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Latest revision as of 12:20, 18 February 2019
Published in Int. J. Numer. Meths. Engng. Vol. 39 (22), pp. 3839-3866, 1996
doi: 10.1002/(SICI)1097-0207(19961130)39:22<3839::AID-NME27>3.0.CO;2-R
Abstract
The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non‐self adjoint equations typical of convective‐diffusive transport and also to the analysis of compressible fluid mechanics problem are presented.
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Published on 01/01/1996
DOI: 10.1002/(SICI)1097-0207(19961130)39:22<3839::AID-NME27>3.0.CO;2-R
Licence: CC BY-NC-SA license
Web of Science Core Collection® Times cited: 512
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OpenCitations.net Times cited: 277
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- F. Saucedo-Zendejo, E. Resnediz-Flores. A Semi-implicit Generalized Finite Differences Approach to Simulate Natural Convective Viscous Flows. (2018) DOI 10.1007/978-3-319-93587-4_29
- G. Liu, G. Xu. A gradient smoothing method (GSM) for fluid dynamics problems. Int. J. Numer. Meth. Fluids 58(10) DOI 10.1002/fld.1788
- E. Ortega, E. Oñate, S. Idelsohn. A finite point method for adaptive three-dimensional compressible flow calculations. Int. J. Numer. Meth. Fluids 60(9) DOI 10.1002/fld.1892
- M. Afshar, M. Lashckarbolok, G. Shobeyri. Collocated discrete least squares meshless (CDLSM) method for the solution of transient and steady-state hyperbolic problems. Int. J. Numer. Meth. Fluids 60(10) DOI 10.1002/fld.1897
- X. Zhang, J. Ouyang, L. Zhang. The characteristic-based split (CBS) meshfree method for free surface flow problems in ALE formulation. Int. J. Numer. Meth. Fluids 65(7) (2011) DOI 10.1002/fld.2213
- C. Cyron, K. Nissen, V. Gravemeier, W. Wall. Information flux maximum-entropy approximation schemes for convection-diffusion problems. Int. J. Numer. Meth. Fluids 64(10-12) (2010) DOI 10.1002/fld.2271
- Z. Sun, Y. Liang, G. Xi. Numerical simulation of the flow in straight blade agitator with the MPS method. Int. J. Numer. Meth. Fluids 67(12) (2010) DOI 10.1002/fld.2474
- M. Cheng, G. Liu. A novel finite point method for flow simulation. Int. J. Numer. Meth. Fluids 39(12) (2002) DOI 10.1002/fld.365
- D. Kennett, S. Timme, J. Angulo, K. Badcock. An implicit meshless method for application in computational fluid dynamics. Int. J. Numer. Meth. Fluids 71(8) (2012) DOI 10.1002/fld.3698
- E. Ortega, E. Oñate, S. Idelsohn, R. Flores. A meshless finite point method for three-dimensional analysis of compressible flow problems involving moving boundaries and adaptivity. Int. J. Numer. Meth. Fluids 73(4) (2013) DOI 10.1002/fld.3799
- E. Ortega, E. Oñate, S. Idelsohn, R. Flores. Application of the finite point method to high-Reynolds number compressible flow problems. Int. J. Numer. Meth. Fluids 74(10) (2014) DOI 10.1002/fld.3871
- S. Idelsohn, J. Marti, P. Becker, E. Oñate. Analysis of multifluid flows with large time steps using the particle finite element method. Int. J. Numer. Meth. Fluids 75(9) (2014) DOI 10.1002/fld.3908
- L. Sun, G. Zhao, J. Zhao. Particle manifold method (PMM): A new continuum-discontinuum numerical model for geomechanics. Int. J. Numer. Anal. Meth. Geomech. 37(12) (2012) DOI 10.1002/nag.2104
- A. Bobet, V. García Marín. A stress and displacement discontinuity element method for elastic transversely anisotropic rock. Int. J. Numer. Anal. Meth. Geomech. 38(18) (2014) DOI 10.1002/nag.2284
- M. Oliaei, K. Soga, A. Pak. Some numerical issues using element-free Galerkin mesh-less method for coupled hydro-mechanical problems. Int. J. Numer. Anal. Meth. Geomech. 33(7) DOI 10.1002/nag.747
- P. Zhang, X. Zhang. Numerical Modeling of Stokes Flow in a Circular Cavity by Variational Multiscale Element Free Galerkin Method. Mathematical Problems in Engineering 2014 DOI 10.1155/2014/451546
- S. Moazam, B. Boroomand, S. Naimi, M. Celikag. Wave Propagation in Unbounded Domains under a Dirac Delta Function with FPM. Mathematical Problems in Engineering 2014 DOI 10.1155/2014/470346
- N. Zhao, H. Ren. The Interpolating Element-Free Galerkin Method for 2D Transient Heat Conduction Problems. Mathematical Problems in Engineering 2014 DOI 10.1155/2014/712834
