow analysis." Sladek, Jan and Sladek, Vladimir (ed.) Advances in meshless methods. USA. Tech Science Press. pp. 241-262
A domain-type boundary-integral-equation method for two-dimensional biharmonic Dirichlet problem
Mai-Duy, N., Tran-Cong, T. and Tanner, R. I.. 2006. "A domain-type boundary-integral-equation method for two-dimensional biharmonic Dirichlet problem." Engineering Analysis with Boundary Elements. 30 (10), pp. 809-817. https://doi.org/10.1016/j.enganabound.2006.06.002
Compact local integrated-RBF approximations for second-order elliptic differential problems
Mai-Duy, N. and Tran-Cong, T.. 2011. "Compact local integrated-RBF approximations for second-order elliptic differential problems." Journal of Computational Physics. 230 (12), pp. 4772-4794. https://doi.org/10.1016/j.jcp.2011.03.002
A simple and effective preconditioner for integrated-RBF-based Cartesian-grid schemes
Mai-Duy, Nam and Tran-Cong, Thanh. 2010. "A simple and effective preconditioner for integrated-RBF-based Cartesian-grid schemes." Pepper, D. W. and Atluri, Satya N. (ed.) 2010 International Conference on Computational and Experimental Engineering & Sciences 2010. Las Vegas, United States of America 28 Mar - 01 Apr 2010 USA. https://doi.org/10.3970/icces.2010.014.051
Towards an analysis of shear suspension flows using radial basis functions
Le-Cao, K., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2010. "Towards an analysis of shear suspension flows using radial basis functions." CMES Computer Modeling in Engineering and Sciences. 67 (3), pp. 265-294. https://doi.org/10.3970/cmes.2010.067.265
A new integrated-RBF-based domain-embedding scheme for solving fluid-flow problems
Le-Cao, K., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2010. "A new integrated-RBF-based domain-embedding scheme for solving fluid-flow problems." Khalili, N., Valliappan, S., Li, Q. and Russell, A. (ed.) 9th World Congress on Computational Mechanics and 4th Asian-Pacific Congress on Computational Mechanics (WCCM/APCOM 2010). Sydney, Australia 19 - 23 Jul 2010 United Kingdom. Informa UK(IOP Books). https://doi.org/10.1088/1757-899X/10/1/012021
Galerkin/collocation methods based on 1D-integrated-RBFNs for viscoelastic flows
Ho-Minh, D., Mai-Duy, Nam and Tran-Cong, Thanh. 2010. "Galerkin/collocation methods based on 1D-integrated-RBFNs for viscoelastic flows." CMES Computer Modeling in Engineering and Sciences. 70 (3), pp. 217-251. https://doi.org/10.3970/cmes.2010.070.217
A Cartesian-grid integrated-RBF Galerkin technique
Ho-Minh, D., Mai-Duy, N. and Tran-Cong, T.. 2010. "A Cartesian-grid integrated-RBF Galerkin technique." Sarler, Bozidar and Atluri, Satya N. (ed.) Recent studies in meshless and other novel computational methods. Duluth, GA. USA. Tech Science Press. pp. 87-102
A numerical scheme based on local integrated RBFNs and Cartesian grids for solving second-order elliptic problems in two dimensions
Mai-Duy, N. and Tran-Cong, T.. 2010. "A numerical scheme based on local integrated RBFNs and Cartesian grids for solving second-order elliptic problems in two dimensions." Sarler, Bozidar and Atluri, Satya N. (ed.) Recent studies in meshless and other novel computational methods. Duluth, GA. United States. Tech Science Press. pp. 17-33
A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems
Mai-Duy, Nam and Tran-Cong, Thanh. 2010. "A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems." Numerical Methods for Partial Differential Equations. 26 (6), pp. 1443-1462. https://doi.org/10.1002/num.20502
Dynamic simulation of non-spherical particulate suspensions
Kittipoomwong, Prakorn, See, Howard and Mai-Duy, Nam. 2010. "Dynamic simulation of non-spherical particulate suspensions." Rheologica Acta: an international journal of rheology. 49 (6), pp. 597-606. https://doi.org/10.1007/s00397-009-0412-6
A moving IRBFN-based integration-free meshless method
