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Journal articles on the topic 'Radical point interpolation method'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Shivanian, Elyas. "Pseudospectral Meshless Radial Point Hermit Interpolation Versus Pseudospectral Meshless Radial Point Interpolation." International Journal of Computational Methods 17, no. 07 (May 7, 2019): 1950023. http://dx.doi.org/10.1142/s0219876219500233.

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This paper develops pseudospectral meshless radial point Hermit interpolation (PSMRPHI) and pseudospectral meshless radial point interpolation (PSMRPI) in order to apply to the elliptic partial differential equations (PDEs) held on irregular domains subject to impedance (convective) boundary conditions. Elliptic PDEs in simplest form, i.e., Laplace equation or Poisson equation, play key role in almost all kinds of PDEs. On the other hand, impedance boundary conditions, from their application in electromagnetic problems, or convective boundary conditions, from their application in heat transfer problems, are nearly more complicated forms of the boundary conditions in boundary value problems (BVPs). Based on this problem, we aim also to compare PSMRPHI and PSMRPI which belong to more influence type of meshless methods. PSMRPI method is based on a combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as basis functions in the frame of PSMRPI and PSMRPHI methods. While the latter one has been rarely used in applications, we observe that is more accurate and reliable than PSMRPI method.

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2

Zhang, G. Y., Y. Li, X. X. Gao, D. Hui, S. Q. Wang, and Z. Zong. "Smoothed Point Interpolation Method for Elastoplastic Analysis." International Journal of Computational Methods 12, no. 04 (August 2015): 1540013. http://dx.doi.org/10.1142/s0219876215400137.

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This work formulates the node-based smoothed radial point interpolation method (NS-RPIM), a typical model of smoothed point interpolation method, for the elastoplastic analysis of two-dimensional solids with gradient-dependent plasticity. The NS-RPIM uses radial point interpolation shape functions for field approximation and node-based gradient smoothing for strain field construction. The formulation is based on the parametric variational principle (PVP) in the form of complementarity with the gradient-dependent plasticity being represented by means of the linearization of the yield criterion and the flow rule. Numerical study results have demonstrated the accuracy and stability of the proposed approach for elastoplastic analysis.

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3

Ramalho, Luís D. C., Jorge Belinha, and Raul D. S. G. Campilho. "Fracture propagation using the radial point interpolation method." Fatigue & Fracture of Engineering Materials & Structures 43, no. 1 (July 15, 2019): 77–91. http://dx.doi.org/10.1111/ffe.13046.

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4

SOARES, DELFIM, ANNE SCHÖNEWALD, and OTTO VON ESTORFF. "AN EFFICIENT SMOOTHED POINT INTERPOLATION METHOD FOR DYNAMIC ANALYSES." International Journal of Computational Methods 10, no. 01 (February 2013): 1340007. http://dx.doi.org/10.1142/s0219876213400070.

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In this work, a new procedure to compute the mass matrix in the smoothed point interpolation method is discussed. Therefore, the smoothed subdomains are employed to evaluate the mass matrix, which have already been computed for the construction of the stiffness matrix, rendering a more efficient methodology. The procedure is discussed, taking into account the edge-based, cell-based, and node-based smoothed point interpolation methods, as well as different T-schemes for the construction of the support domain of the approximating shape function, which is here formulated based on the radial point interpolation method. Numerical results of different dynamic analyses are presented, illustrating the potentialities of the proposed methodology.

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5

Zhai, Wei Gang, Xing Hui Cai, Jiang Ren Lu, and Xin Li Sun. "A Local Radial Point Interpolation Method for Two-Dimensional Schrödinger Equation." Applied Mechanics and Materials 268-270 (December 2012): 1888–93. http://dx.doi.org/10.4028/www.scientific.net/amm.268-270.1888.

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A local radial point interpolation method is employed to the simulation of the time dependent Schrödinger equation with arbitrary potential function. Local weak form of the time dependent Schrödinger equation is obtained and radial point interpolation shape functions are applied in the space discretization. Computations are carried out for an example of time dependent Schrödinger equation having analytical solutions. Numerical results agreed with analytical solutions very well.