- Y. Cheng, W. Wang, M. Peng, Z. Zhang. Mathematical Aspects of Meshless Methods. Mathematical Problems in Engineering 2014 DOI 10.1155/2014/756297
- L. Pérez Pozo, A. Campos, S. Lascano, S. Oller, A. Rodríguez-Ferran. A Finite Points Method Approach for Strain Localization Using the Gradient Plasticity Formulation. Mathematical Problems in Engineering 2014 DOI 10.1155/2014/782079
- L. Gavete, M. Gavete, F. Ureña, J. Benito. An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences. Mathematical Problems in Engineering 2015 DOI 10.1155/2015/283757
- G. Li, X. Jin, N. Alum. Meshless Methods for Numerical Solution of Partial Differential Equations. DOI 10.1007/978-1-4020-3286-8_128
- H. Zhu, Y. Miao, Y. Cai. MESHLESS NATURAL NEIGHBOUR METHOD AND ITS APPLICATION IN ELASTO-PLASTIC PROBLEMS. DOI 10.1007/978-1-4020-3953-9_71
- F. Ureña, J. Benito, R. Alvarez, L. Gavete. Computational Error Approximation and H-Adaptive Algorithm for the 3-D Generalized Finite Difference Method. International Journal for Computational Methods in Engineering Science and Mechanics 6(1) DOI 10.1080/15502280590888630
- Y. Hon, S. Li, M. Huang. A Meshless Computational Method for the Shear Flow of Johnson-Segalman Fluid. International Journal for Computational Methods in Engineering Science and Mechanics 6(1) DOI 10.1080/15502280590888658
- H. Li, J. Cheng, T. Ng. A New Variation of Point Collocation: The Meshless Finite Mixture (MFM) Method. International Journal for Computational Methods in Engineering Science and Mechanics 6(1) DOI 10.1080/15502280590888667
- B. Farahani, J. Berardo, R. Drgas, J. César de Sá, A. Ferreira, J. Belinha. The Axisymmetric Analysis of Circular Plates Using the Radial Point Interpolation Method. International Journal for Computational Methods in Engineering Science and Mechanics 16(6) (2015) DOI 10.1080/15502287.2015.1103819
- A. Chhillar, R. Singh. Critical evaluation of spline, exponential and Gaussian test functions for elastostatic analysis of metal parts using meshless method. International Journal for Computational Methods in Engineering Science and Mechanics 17(5-6) (2016) DOI 10.1080/15502287.2016.1246492
- Y. Hwang. Development of a particle method of characteristics (PMOC) for one-dimensional shock waves. Shock Waves 28(2) (2017) DOI 10.1007/s00193-017-0720-1
- J. Cante, M. Riera, J. Oliver, J. Prado, A. Isturiz, C. Gonzalez. Flow regime analyses during the filling stage in powder metallurgy processes: experimental study and numerical modelling. Granular Matter 13(1) (2010) DOI 10.1007/s10035-010-0225-4
- P. Randles, A. Petschek, L. Libersky, C. Dyka. Stability of DPD and SPH. DOI 10.1007/978-3-642-56103-0_24
- W. Ju-Feng, S. Feng-Xin, C. Rong-Jun. Element-free Galerkin method for a kind of KdV equation. Chinese Phys. B 19(6) (2010) DOI 10.1088/1674-1056/19/6/060201
- C. Li, C. Yu-Min. The complex variable reproducing kernel particle method for two-dimensional elastodynamics. Chinese Phys. B 19(9) (2010) DOI 10.1088/1674-1056/19/9/090204
- J. Wang, F. Bai, Y. Cheng. A meshless method for the nonlinear generalized regularized long wave equation. Chinese Phys. B 20(3) (2011) DOI 10.1088/1674-1056/20/3/030206
- X. Liu. Radial point collocation method (RPCM) for solving convection-diffusion problems. J. Zhejiang Univ. - Sci. A 7(6) (2006) DOI 10.1631/jzus.2006.a1061
- Y. LU. A meshless method based on moving least squares for the simulation of free surface flows. JZUS-A 17 DOI 10.1631/jzus.a1500053
- F. Yan, X. Feng, H. Zhou. Meshless method of dual reciprocity hybrid radial boundary node method for elasticity. Acta Mechanica Solida Sinica 23(5) DOI 10.1016/s0894-9166(10)60047-x
- Y. Guo, S. Kamitani. The Over-Range Collocation Method for Nonlinear Analyses. AMM 300-301 (2013) DOI 10.4028/www.scientific.net/amm.300-301.942
- N. Ding, Y. Zhang, H. Wang, J. Xu. Influence Study of the Influence Domain to Numerical Simulation Results with Meshless Method. AMM 448-453 (2013) DOI 10.4028/www.scientific.net/amm.448-453.3223
- X. Cui, G. Liu, G. Li. A smoothed Hermite radial point interpolation method for thin plate analysis. Arch Appl Mech 81(1) (2009) DOI 10.1007/s00419-009-0392-0
- N. Chuathong, S. Kaennakham. Numerical Solution to Coupled Burgers’ Equations by Gaussian-Based Hermite Collocation Scheme. Journal of Applied Mathematics 2018 DOI 10.1155/2018/3416860