Le, Phong B. H., Rabczuk, Timon, Mai-Duy, Nam and Tran-Cong, Thanh. 2010. "A moving IRBFN-based integration-free meshless method." CMES Computer Modeling in Engineering and Sciences. 61 (1), pp. 63-109. https://doi.org/10.3970/cmes.2010.061.063
A moving IRBFN-based Galerkin meshless method
Le, Phong B. H., Rabczuk, Timon, Mai-Duy, Nam and Tran-Cong, Thanh. 2010. "A moving IRBFN-based Galerkin meshless method." CMES Computer Modeling in Engineering and Sciences. 66 (1), pp. 25-52. https://doi.org/10.3970/cmes.2010.066.025
A control volume technique based on integrated RBFNs for the convection-diffusion equation
Mai-Duy, Nam and Tran-Cong, Thanh. 2010. "A control volume technique based on integrated RBFNs for the convection-diffusion equation." Numerical Methods for Partial Differential Equations. 26 (2), pp. 426 -447. https://doi.org/10.1002/num.20444
A cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems
Le, Phong B. H., Mai-Duy, Nam, Tran-Cong, Thanh and Baker, Graham. 2010. "A cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems." International Journal for Numerical Methods in Engineering. 82 (4), pp. 435-463. https://doi.org/10.1002/nme.2771
Simulation of fluid flows at high Reynolds/Rayleigh numbers using integrated radial basis functions
Ho-Minh, D., Le-Cao, K., Mai-Duy, N. and Tran-Cong, T.. 2010. "Simulation of fluid flows at high Reynolds/Rayleigh numbers using integrated radial basis functions." Mallinson, G. D. and Cater, J. E. (ed.) 17th Australasian Fluid Mechanics Conference (AFMC 2010). Auckland, New Zealand 05 - 09 Dec 2010 Auckland, New Zealand.
Point-wise integrated-RBF-based discretisation of differential equations
Mai-Duy, Nam and Tran-Cong, Thanh. 2010. "Point-wise integrated-RBF-based discretisation of differential equations." Lu, Jane Wei-Zhen, Leung, Andrew Y. T., Lu, Vai Pan and Mok, Kai Meng (ed.) 2nd International Symposium on Computational Mechanics (ISCM II) in conjunction with EPMESC 2009. Hong Kong, China 30 Nov - 03 Dec 2009 College Park, MD. United States. AIP Publishing. https://doi.org/10.1063/1.3452151
A cartesian-grid integrated-RBF method for viscoelastic flows
Ho-Minh, D., Mai-Duy, N. and Tran-Cong, T.. 2010. "A cartesian-grid integrated-RBF method for viscoelastic flows." Khalili, N., Valliappan, S., Li, Q. and Russell, A. (ed.) 9th World Congress on Computational Mechanics and 4th Asian-Pacific Congress on Computational Mechanics (WCCM/APCOM 2010). Sydney, Australia 19 - 23 Jul 2010 Bristol, United Kingdom. Informa UK(IOP Books). https://doi.org/10.1088/1757-899X/10/1/012210
An upwind control-volume method based on integrated RBFs for fluid-flow problems
Mai-Duy, N. and Tran-Cong, T.. 2010. "An upwind control-volume method based on integrated RBFs for fluid-flow problems." Khalili, N., Valliappan, S., Li, Q. and Russell, A. (ed.) 9th World Congress on Computational Mechanics and 4th Asian-Pacific Congress on Computational Mechanics (WCCM/APCOM 2010). Sydney, Australia 19 - 23 Jul 2010 Bristol, United Kingdom. Informa UK(IOP Books). https://doi.org/10.1088/1757-899X/10/1/012023
Integrated-RBF network method for free vibration analysis of laminated composite plates
Ngo-Cong, D., Mai-Duy, N., Karunasena, W. and Tran-Cong, T.. 2010. "Integrated-RBF network method for free vibration analysis of laminated composite plates." Khalili, N., Valliappan, S., Li, Q. and Russell, A. (ed.) 9th World Congress on Computational Mechanics and 4th Asian-Pacific Congress on Computational Mechanics (WCCM/APCOM 2010). Sydney, Australia 19 - 23 Jul 2010 Bristol, United Kingdom. Informa UK(IOP Books). https://doi.org/10.1088/1757-899X/10/1/012236
An efficient BEM for numerical solution of the biharmonic boundary value problem
Mai-Duy, N. and Tanner, R. I.. 2004. "An efficient BEM for numerical solution of the biharmonic boundary value problem." Atluri, Satya N. and Tadeu, Antonia J. B. (ed.) International Conference on Computational and Experimental Engineering & Sciences (ICCES 2004): Advances in Computational & Experimental Engineering & Sciences. Madeira, Portugal 26 - 29 Jul 2004 Duluth, GA. United States.