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6

Hamrani, Abderrachid, Idir Belaidi, Eric Monteiro, and Philippe Lorong. "On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method." Advances in Applied Mathematics and Mechanics 9, no. 1 (October 11, 2016): 43–72. http://dx.doi.org/10.4208/aamm.2015.m1115.

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AbstractIn order to overcome the possible singularity associated with the Point Interpolation Method (PIM), the Radial Point Interpolation Method (RPIM) was proposed by G. R. Liu. Radial basis functions (RBF) was used in RPIM as basis functions for interpolation. All these radial basis functions include shape parameters. The choice of these shape parameters has been and stays a problematic theme in RBF approximation and interpolation theory. The object of this study is to contribute to the analysis of how these shape parameters affect the accuracy of the radial PIM. The RPIM is studied based on the global Galerkin weak form performed using two integration technics: classical Gaussian integration and the strain smoothing integration scheme. The numerical performance of this method is tested on their behavior on curve fitting, and on three elastic mechanical problems with regular or irregular nodes distributions. A range of recommended shape parameters is obtained from the analysis of different error indexes and also the condition number of the matrix system. All resulting RPIM methods perform very well in term of numerical computation. The Smoothed Radial Point Interpolation Method (SRPIM) shows a higher accuracy, especially in a situation of distorted node scheme.

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7

Shivanian, Elyas. "Formulation of pseudospectral meshless radial point Hermit interpolation for the Motz problem and comparison to pseudospectral meshless radial point interpolation." Multidiscipline Modeling in Materials and Structures 16, no. 1 (August 26, 2019): 1–20. http://dx.doi.org/10.1108/mmms-04-2019-0084.

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Purpose The purpose of this paper is to develop pseudospectral meshless radial point Hermit interpolation (PSMRPHI) for applying to the Motz problem. Design/methodology/approach The author aims to propose a kind of PSMRPHI method. Findings Based on the Motz problem, the author aims also to compare PSMRPHI and PSMRPI which belong to more influence type of meshless methods. Originality/value Although the PSMRPHI method has been infrequently used in applications, the author proves it is more accurate and trustworthy than the PSMRPI method.

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8

LIU, G. R., and G. Y. ZHANG. "EDGE-BASED SMOOTHED POINT INTERPOLATION METHODS." International Journal of Computational Methods 05, no. 04 (December 2008): 621–46. http://dx.doi.org/10.1142/s0219876208001662.

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This paper formulates an edge-based smoothed point interpolation method (ES-PIM) for solid mechanics using three-node triangular meshes. In the ES-PIM, displacement fields are construed using the point interpolation method (polynomial PIM or radial PIM), and hence the shape functions possess the Kronecker delta property, facilitates the enforcement of Dirichlet boundary conditions. Strains are obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations and the formation is weakened weak formulation. Four schemes of selecting nodes for interpolation using the PIM have been introduced in detail and ES-PIM models using these four schemes have been developed. Numerical studies have demonstrated that the ES-PIM possesses the following good properties: (1) the ES-PIM models have a close-to-exact stiffness, which is much softer than for the overly-stiff FEM model and much stiffer than for the overly-soft node-based smoothed point interpolation method (NS-PIM) model; (2) results of ES-PIMs are generally of superconvergence and "ultra-accurate"; (3) no additional degrees of freedom are introduced, the implementation of the method is straightforward, and the method can achieve much better efficiency than the FEM using the same set of triangular meshes.

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9

STADLER, DOMEN, DAMJAN ČELIČ, ANDREJ LIPEJ, and FRANC KOSEL. "MODIFIED CHOLESKY DECOMPOSITION FOR SOLVING THE MOMENT MATRIX IN THE RADIAL POINT INTERPOLATION METHOD." International Journal of Computational Methods 11, no. 06 (December 2014): 1350088. http://dx.doi.org/10.1142/s0219876213500886.

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The radial point interpolation method is frequently employed in numerical computations. It can be used to interpolate scattered data, as shape functions in meshless methods and mesh deformation scheme, etc. The main problem in calculating the radial point interpolation is solving the moment matrix of the interpolation scheme, which is usually done with LU decomposition. A new decomposition technique based on the Cholesky decomposition is introduced in this paper. A comparison of the error, the consumed time and the results between the new decomposition technique and the LU method is presented for two different numerical methods.