- S. Hsiao, M. Shih, N. Wu. Simulation of Propagation and Run-Up of Three Dimensional Landslide-Induced Waves Using a Meshless Method. Water 10(5) (2018) DOI 10.3390/w10050552
- J. ZHOU, X. WANG, Z. ZHANG, L. ZHANG. ON SOME ENRICHMENTS OF REPRODUCING KERNEL PARTICLE METHOD. Int. J. Comput. Methods 01(03) (2012) DOI 10.1142/s0219876204000265
- L. VRANKAR, G. TURK, F. RUNOVC. A COMPARISON OF THE EFFECTIVENESS OF USING THE MESHLESS METHOD AND THE FINITE DIFFERENCE METHOD IN GEOSTATISTICAL ANALYSIS OF TRANSPORT MODELING. Int. J. Comput. Methods 02(02) (2011) DOI 10.1142/s0219876205000405
- M. MACRI, J. TICHY, S. DE. SOME EXAMPLES OF THE METHOD OF FINITE SPHERES WITH ENRICHMENT. Int. J. Comput. Methods 02(04) (2011) DOI 10.1142/s0219876205000648
- Y. GU. MESHFREE METHODS AND THEIR COMPARISONS. Int. J. Comput. Methods 02(04) (2011) DOI 10.1142/s0219876205000673
- S. LIU, H. WANG, H. ZHANG. SMOOTHED FINITE ELEMENTS LARGE DEFORMATION ANALYSIS. Int. J. Comput. Methods 07(03) (2011) DOI 10.1142/s0219876210002246
- H. ZHU, X. ZHUANG, Y. CAI, G. MA. HIGH ROCK SLOPE STABILITY ANALYSIS USING THE ENRICHED MESHLESS SHEPARD AND LEAST SQUARES METHOD. Int. J. Comput. Methods 08(02) (2011) DOI 10.1142/s0219876211002551
- S. CHEN, Q. LI, Y. LIU, J. XIA, Z. XUE. DYNAMIC ELASTOPLASTIC ANALYSIS USING THE MESHLESS LOCAL NATURAL NEIGHBOR INTERPOLATION METHOD. Int. J. Comput. Methods 08(03) (2011) DOI 10.1142/s0219876211002629
- Y. GU, P. ZHUANG, Q. LIU. AN ADVANCED MESHLESS METHOD FOR TIME FRACTIONAL DIFFUSION EQUATION. Int. J. Comput. Methods 08(04) (2011) DOI 10.1142/s0219876211002745
- B. JIANG. LEAST-SQUARES MESHFREE COLLOCATION METHOD. Int. J. Comput. Methods 09(02) (2012) DOI 10.1142/s0219876212400312
- C. BUACHART, W. KANOK-NUKULCHAI, E. ORTEGA, E. OÑATE. A SHALLOW WATER MODEL BY FINITE POINT METHOD. Int. J. Comput. Methods 11(01) (2013) DOI 10.1142/s0219876213500473
- G. Liu. An Overview on Meshfree Methods: For Computational Solid Mechanics. Int. J. Comput. Methods 13(05) (2016) DOI 10.1142/s0219876216300014
- J. Belinha, J. Azevedo, L. Dinis, R. Natal Jorge. The Natural Neighbor Radial Point Interpolation Method in Computational Fracture Mechanics: A 2D Preliminary Study. Int. J. Comput. Methods 14(04) (2017) DOI 10.1142/s0219876217500451
- X. Bi, S. Mu, Q. Liu, Q. Liu, B. Liu, P. Zhuang, J. Gao, H. Jiang, X. Li, B. Li. Advanced Implicit Meshless Approaches for the Rayleigh–Stokes Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative. Int. J. Comput. Methods 15(05) (2018) DOI 10.1142/s0219876218500329
- F. Zhang, X. Zhang, K. Sze, Y. Liang, Y. Liu. Improved Incompressible Material Point Method Based on Particle Density Correction. Int. J. Comput. Methods 15(07) (2018) DOI 10.1142/s0219876218500615
- G. Liu. A Novel Pick-Out Theory and Technique for Constructing the Smoothed Derivatives of Functions for Numerical Methods. Int. J. Comput. Methods 15(03) (2018) DOI 10.1142/s0219876218500706
- J. Cho, Y. Jee. An adaptive mesh-independent numerical integration for meshless local petrov-galerkin method. KSME International Journal 17(7) DOI 10.1007/bf02982983
- Y. Choi, S. Kim. Bending analysis of mindlin-reissner plates by the element free galerkin method with penalty technique. KSME International Journal 17(1) DOI 10.1007/bf02984287
- L. Chen, K. Liew, Y. Cheng. The coupling of complex variable-reproducing kernel particle method and finite element method for two-dimensional potential problems. Interaction and multiscale mechanics 3(3) DOI 10.12989/imm.2010.3.3.277
- J. Cheng, H. Lee, H. Li. Development of a meshless finite mixture (MFM) method. Structural Engineering and Mechanics 17(5) DOI 10.12989/sem.2004.17.5.671
- L. Nitsche, W. Zhang. Atomistic SPH and a link between diffusion and interfacial tension. AIChE J. 48(2) (2006) DOI 10.1002/aic.690480203
- M. Alizadeh, S. Jahromi, S. Nasihatkon. Applying Finite Point Method in Solidification Modeling during Continuous Casting Process. ISIJ Int. 50(3) DOI 10.2355/isijinternational.50.411
- K. Choi, H. Kim. Modeling the Behavior of Trapped Air in Die Cavity During Sheet Metal Forming. Transactions of Materials Processing 20(5) DOI 10.5228/kstp.2011.20.5.377