A Cartesian-grid discretisation scheme based on local integrated RBFNs for two-dimensional elliptic problems
Mai-Duy, Nam and Tran-Cong, Thanh. 2009. "A Cartesian-grid discretisation scheme based on local integrated RBFNs for two-dimensional elliptic problems." CMES Computer Modeling in Engineering and Sciences. 51 (3), pp. 213-238. https://doi.org/10.3970/cmes.2009.051.213
On the use of integrated radial basis function schemes in weighted residuals statements for elliptic problems
Mai-Duy, Nam and Tran-Cong, Thanh. 2009. "On the use of integrated radial basis function schemes in weighted residuals statements for elliptic problems." Brebbia, Carlos A. (ed.) 31st International Conference on Boundary Elements and Other Mesh Reduction Methods (BEM/MRM 31). New Forest, United Kingdom 02 - 04 Sep 2009 Southampton, United Kingdom. https://doi.org/10.2495/BE090161
An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis
Nguyen-Van, Hieu, Mai-Duy, Nam and Tran-Cong, Thanh. 2009. "An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis." CMES Computer Modeling in Engineering and Sciences. 49 (2), pp. 81-110. https://doi.org/10.3970/cmes.2009.049.081
Numerical analysis of corrugated tube flow using RBFNs
Mai-Duy, Nam and Tanner, Roger I.. 2004. "Numerical analysis of corrugated tube flow using RBFNs." Lee, Jae Wook and Lee, Seung Jong (ed.) 14th International Congress on Rheology. Seoul, Korea 22 - 27 Aug 2004 Seoul, Korea.
An effective spectral collocation method for the direct solution of high-order ODEs
Mai-Duy, Nam. 2006. "An effective spectral collocation method for the direct solution of high-order ODEs." Communications in Numerical Methods in Engineering. 22 (6), pp. 627-642. https://doi.org/10.1002/cnm.841
Indirect RBFN method with scattered points for numerical solution of PDEs
Mai-Duy, Nam. 2004. "Indirect RBFN method with scattered points for numerical solution of PDEs." CMES Computer Modeling in Engineering and Sciences. 6 (2), pp. 209-226.
An effective high order interpolation scheme in BIEMs for biharmonic boundary value problems
Mai-Duy, N. and Tanner, R. I.. 2005. "An effective high order interpolation scheme in BIEMs for biharmonic boundary value problems." Engineering Analysis with Boundary Elements. 29 (3), pp. 210-223. https://doi.org/10.1016/j.enganabound.2005.01.005
Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows
Mai-Duy, Nam and Tran-Cong, Thanh. 2009. "Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows." Computers and Structures. 87 (11-12), pp. 642-650. https://doi.org/10.1016/j.compstruc.2008.09.004
An effective integrated-RBFN Cartesian-grid discretization for the stream function-vorticity-temperature formulation in nonrectangular domains
Le-Cao, K., Mai-Duy, N. and Tran-Cong, T.. 2009. "An effective integrated-RBFN Cartesian-grid discretization for the stream function-vorticity-temperature formulation in nonrectangular domains." Numerical Heat Transfer Part B: Fundamentals. 55 (6), pp. 480-502. https://doi.org/10.1080/10407790902827470
An integrated-RBF technique based on Galerkin formulation for elliptic differential equations
Mai-Duy, Nam and Tran-Cong, Thanh. 2009. "An integrated-RBF technique based on Galerkin formulation for elliptic differential equations." Engineering Analysis with Boundary Elements. 33 (2), pp. 191-199. https://doi.org/10.1016/j.enganabound.2008.05.001
A Galerkin-RBF approach for the streamfunction-vorticity-temperature formulation of natural convection in 2D enclosured domains
Ho-Minh, D., Mai-Duy, Nam and Tran-Cong, Thanh. 2009. "A Galerkin-RBF approach for the streamfunction-vorticity-temperature formulation of natural convection in 2D enclosured domains." CMES Computer Modeling in Engineering and Sciences. 44 (3), pp. 219-248. https://doi.org/10.3970/cmes.2009.044.219
A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains
Mai-Duy, Nam, See, Howard and Tran-Cong, Thanh. 2009. "A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 33 (1), pp. 284-299. https://doi.org/10.1016/j.apm.2007.11.002
A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations
Mai-Duy, Nam, Ho-Minh, D. and Tran-Cong, Thanh. 2009. "A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations." International Journal of Computer Mathematics. 86 (10-11), pp. 1746-1759. https://doi.org/10.1080/00207160802647365
A meshless technique based on integrated radial basis function networks for elliptic partial differential equations
Mai-Duy, N. and Tran-Cong, T.. 2008. "A meshless technique based on integrated radial basis function networks for elliptic partial differential equations." Griebel, Michael and Schweitzer, Marc Alexander (ed.) 4th International Workshop on Meshfree Methods for Partial Differential Equations. Bonn, Germany 17 - 20 Sep 2007 Berlin, Germany. https://doi.org/10.1007/978-3-540-79994-8_9
On the use of integrated RBFs in Galerkin approximation for elliptic problems
Mai-Duy, Nam and Tran-Cong, Thanh. 2008. "On the use of integrated RBFs in Galerkin approximation for elliptic problems." Skerget, Leopold and Brebbia, Carlos A. (ed.) BEM/MRM 30: 30th International Conference on Boundary Elements and Other Mesh Reduction Methods. Maribor, Slovenia 07 - 09 Jul 2008 Southampton, United Kingdom. https://doi.org/10.2495/BE080171
An effective high-order point-collocation numerical approach based on integrated approximants for elliptic differential equations
Mai-Duy, N. and Tran-Cong, T.. 2008. "An effective high-order point-collocation numerical approach based on integrated approximants for elliptic differential equations." Alvarez, Matias P. (ed.) Leading-edge applied mathematical modeling research. New York, NY. United States. Nova Science Publishers. pp. 215-250
A multidomain integrated-radial-basis-function collocation method for elliptic problems
Mai-Duy, Nam and Tran-Cong, Thanh. 2008. "A multidomain integrated-radial-basis-function collocation method for elliptic problems." Numerical Methods for Partial Differential Equations. 24 (5), pp. 1301-1320. https://doi.org/10.1002/num.20319
Free vibration analysis of laminated plate/shell structures based on FSDT with a stabilized nodal-integrated quadrilateral element
Nguyen-Van, H., Mai-Duy, N. and Tran-Cong, T.. 2008. "Free vibration analysis of laminated plate/shell structures based on FSDT with a stabilized nodal-integrated quadrilateral element." Journal of Sound and Vibration. 313 (1-2), pp. 205-223. https://doi.org/10.1016/j.jsv.2007.11.043
Nodal integration finite element techniques for analysis of piezoelectric solids
Nguyen-Van, Hieu, Le, Thong, Mai-Duy, Nam and Tran-Cong, Thanh. 2008. "Nodal integration finite element techniques for analysis of piezoelectric solids." 2008 International Conference on Computational Solid Mechanics (CSM2008). Ho Chi Minh City, Vietnam 27 - 30 Nov 2008 Ho Chi Minh City, Vietnam.
An integral-collocation-based fictitious-domain technique for solving elliptic problems
Mai-Duy, Nam, See, Howard and Tran-Cong, Thanh. 2008. "An integral-collocation-based fictitious-domain technique for solving elliptic problems." Communications in Numerical Methods in Engineering. 24 (11), pp. 1291-1314. https://doi.org/10.1002/cnm.1033
A point-collocation method based on integrated Chebyshev polynomials for elliptic differential equations in irregular domains
Mai-Duy, N. and Tran-Cong, T.. 2008. "A point-collocation method based on integrated Chebyshev polynomials for elliptic differential equations in irregular domains." Schrefler, B. A. and Perego, U. (ed.) 8th World Congress on Computational Mechanics (WCCM8), and 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008). Venice, Italy 30 Jun - 04 Jul 2008 Barcelona, Spain.