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10

Zhou, Liming, Bin Nie, Chuanxin Ren, Shuhui Ren, and Guangwei Meng. "Dynamic analysis of magneto-electro-elastic nanostructures using node-based smoothed radial point interpolation method combined with micromechanics-based asymptotic homogenization technique." Journal of Intelligent Material Systems and Structures 31, no. 20 (August 10, 2020): 2342–61. http://dx.doi.org/10.1177/1045389x20935572.

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The node-based smoothed radial point interpolation method combined with the asymptotic homogenization method was proposed, as an addition to the finite element method, to address the static and dynamic reactions of magneto-electro-elastic coupling micromechanical problems. First, several basic equations for relevant problems were derived. Second, asymptotic homogenization method was utilized to determine the material properties of magneto-electro-elastic nanomaterials. Third, node-based smoothed radial point interpolation method was applied to obtain the discrete equations of magneto-electro-elastic nanostructures. Then, the Newmark method was introduced to solve the response of microcosmic problems. Finally, several numerical examples were calculated to prove the accuracy, convergence, and reliability of node-based smoothed radial point interpolation method by comparing the results of node-based smoothed radial point interpolation method with those of finite element method.

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11

Dinis, L. M. J. S., R. M. Natal Jorge, and J. Belinha. "The natural neighbour radial point interpolation method: dynamic applications." Engineering Computations 26, no. 8 (November 13, 2009): 911–49. http://dx.doi.org/10.1108/02644400910996835.

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12

HASEGAWA, KYOKO, SUSUMU NAKATA, and SATOSHI TANAKA. "MESHFREE ELASTODYNAMIC ANALYSIS OF THREE-DIMENSIONAL SOLIDS USING RADIAL POINT INTERPOLATION METHOD." International Journal of Modeling, Simulation, and Scientific Computing 02, no. 01 (March 2011): 83–95. http://dx.doi.org/10.1142/s1793962311000372.

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Meshfree methods are effective tools for solving partial differential equations. The radial point interpolation method, a partial differential equation solver based on a meshfree approach, enables accurate imposition of displacement boundary conditions and has been successfully applied to elastostatic analysis of various kinds of three-dimensional solids. In this method, stiffness matrix construction accounts for the majority of CPU time required for the entire process, resulting in high computational costs, especially when higher-order numerical integration is applied for accurate matrix construction. An alternative method, modified radial point interpolation, was proposed to overcome this shortcoming and has accomplished fast computation of elastostatic solid analysis. The purpose of this study is to develop an algorithm for time-dependent simulation of three-dimensional elastic solids. We show that the modified radial point interpolation method also accelerates the construction of the mass matrix required for time-dependent analysis in addition to that of the stiffness matrix. In our approach, the problem domain is assumed to have an implicit function representation that can be constructed from a set of surface points measured using a three-dimensional scanning system. Several numerical tests for elastodynamic analysis of complex shape models are presented.

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13

Lu, Fuqiang, Fengyuan Zhang, Tian Wang, Guozhong Tian, and Feng Wu. "High-Order Semi-Lagrangian Schemes for the Transport Equation on Icosahedron Spherical Grids." Atmosphere 13, no. 11 (October 31, 2022): 1807. http://dx.doi.org/10.3390/atmos13111807.

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The transport process is an important part of the research of fluid dynamics, especially when it comes to tracer advection in the atmosphere or ocean dynamics. In this paper, a series of high-order semi-Lagrangian methods for the transport process on the sphere are considered. The methods are formulated entirely in three-dimensional Cartesian coordinates, thus avoiding any apparent artificial singularities associated with surface-based coordinate systems. The underlying idea of the semi-Lagrangian method is to find the value of the field/tracer at the departure point through interpolating the values of its surrounding grid points to the departure point. The implementation of the semi-Lagrangian method is divided into the following two main procedures: finding the departure point by integrating the characteristic equation backward and then interpolate on the departure point. In the first procedure, three methods are utilized to solve the characteristic equation for the locations of departure points, including the commonly used midpoint-rule method and two explicit high-order Runge–Kutta (RK) methods. In the second one, for interpolation, four new methods are presented, including 1) linear interpolation; 2) polynomial fitting based on the least square method; 3) global radial basis function stencils (RBFs), and 4) local RBFs. For the latter two interpolation methods, we find that it is crucial to select an optimal value for the shape parameter of the basis function. A Gauss hill advection case is used to compare and contrast the methods in terms of their accuracy, and conservation properties. In addition, the proposed method is applied to standard test cases, which include solid body rotation, shear deformation of twin slotted cylinders, and the evolution of a moving vortex. It demonstrates that the proposed method could simulate all test cases with reasonable accuracy and efficiency.