- N. Wu, T. Tsay. A robust local polynomial collocation method. Int. J. Numer. Meth. Engng 93(4) (2012) DOI 10.1002/nme.4380
- S. Chi, J. Chen, H. Hu, J. Yang. A gradient reproducing kernel collocation method for boundary value problems. Int. J. Numer. Meth. Engng 93(13) (2013) DOI 10.1002/nme.4432
- J. Wang, G. Liu. A point interpolation meshless method based on radial basis functions. Int. J. Numer. Meth. Engng. 54(11) (2002) DOI 10.1002/nme.489
- F. Mossaiby, M. Ghaderian, R. Rossi. Implementation of a generalized exponential basis functions method for linear and non-linear problems. Int. J. Numer. Meth. Engng 105(3) (2015) DOI 10.1002/nme.4985
- Y. Guo, G. Yagawa. A meshless method with conforming and nonconforming sub-domains. Int. J. Numer. Meth. Engng 110(9) (2016) DOI 10.1002/nme.5431
- P. Suchde, J. Kuhnert, S. Schröder, A. Klar. A flux conserving meshfree method for conservation laws. Int. J. Numer. Meth. Engng 112(3) (2017) DOI 10.1002/nme.5511
- V. Shrivastava, N. Aluru. A fast boundary cloud method for exterior 2D electrostatic analysis. Int. J. Numer. Meth. Engng. 56(2) (2002) DOI 10.1002/nme.562
- E. Pardo. Blurred derivatives and meshless methods. Int. J. Numer. Meth. Engng. 56(2) (2002) DOI 10.1002/nme.567
- S. Park, K. Kwon, S. Youn. A study on the convergence of least-squares meshfree method under inaccurate integration. Int. J. Numer. Meth. Engng. 56(10) (2003) DOI 10.1002/nme.613
- C. Zuppa, A. Cardona. A collocation meshless method based on local optimal point interpolation. Int. J. Numer. Meth. Engng. 57(4) (2003) DOI 10.1002/nme.687
- S. Idelsohn, E. Oñate, N. Calvo, F. Del Pin. The meshless finite element method. Int. J. Numer. Meth. Engng. 58(6) (2003) DOI 10.1002/nme.798
- L. Gavete, M. Gavete, B. Alonso, A. Martín. A posteriorierror approximation in EFG method. Int. J. Numer. Meth. Engng. 58(15) (2003) DOI 10.1002/nme.850
- S. Atluri, S. Shen. The basis of meshless domain discretization: the meshless local Petrov?Galerkin (MLPG) method. Adv Comput Math 23(1-2) DOI 10.1007/s10444-004-1813-9
- K. Choi, H. Kim. A Sheet Metal Forming Simulation of a Fuel Filler Door Considering the Behavior of Air in a Die Cavity. steel research int. 86(8) (2015) DOI 10.1002/srin.201500113
- Y. Gu, L. Zhang. A Concurrent Multiscale Method Based on the Meshfree Method and Molecular Dynamics Analysis. Multiscale Model. Simul. 5(4) DOI 10.1137/060654232
- L. Shen, G. Lv, Z. Shen. A Finite Point Method Based on Directional Differences. SIAM J. Numer. Anal. 47(3) DOI 10.1137/08072200x
- E. Kwan-yu Chiu, Q. Wang, R. Hu, A. Jameson. A Conservative Mesh-Free Scheme and Generalized Framework for Conservation Laws. SIAM J. Sci. Comput. 34(6) DOI 10.1137/110842740
- S. Samimi, A. Pak. EFG mesh-less method for coupled hydro-mechanical analysis of unsaturated porous media. (2014) DOI 10.1201/b17034-81
- Z. Jannesari, M. Tatari. Element-free Galerkin method to the interface problems with application in electrostatic. Int. J. Numer. Model. 29(6) (2016) DOI 10.1002/jnm.2167
- T. Rabczuk, X. Zhuang. Meshless Discretization Methods. (2017) DOI 10.1007/978-3-662-53605-6_15-1
- N. Aluru, G. Li. Finite cloud method: a true meshless technique based on a fixed reproducing kernel approximation. Int. J. Numer. Meth. Engng. 50(10) (2001) DOI 10.1002/nme.124
- B. Boroomand, A. Tabatabaei, E. Oñate. Simple modifications for stabilization of the finite point method. Int. J. Numer. Meth. Engng. 63(3) (2005) DOI 10.1002/nme.1278
- K. Liew, J. Ren, J. Reddy. Numerical simulation of thermomechanical behaviours of shape memory alloys via a non-linear mesh-free Galerkin formulation. Int. J. Numer. Meth. Engng 63(7) (2005) DOI 10.1002/nme.1320
- A. Sadeghirad, S. Mohammadi. Equilibrium on line method (ELM) for imposition of Neumann boundary conditions in the finite point method (FPM). Int. J. Numer. Meth. Engng 69(1) (2006) DOI 10.1002/nme.1755
- L. Kucherov, E. Tadmor, R. Miller. Umbrella spherical integration: a stable meshless method for non-linear solids. Int. J. Numer. Meth. Engng 69(13) (2007) DOI 10.1002/nme.1871
- J. Lu, J. Qian, W. Han. Discrete gradient method in solid mechanics. Int. J. Numer. Meth. Engng 74(4) (2008) DOI 10.1002/nme.2187
- S. Park, S. Youn. The least‐squares meshfree method. Int. J. Numer. Meth. Engng. 52(9) DOI 10.1002/nme.248