A multidomain integrated RBF collocation method for elliptic differential equations
Mai-Duy, Nam and Tran-Cong, Thanh. 2008. "A multidomain integrated RBF collocation method for elliptic differential equations." Schrefler, B. A. and Perego, U. (ed.) 8th World Congress on Computational Mechanics (WCCM8), and 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008). Venice, Italy 30 Jun - 04 Jul 2008 Barcelona, Spain.
An efficient domain-decomposition pseudo-spectral method for solving elliptic differential equations
Mai-Duy, Nam and Tran-Cong, Thanh. 2008. "An efficient domain-decomposition pseudo-spectral method for solving elliptic differential equations." Communications in Numerical Methods in Engineering. 24 (10), pp. 795-806. https://doi.org/10.1002/cnm.987
A node-based element for analysis of planar piezoelectric structures
Nguyen-Van, Hieu, Mai-Duy, Nam and Tran-Cong, Thanh. 2008. "A node-based element for analysis of planar piezoelectric structures." CMES Computer Modeling in Engineering and Sciences. 36 (1), pp. 65-95. https://doi.org/10.3970/cmes.2008.036.065
A meshless modeling of dynamic strain localization in quasi-brittle materials using radial basis function networks
Le, P., Mai-Duy, N., Tran-Cong, T. and Baker, G.. 2008. "A meshless modeling of dynamic strain localization in quasi-brittle materials using radial basis function networks." CMES Computer Modeling in Engineering and Sciences. 25 (1), pp. 43-67. https://doi.org/10.3970/cmes.2008.025.043
A second-order continuity domain-decomposition technique based on integrated Chebyshev polynomials for two-dimensional elliptic problems
Mai-Duy, Nam and Tran-Cong, Thanh. 2008. "A second-order continuity domain-decomposition technique based on integrated Chebyshev polynomials for two-dimensional elliptic problems." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 32 (12), pp. 2851-2862. https://doi.org/10.1016/j.apm.2007.10.003
A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures
Nguyen-Van, Hieu, Mai-Duy, Nam and Tran-Cong, Thanh. 2008. "A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures." CMES Computer Modeling in Engineering and Sciences. 23 (3), pp. 209-222. https://doi.org/10.3970/cmes.2008.023.209
A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuli
Mai-Duy, Nam, Le-Cao, Khoa and Tran-Cong, Thanh. 2008. "A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuli." International Journal for Numerical Methods in Fluids. 57 (12), pp. 1709-1730. https://doi.org/10.1002/fld.1675
A RBF-based fictitious-domain technique for Dirichlet boundary value problems in multiply-connected domains
Mai-Duy, Nam and Tran-Cong, Thanh. 2007. "A RBF-based fictitious-domain technique for Dirichlet boundary value problems in multiply-connected domains." Yagawa, G., Iu, V. P., Kashiyama, K., Miyazaki, N., Arantes e Oliveira, E., Valliappan, S., Yabe, T. and Yuan, M. W. (ed.) 3rd Asian-Pacific Congress on Computational Mechanics (APCOM'07) and EPMESC XI. Kyoto, Japan 03 - 06 Dec 2007 Japan.
A meshless IRBFN-based numerical simulation of dynamic strain localization in quasi-brittle materials
Le, Phong, Mai-Duy, Nam, Tran-Cong, Thanh and Baker, Graham. 2007. "A meshless IRBFN-based numerical simulation of dynamic strain localization in quasi-brittle materials." Taylor, R. L., Papadopoulos, P. and Zohdi, T. I. (ed.) USNCCM9: 9th US National Congress on Computational Mechanics. San Francisco, United States 22 - 26 Jul 2007 Austin, TX. United States.