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14

Tootoonchi, Arash, Arman Khoshghalb, and Nasser Khalili. "Meshfree Method Analysis of Biot's Consolidation Using Cell-Based Smoothed Point Interpolation Method." Applied Mechanics and Materials 846 (July 2016): 409–14. http://dx.doi.org/10.4028/www.scientific.net/amm.846.409.

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A set of cell-based smoothed point interpolation methods are proposed for the numerical analysis of Biot’s formulation. In the proposed methods, the problem domain is discretized using a triangular background mesh. Shape functions are constructed using either polynomial or radial point interpolation method (PIM), leading to the delta function property of shape functions and consequently, easy implementation of essential boundary conditions. The Biot’s equations are discretised in space and time. A variety of support domain selection schemes (T-schemes) are investigated. The accuracy and convergence rate of the proposed methods are examined by comparing the numerical results with the analytical solution for the benchmark problem of one dimensional consolidation.

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15

Tan, J. Y., L. H. Liu, and B. X. Li. "Least-Squares Radial Point Interpolation Collocation Meshless Method for Radiative Heat Transfer." Journal of Heat Transfer 129, no. 5 (June 30, 2006): 669–73. http://dx.doi.org/10.1115/1.2712861.

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A least-squares radial point interpolation collocation meshless method based on the discrete ordinates equation is developed for solving the radiative transfer in absorbing, emitting, and scattering media, in which compact support radial basis functions augmented with polynomial basis are employed to construct the trial functions. In addition to the collocation nodes, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three typical examples of radiative transfer in semitransparent media are examined to verify this new solution method. The numerical results are compared with other benchmark approximate solutions in references. By comparison, the results show that the least-squares radial point interpolation collocation meshless method has good accuracy in solving radiative transfer problems within absorbing, emitting, and scattering media.

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16

Iryanto, Syam Budi, Furqon Hensan Muttaqien, and Rifki Sadikin. "Irregular Grid Interpolation using Radial Basis Function for Large Cylindrical Volume." Jurnal Ilmu Komputer dan Informasi 13, no. 1 (March 14, 2020): 17. http://dx.doi.org/10.21609/jiki.v13i1.805.

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Irregular grid interpolation is one of the numerical functions that often used to approximate value on an arbitrary location in the area closed by non-regular grid pivot points. In this paper, we propose method for achieving efficient computation time of radial basis function-based non-regular grid interpolation on a cylindrical coordinate. Our method consist of two stages. The first stage is the computation of weights from solving linear RBF systems constructed by known pivot points. We divide the volume into many subvolumes. At second stages, interpolation on an arbitrary point could be done using weights calculated on the first stage. At first, we find the nearest point with the query point by structuring pivot points in a K-D tree structure. After that, using the closest pivot point, we could compute the interpolated value with RBF functions. We present the performance of our method based on computation time on two stages and its precision by calculating the mean square error between the interpolated values and analytic functions. Based on the performance evaluation, our method is acceptable.

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17

Al-Saif, Nahdh S. M., and Ameen Sh Ameen. "Numerical Solution of Mixed Volterra – Fredholm Integral Equation Using the Collocation Method." Baghdad Science Journal 17, no. 3 (September 1, 2020): 0849. http://dx.doi.org/10.21123/bsj.2020.17.3.0849.

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Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained from the numerical experiments in order to investigate the accuracy and the efficiency of scheme.

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18

Dong, Wen Sheng, Zheng Lei, and Xue Mei Liu. "Solution of Material Mechanics by RPIM Meshless Method." Advanced Materials Research 740 (August 2013): 211–16. http://dx.doi.org/10.4028/www.scientific.net/amr.740.211.