- J. Chen, L. Wang, H. Hu, S. Chi. Subdomain radial basis collocation method for heterogeneous media. Int. J. Numer. Meth. Engng 80(2) DOI 10.1002/nme.2624
- H. Netuzhylov, A. Zilian. Space-time meshfree collocation method: Methodology and application to initial-boundary value problems. Int. J. Numer. Meth. Engng 80(3) DOI 10.1002/nme.2638
- X. Cui, G. Liu, G. Li, G. Zhang. A thin plate formulation without rotation DOFs based on the radial point interpolation method and triangular cells. Int. J. Numer. Meth. Engng. 85(8) (2010) DOI 10.1002/nme.3000
- L. Gavete, J. Cuesta, A. Ruiz. A procedure for approximation of the error in the EFG method. Int. J. Numer. Meth. Engng. 53(3) (2001) DOI 10.1002/nme.307
- E. Ortega, E. Oñate, S. Idelsohn, C. Buachart. An adaptive finite point method for the shallow water equations. Int. J. Numer. Meth. Engng. 88(2) (2011) DOI 10.1002/nme.3171
- X. Li. The meshless Galerkin boundary node method for Stokes problems in three dimensions. Int. J. Numer. Meth. Engng. 88(5) (2011) DOI 10.1002/nme.3181
- P. Zhuang, Y. Gu, F. Liu, I. Turner, P. Yarlagadda. Time-dependent fractional advection-diffusion equations by an implicit MLS meshless method. Int. J. Numer. Meth. Engng. 88(13) (2011) DOI 10.1002/nme.3223
- H. Gao, G. Wei. Complex Variable Meshless Manifold Method for Transient Heat Conduction Problems. Int. J. Appl. Mechanics 09(05) (2017) DOI 10.1142/s1758825117500673
- E. Gabreil, S. Tait, A. Nichols, G. Dolcetti. 3D SPH Simulation of Dynamic Water Surface and Its Interaction with Underlying Flow Structure for Turbulent Open Channel Flows Over Rough Beds. International Journal of Ocean and Coastal Engineering 01(02) (2019) DOI 10.1142/s2529807018400031
- C. Li, S. Xiong, J. Rodrigues, P. Martins. Simulation of Bulk Metal Forming by Means of Finite Integral Mesh Free Methods. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 219(9) (2016) DOI 10.1243/095440605x31797
- Y. GUO, K. SHIOYA, K. OOBUCHI, G. YAGAWA, S. KAMITANI. Accuracy improvement of collocation method by using the over-range collocation points for 2-D and 3-D problems. 1(2) DOI 10.1299/mej.2014cm0008
- Y. Lu, A. Hu, X. Chang, Z. Li, Y. Wei. Grid-Free Modelling Based on the Finite Particle Method for Incompressible Viscous Flow Problems. Shock and Vibration 2019 DOI 10.1155/2019/4610524
- H. Ding, C. Shu, K. Yeo, Z. Lu. SIMULATION OF NATURAL CONVECTION IN ECCENTRIC ANNULI BETWEEN A SQUARE OUTER CYLINDER AND A CIRCULAR INNER CYLINDER USING LOCAL MQ-DQ METHOD. Numerical Heat Transfer, Part A: Applications 47(3) DOI 10.1080/10407780590889545
- Y. Liu, X. Zhang, M. Lu. A MESHLESS METHOD BASED ON LEAST-SQUARES APPROACH FOR STEADY- AND UNSTEADY-STATE HEAT CONDUCTION PROBLEMS. Numerical Heat Transfer, Part B: Fundamentals 47(3) DOI 10.1080/10407790590901648
- J. Fang, G. Zhao, J. Zhao, A. Parriaux. On the Truly Meshless Solution of Heat Conduction Problems in Heterogeneous Media. Numerical Heat Transfer, Part B: Fundamentals 55(1) DOI 10.1080/10407790802605067
- Y. Hwang. Smoothing Difference Scheme in a Moving Particle Method. Numerical Heat Transfer, Part B: Fundamentals 60(3) DOI 10.1080/10407790.2011.601156
- Y. Hwang. A Moving Particle Method with Embedded Pressure Mesh (MPPM) for Incompressible Flow Calculations. Numerical Heat Transfer, Part B: Fundamentals 60(5) DOI 10.1080/10407790.2011.601178
- X. Wu, Y. Dai, W. Tao. MLPG/SUPG Method for Convection-Dominated Problems. Numerical Heat Transfer, Part B: Fundamentals 61(1) DOI 10.1080/10407790.2011.630962
- X. Zhang, P. Zhang. Heterogeneous Heat Conduction Problems by an Improved Element-Free Galerkin Method. Numerical Heat Transfer, Part B: Fundamentals 65(4) (2014) DOI 10.1080/10407790.2013.857221
- Z. Chen, Z. Li, W. Tao. A new stability parameter in streamline upwind meshless Petrov–Galerkin method for convection–diffusion problems at large Peclet number. Numerical Heat Transfer, Part B: Fundamentals 74(5) (2019) DOI 10.1080/10407790.2019.1580050
- Z. Zhu, H. Li, J. Li, P. Wang. The investigation of bidisciplinary (aerodynamics/electromagnetics) optimization methods. (2012) DOI 10.2514/6.2001-1108
- B. Song, R. Amano. Development of generalized difference method to fluid flow and heat transfer. (2012) DOI 10.2514/6.2001-1117