A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems
Mai-Duy, Nam and Tanner, Roger I.. 2007. "A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems." Journal of Computational and Applied Mathematics. 201 (1), pp. 30-47. https://doi.org/10.1016/j.cam.2006.01.030
A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs
Mai-Duy, N. and Tanner, R. I.. 2007. "A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs." International Journal of Numerical Methods for Heat and Fluid Flow. 17 (2), pp. 165-186. https://doi.org/10.1108/09615530710723948
Solving partial differential equations with point collocation and one-dimensional integrated interpolation schemes
Mai-Duy, Nam and Tran-Cong, Thanh. 2007. "Solving partial differential equations with point collocation and one-dimensional integrated interpolation schemes." Han, Z., Lee, S. W. and Nakagaki, M. (ed.) 14th International Conference on Computational & Experimental Engineering and Sciences. Miami, Florida, USA 01 - 03 Jan 2007 United States.
Computation of laminated composite plates using integrated radial basis function networks
Mai-Duy, Nam, Khennane, Amar and Tran-Cong, Thanh. 2007. "Computation of laminated composite plates using integrated radial basis function networks." Computers, Materials and Continua. 5 (1), pp. 63-77. https://doi.org/10.3970/cmc.2007.005.063
A numerical study of strain localization in elasto-thermo-viscoplastic materials using radial basis function networks
Le, Phong, Mai-Duy, Nam, Tran-Cong, Thanh and Baker, Graham. 2007. "A numerical study of strain localization in elasto-thermo-viscoplastic materials using radial basis function networks." Computers, Materials and Continua. 5 (2), pp. 129-150. https://doi.org/10.3970/cmc.2007.005.129
A simple and accurate four-node quadrilateral element using stabilized nodal integration for laminated plates
Nguyen-Van, Hieu, Mai-Duy, Nam and Tran-Cong, Thanh. 2007. "A simple and accurate four-node quadrilateral element using stabilized nodal integration for laminated plates." Computers, Materials and Continua. 6 (3), pp. 159-176. https://doi.org/10.3970/cmc.2007.006.159
Computation of transient viscous flows using indirect radial basis function networks
Mai-Duy, Nam, Mai-Cao, Lan and Tran-Cong, Thanh. 2007. "Computation of transient viscous flows using indirect radial basis function networks." CMES Computer Modeling in Engineering and Sciences. 18 (1), pp. 59-78. https://doi.org/10.3970/cmes.2007.018.059
A Cartesian-grid collocation method based on radial-basis-function networks for solving PDEs in irregular domains
Mai-Duy, Nam and Tran-Cong, Thanh. 2007. "A Cartesian-grid collocation method based on radial-basis-function networks for solving PDEs in irregular domains." Numerical Methods for Partial Differential Equations. 23 (5), pp. 1192-1210. https://doi.org/10.1002/num.20217
Analysis of laminated composite plate/shell structures using a stabilized nodal-integrated quadrilateral element
Nguyen-Van, Hieu, Mai-Duy, Nam and Tran-Cong, Thanh. 2007. "Analysis of laminated composite plate/shell structures using a stabilized nodal-integrated quadrilateral element." Mendis, P. A., Cao, D. T. and Ngo, T. (ed.) 1st International Conference on Modern Design, Construction & Maintenance of Structures. Hanoi, Vietnam 10 - 11 Dec 2007 Hanoi, Vietnam.
Analysis of viscoelastic flow by a radial basis function networks method
Ho-Minh, D., Mai-Duy, Nam and Tran-Cong, Thanh. 2007. "Analysis of viscoelastic flow by a radial basis function networks method." Jacobs, Peter A., McIntyre, Tim, Cleary, Matthew J., Buttsworth, David R., Mee, David, Clements, Rose, Morgan, Richard and Lemckert, Charles (ed.) 16th Australasian Fluid Mechanics Conference (AFMC 2007). Gold Coast, Australia 03 - 07 Dec 2007 Brisbane, Australia.
Radial-basis-function calculations of buoyancy-driven flow in concentric and eccentric annuli
Le-Cao, Khoa, Mai-Duy, Nam and Tran-Cong, Thanh. 2007. "Radial-basis-function calculations of buoyancy-driven flow in concentric and eccentric annuli." Jacobs, Peter A., McIntyre, Tim, Cleary, Matthew J., Buttsworth, David R., Mee, David, Clements, Rose, Morgan, Richard and Lemckert, Charles (ed.) 16th Australasian Fluid Mechanics Conference (AFMC 2007). Gold Coast, Australia 03 - 07 Dec 2007 Brisbane, Australia.