- J. Cho, Y. Choi, D. Kim, S. Kim. Node activation technique for finite element system. (2012) DOI 10.2514/6.2001-1256
- J. Cho, D. Kim, S. Kim. Three Dimensional Stress Analysis by Node Activation Method. (2012) DOI 10.2514/6.2002-1217
- L. Remaki, H. Beaugendre. An Anisotropic Isovalue-Oriented Artificial Viscosity Method. (2012) DOI 10.2514/6.2003-73
- H. Abdi, A. Arefmanesh. Streamline Upwind Meshless Local Petrov-Galerkin Method with Unity as the Test Function for Thermofluid Problems. (2012) DOI 10.2514/6.2006-3085
- A. Yohannes, T. Lacy, Y. Hwang. Hybrid Boundary Element Method for Two-Dimensional Linear Elastic Fracture Analysis. (2012) DOI 10.2514/6.2007-2378
- A. Katz, A. Jameson. A Meshless Volume Scheme. (2012) DOI 10.2514/6.2009-3534
- E. Chiu, A. Jameson. An Edge-Averaged Semi-Meshless Framework for Numerical Solution of Conservation Laws. (2012) DOI 10.2514/6.2010-1269
- D. Kennett, S. Timme, J. Angulo, K. Badcock. An Implicit Semi-Meshless Scheme with Stencil Selection for Anisotropic Point Distributions. (2012) DOI 10.2514/6.2011-3234
- E. Chiu, Q. Wang, A. Jameson. A Conservative Meshless Scheme: General Order Formulation and Application to Euler Equations. (2012) DOI 10.2514/6.2011-651
- A. Ramos, R. McDonald. A Meshless Finite Difference Scheme for Compressible Potential Flows. (2012) DOI 10.2514/6.2011-654
- I. Flamarique Ederra, T. Rendall, A. Gaitonde, D. Jones, C. Allen. Conservative Unsteady Simulation of Arbitrary Motion in Two-dimensional Spacetime Using Central Difference, Upwind and Hybrid Formulations. (2017) DOI 10.2514/6.2017-3448
- S. Mei. HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation. Journal of Applied Mathematics 2013 DOI 10.1155/2013/248246
- E. Soudah, E. Ng, T. Loong, M. Bordone, U. Pua, S. Narayanan. CFD Modelling of Abdominal Aortic Aneurysm on Hemodynamic Loads Using a Realistic Geometry with CT. Computational and Mathematical Methods in Medicine 2013 DOI 10.1155/2013/472564
- T. Rabczuk. Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives. ISRN Applied Mathematics 2013 DOI 10.1155/2013/849231
- X. Qin, X. Duan, L. Su, X. Shen, G. Hu. Numerical Simulation of Soil Water Movement under Subsurface Irrigation. Mathematical Problems in Engineering 2014 DOI 10.1155/2014/126398
- L. de Dinis, R. Jorge, J. Belinha. The Radial Natural Neighbours Interpolators Extended to ElastoplastiCity. DOI 10.1007/978-1-4020-8821-6_11
- N. Wu, B. Chen, T. Tsay. A Review on the Modified Finite Point Method. Mathematical Problems in Engineering 2014 DOI 10.1155/2014/350364
- S. Patel, A. Rastogi. Groundwater Estimation using Global Strong Form Collocation-based Meshfree Method in a Field like Synthetic Confined Aquifer Domain. KSCE J Civ Eng 23(6) (2019) DOI 10.1007/s12205-019-1852-x
- H. Qiang, W. Gao. Meshless local discontinuous Petrov-Galerkin method with application to blasting problems. Trans. Tianjin Univ. 14(5) (2008) DOI 10.1007/s12209-008-0064-0
- V. Perminov, T. Rein, S. Karabtcev. NEM and MFEM Simulation of Interaction between Time-dependent Waves and Obstacles. IOP Conf. Ser.: Mater. Sci. Eng. 81 (2015) DOI 10.1088/1757-899x/81/1/012099
- M. Ebrahimnejad, N. Fallah, A. Khoei. Three types of meshless finite volume method for the analysis of two-dimensional elasticity problems. Comp. Appl. Math. 36(2) (2015) DOI 10.1007/s40314-015-0273-9
- M. Khaksarfard, Y. Ordokhani, E. Babolian. An approximate method for solution of nonlocal boundary value problems via Gaussian radial basis functions. SeMA 76(1) (2018) DOI 10.1007/s40324-018-0165-1
- C. Spa, R. Rivas, L. Pérez. Impedance boundary conditions for a time-domain finite-point method. J Braz. Soc. Mech. Sci. Eng. 40(6) (2018) DOI 10.1007/s40430-018-1247-9
- O. Eugenio. Finite increment calculus (FIC): a framework for deriving enhanced computational methods in mechanics. Adv. Model. and Simul. in Eng. Sci. 3(1) (2016) DOI 10.1186/s40323-016-0065-9
- E. Jaberzadeh, M. Azhari. Local buckling of moderately thick stepped skew viscoelastic composite plates using the element-free Galerkin method. Acta Mech 226(4) (2014) DOI 10.1007/s00707-014-1232-z
- A. Shojaei, F. Mossaiby, M. Zaccariotto, U. Galvanetto. The meshless finite point method for transient elastodynamic problems. Acta Mech 228(10) (2017) DOI 10.1007/s00707-017-1894-4
- Y. Lu, A. Hu, Y. Liu. A finite pointset method for the numerical simulation of free surface flow around a ship. J Mar Sci Technol 21(2) (2015) DOI 10.1007/s00773-015-0342-1
- T. Rabczuk, S. Bordas, H. Askes. Meshfree Discretization Methods for Solid Mechanics. (2010) DOI 10.1002/9780470686652.eae162
- E. Shivanian, A. Rahimi, M. Hosseini. Meshless local radial point interpolation to three-dimensional wave equation with Neumann's boundary conditions. International Journal of Computer Mathematics 93(12) (2015) DOI 10.1080/00207160.2015.1085032
- M. Rostamian, A. Shahrezaee. A meshless method to the numerical solution of an inverse reaction–diffusion–convection problem. International Journal of Computer Mathematics 94(3) (2016) DOI 10.1080/00207160.2015.1119816
- B. Malidareh, S. Hosseini. Collocated discrete subdomain meshless method for dam-break and dam-breaching modelling. Proceedings of the Institution of Civil Engineers - Water Management 172(2) DOI 10.1680/jwama.16.00101
- P. Hopkins. A new class of accurate, mesh-free hydrodynamic simulation methods. 450(1) (2015) DOI 10.1093/mnras/stv195
- P. Hopkins. A constrained-gradient method to control divergence errors in numerical MHD. Mon. Not. R. Astron. Soc. 462(1) (2016) DOI 10.1093/mnras/stw1578
- P. Hopkins. Anisotropic diffusion in mesh-free numerical magnetohydrodynamics. Mon. Not. R. Astron. Soc. 466(3) (2016) DOI 10.1093/mnras/stw3306
- Z. Hu, X. Zheng, W. Duan, Q. Ma. K2_SPH method and its application for 2-D water wave simulation. J. Marine. Sci. Appl. 10(4) (2011) DOI 10.1007/s11804-011-1085-y
- L. Zhang, A. Ademiloye, K. Liew. Meshfree and Particle Methods in Biomechanics: Prospects and Challenges. Arch Computat Methods Eng 26(5) (2018) DOI 10.1007/s11831-018-9283-2
- A. Khoei, M. Samimi, A. Azami. Reproducing Kernel Particle Method in Plasticity of Pressure-Sensitive Material with Reference to Powder Forming Process. Comput Mech 39(3) (2006) DOI 10.1007/s00466-005-0022-9
- Y. Gu, G. Liu. Meshless techniques for convection dominated problems. Comput Mech 38(2) (2005) DOI 10.1007/s00466-005-0736-8
- E. Ortega, E. Oñate, S. Idelsohn. An improved finite point method for tridimensional potential flows. Comput Mech 40(6) (2007) DOI 10.1007/s00466-006-0154-6
- G. Liu, X. Xu, G. Zhang, Y. Gu. An extended Galerkin weak form and a point interpolation method with continuous strain field and superconvergence using triangular mesh. Comput Mech 43(5) (2008) DOI 10.1007/s00466-008-0336-5
- B. Boroomand, M. Najjar, E. Oñate. The generalized finite point method. Comput Mech 44(2) (2009) DOI 10.1007/s00466-009-0363-x
- S. Mulay, H. Li, S. See. On the random differential quadrature (RDQ) method: consistency analysis and application in elasticity problems. Comput Mech 44(4) (2009) DOI 10.1007/s00466-009-0393-4
- C. Cyron, K. Nissen, V. Gravemeier, W. Wall. Stable meshfree methods in fluid mechanics based on Green’s functions. Comput Mech 46(2) (2009) DOI 10.1007/s00466-009-0405-4
- V. Vavourakis. A meshless local boundary integral equation method for two-dimensional steady elliptic problems. Comput Mech 44(6) (2009) DOI 10.1007/s00466-009-0409-0
- V. Pandurangan, H. Li, T. Ng. A concurrent multiscale method based on the alternating Schwarz scheme for coupling atomic and continuum scales with first-order compatibility. Comput Mech 47(1) (2010) DOI 10.1007/s00466-010-0528-7
- S. Chen, C. Wu, Y. Wang. A Hermite DRK interpolation-based collocation method for the analyses of Bernoulli–Euler beams and Kirchhoff–Love plates. Comput Mech 47(4) (2010) DOI 10.1007/s00466-010-0552-7
- Q. Liu, Y. Gu, P. Zhuang, F. Liu, Y. Nie. An implicit RBF meshless approach for time fractional diffusion equations. Comput Mech 48(1) (2011) DOI 10.1007/s00466-011-0573-x
- M. Tatari, M. Kamranian, M. Dehghan. The finite point method for the p-Laplace equation. Comput Mech 48(6) (2011) DOI 10.1007/s00466-011-0613-6
- J. Costa, C. Tiago, P. Pimenta. Meshless analysis of shear deformable shells: the linear model. Comput Mech 52(4) (2013) DOI 10.1007/s00466-013-0837-8
- H. Deng, Y. Xu, D. Chen, H. Dai, J. Wu, F. Tian. On numerical modeling of animal swimming and flight. Comput Mech 52(6) (2013) DOI 10.1007/s00466-013-0875-2