Boundary integral-based domain decomposition technique for solution of Navier Stokes equations
Mai-Duy, N. and Tran-Cong, T.. 2004. "Boundary integral-based domain decomposition technique for solution of Navier Stokes equations." CMES Computer Modeling in Engineering and Sciences. 6 (1), pp. 59-75. https://doi.org/10.3970/cmes.2004.006.059
Indirect RBFN method with thin plate splines for numerical solution of differential equations
Mai-Duy, N. and Tran-Cong, T.. 2003. "Indirect RBFN method with thin plate splines for numerical solution of differential equations." CMES Computer Modeling in Engineering and Sciences. 4 (1), pp. 85-102. https://doi.org/10.3970/cmes.2003.004.085
BEM-RBF approach for viscoelastic flow analysis
Tran-Cong, T., Mai-Duy, N. and Phan-Thien, N.. 2002. "BEM-RBF approach for viscoelastic flow analysis." Engineering Analysis with Boundary Elements. 26 (9), pp. 757-762. https://doi.org/10.1016/S0955-7997(02)00041-3
Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson's equations
Mai-Duy, Nam and Tran-Cong, Thanh. 2002. "Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson's equations." Engineering Analysis with Boundary Elements. 26 (2), pp. 133-156. https://doi.org/10.1016/S0955-7997(01)00092-3
A fast convergent iterative boundary element method on PVM cluster
Mai-Duy, N., Nguyen-Hong, P. and Tran-Cong, T.. 1998. "A fast convergent iterative boundary element method on PVM cluster." Engineering Analysis with Boundary Elements. 22 (4), pp. 307-316. https://doi.org/10.1016/S0955-7997(98)00071-X
BEM-RBF approach for viscoelastic flow analysis
Tran-Cong, T., Mai-Duy, N. and Phan-Thien, N.. 2001. "BEM-RBF approach for viscoelastic flow analysis." Beskos, D., Brebbia, C., Katsikadelis, J. and Manolis, G. (ed.) 23rd International Conference on the Boundary Element Method (BEM 2001). Lemnos, Greece 07 - 09 May 2001 Southampton, Hants. United Kingdom. https://doi.org/10.2495/BE010301
A meshless IRBFN-based numerical simulation of adiabatic shear band formation in one dimension
Le, Phong, Mai-Duy, Nam, Tran-Cong, Thanh and Baker, Graham. 2006. "A meshless IRBFN-based numerical simulation of adiabatic shear band formation in one dimension." Nguyen, Son Q. and Nguyen, Dung (ed.) 2006 International Conference on Nonlinear Analysis & Engineering Mechanics Today. Ho Chi Minh City, Vietnam 11 - 14 Dec 2006 Paris, France.
A high-order time-kernel BIEM for the Burgers equation
Mai-Duy, Nam, Tran-Cong, Thanh and Tanner, R. I.. 2006. "A high-order time-kernel BIEM for the Burgers equation." Gatmiri, B., Sellier, A. and Aliabadi, M. H. (ed.) International Conference on Boundary Element Techniques VII. Paris, France 04 - 06 Sep 2006 Eastleigh, United Kingdom.
A new high-order time-kernel BIEM for the Burgers equation
Mai-Duy, N., Tran-Cong, T. and Tanner, R. I.. 2006. "A new high-order time-kernel BIEM for the Burgers equation." CMES Computer Modeling in Engineering and Sciences. 16 (3), pp. 177-186. https://doi.org/10.3970/cmes.2006.016.177
Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks
Mai-Duy, N. and Tran-Cong, T.. 2006. "Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks." Engineering Analysis with Boundary Elements. 30 (2), pp. 77-87. https://doi.org/10.1016/j.enganabound.2005.10.004
Comparison of BEM-FFNN and BEM-RBFN methods for GNF flow analysis
Tran, C., Mai-Duy, N. and Tran-Cong, T.. 2000. "Comparison of BEM-FFNN and BEM-RBFN methods for GNF flow analysis." The XIIIth International Congress on Rheology. Cambridge, United Kingdom 20 - 25 Aug 2000 United Kingdom.