- M. Dehghan, R. Salehi. A meshfree weak-strong (MWS) form method for the unsteady magnetohydrodynamic (MHD) flow in pipe with arbitrary wall conductivity. Comput Mech 52(6) (2013) DOI 10.1007/s00466-013-0886-z
- E. Barbieri, N. Petrinic. Three-dimensional crack propagation with distance-based discontinuous kernels in meshfree methods. Comput Mech 53(2) (2013) DOI 10.1007/s00466-013-0910-3
- M. Bessa, J. Foster, T. Belytschko, W. Liu. A meshfree unification: reproducing kernel peridynamics. Comput Mech 53(6) (2014) DOI 10.1007/s00466-013-0969-x
- E. Soleimanifar, B. Boroomand, F. Mossaiby. A meshless method using local exponential basis functions with weak continuity up to a desired order. Comput Mech 53(6) (2014) DOI 10.1007/s00466-014-0979-3
- D. Wang, P. Chen. Quasi-convex reproducing kernel meshfree method. Comput Mech 54(3) (2014) DOI 10.1007/s00466-014-1022-4
- R. Sevilla, E. Barbieri. NURBS distance fields for extremely curved cracks. Comput Mech 54(6) (2014) DOI 10.1007/s00466-014-1067-4
- J. Olliff, B. Alford, D. Simkins. Efficient searching in meshfree methods. Comput Mech 62(6) (2018) DOI 10.1007/s00466-018-1574-9
- A. Mahdavi, S. Chi, H. Zhu. A gradient reproducing kernel collocation method for high order differential equations. Comput Mech 64(5) (2019) DOI 10.1007/s00466-019-01724-0
- L. Gavete, J. Benito, S. Falco, A. Ruiz. Implementation of essential boundary conditions in a meshless method. Commun. Numer. Meth. Engng. 16(6) (2000) DOI 10.1002/1099-0887(200006)16:6<409::aid-cnm349>3.0.co;2-z
- M. Zerroukat, K. Djidjeli, A. Charafi. Explicit and implicit meshless methods for linear advection-diffusion-type partial differential equations. Int. J. Numer. Meth. Engng. 48(1) DOI 10.1002/(sici)1097-0207(20000510)48:1<19::aid-nme862>3.0.co;2-3
- E. O�ate, F. Z�rate. Rotation-free triangular plate and shell elements. Int. J. Numer. Meth. Engng. 47(1-3) DOI 10.1002/(sici)1097-0207(20000110/30)47:1/3<557::aid-nme784>3.0.co;2-9
- R. Löhner, E. Oñate. An advancing front point generation technique. Commun. Numer. Meth. Engng. 14(12) (1998) DOI 10.1002/(sici)1099-0887(199812)14:12<1097::aid-cnm183>3.0.co;2-7
- N. Aluru. A point collocation method based on reproducing kernel approximations. Int. J. Numer. Meth. Engng. 47(6) DOI 10.1002/(sici)1097-0207(20000228)47:6<1083::aid-nme816>3.0.co;2-n
- Z. Luo, N. Zhang, W. Gao, H. Ma. Structural shape and topology optimization using a meshless Galerkin level set method. Int. J. Numer. Meth. Engng 90(3) (2011) DOI 10.1002/nme.3325
- R. Löhner, C. Sacco, E. Oñate, S. Idelsohn. A finite point method for compressible flow. Int. J. Numer. Meth. Engng. 53(8) (2001) DOI 10.1002/nme.334
- T. Ng, H. Li, J. Cheng, K. Lam, Y. Yew. A novel true meshless numerical technique (hM-DOR method) for the deformation control of circular plates integrated with piezoelectric sensors/actuators. Smart Mater. Struct. 12(6) (2003) DOI 10.1088/0964-1726/12/6/013
- X. Pan, H. Yuan. Applications of meshless methods for damage computations with finite strains. Modelling Simul. Mater. Sci. Eng. 17(4) (2009) DOI 10.1088/0965-0393/17/4/045005
- A. Asadpour. Thermo-elastic extended meshfree method for fracture without crack tip enrichment. Front. Struct. Civ. Eng. 9(4) (2015) DOI 10.1007/s11709-015-0319-5
- H. Abdessalam, B. Abbès, Y. Li, Y. Guo, E. Kwassi, J. Romain. Parameter Identification by Inverse Analysis Coupled with a Finite Pointset Method for Polyurethane Foam Expansion. KEM 611-612 (2014) DOI 10.4028/www.scientific.net/kem.611-612.868
- A. Arefmanesh, M. Nikfar. Analysis of natural convection in a nanofluid-filled triangular enclosure induced by cold and hot sources on the walls using stabilised MLPG method. Can. J. Chem. Eng. 91(10) (2013) DOI 10.1002/cjce.21790
- F. Zhang, X. Zhang, Y. Liu. An augmented incompressible material point method for modeling liquid sloshing problems. Int J Mech Mater Des 14(1) (2017) DOI 10.1007/s10999-017-9366-5
- J. Song, Y. Fu, T. Kim, Y. Yoon, J. Michopoulos, T. Rabczuk. Phase field simulations of coupled microstructure solidification problems via the strong form particle difference method. Int J Mech Mater Des 14(4) (2017) DOI 10.1007/s10999-017-9386-1
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