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With the compact support of radial point interpolation shape functions (RPIM), the stiffness matrix of system equation can be sparse, so its very suitable for meshless methods.This interpolation method have the Kronecker delta function property, so the essential boundary conditions can be enforced directly and accurately without any additional treatment. In this paper, the radial point interpolation shape function is used, calculate the shape function in different node distribution cases, analyse the compact support and Kronecker delta function,use penalty method to apply the essential boundary conditions. In this paper, the RPIM is applied to solving the deformation in one and two dimensional solids by different loads, the results demonstrated that the meshfree RPIM can effectively solve material mechanics problems.

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19

Cai, Xing Hui, Cheng Ying Shi, Peng Xu, Man Lin Zhu, and Guo Liang Wang. "A Meshfree Weak-Strong-Form Method for Magnetohydrodynamic Flow in a Pipe." Advanced Materials Research 490-495 (March 2012): 1883–87. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.1883.

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In this paper, a meshfree weak-strong form method is presented to compute the fully developed magnetohydrodynmic flow in a pipe. The radial basis function point interpolation approximation is adopted to construct the shape functions. For the nodes whose local quadrature domain is intersect with the natural boundaries, a local weak form of radial point interpolation method is applied. Otherwise, a strong form of meshfree point collocation method is employed. Numerical simulations are carried out for fully developed magnetohydrodynmic flow in a rectangular pipe with arbitrary electrical conductivity.

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20

Kiran, R., and Kalarickaparambil Joseph Vinoy. "A Stochastic Radial Point Interpolation Method for Wideband Uncertainty Analysis." IEEE Antennas and Wireless Propagation Letters 20, no. 9 (September 2021): 1755–59. http://dx.doi.org/10.1109/lawp.2021.3095913.

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21

Rokrok, B., H. Minuchehr, and A. Zolfaghari. "Application of Radial Point Interpolation Method to Neutron Diffusion field." Trends in Applied Sciences Research 7, no. 1 (January 1, 2012): 18–31. http://dx.doi.org/10.3923/tasr.2012.18.31.

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22

Imani, Sadjad, Mostafa Bolhasani, Seyed Ali Ghorashi, and Mehdi Rashid. "Waveform Design in MIMO Radar Using Radial Point Interpolation Method." IEEE Communications Letters 22, no. 10 (October 2018): 2076–79. http://dx.doi.org/10.1109/lcomm.2018.2864302.

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23

Kazemi, Z., M. R. Hematiyan, and R. Vaghefi. "Meshfree radial point interpolation method for analysis of viscoplastic problems." Engineering Analysis with Boundary Elements 82 (September 2017): 172–84. http://dx.doi.org/10.1016/j.enganabound.2017.06.012.

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24

Schönewald, Anne, Delfim Soares, and Otto von Estorff. "A smoothed radial point interpolation method for application in porodynamics." Computational Mechanics 50, no. 4 (February 8, 2012): 433–43. http://dx.doi.org/10.1007/s00466-012-0682-1.

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25

Liu, X., G. R. Liu, K. Tai, and K. Y. Lam. "Radial point interpolation collocation method (RPICM) for partial differential equations." Computers & Mathematics with Applications 50, no. 8-9 (October 2005): 1425–42. http://dx.doi.org/10.1016/j.camwa.2005.02.019.

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26

Wang, J. G., and G. R. Liu. "A point interpolation meshless method based on radial basis functions." International Journal for Numerical Methods in Engineering 54, no. 11 (2002): 1623–48. http://dx.doi.org/10.1002/nme.489.

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27

Liu, G. R., Jian Zhang, Hua Li, K. Y. Lam, and Bernard B. T. Kee. "Radial point interpolation based finite difference method for mechanics problems." International Journal for Numerical Methods in Engineering 68, no. 7 (April 11, 2006): 728–54. http://dx.doi.org/10.1002/nme.1733.

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28

SOARES, DELFIM. "DYNAMIC ELASTOPLASTIC ANALYSES BY SMOOTHED POINT INTERPOLATION METHODS." International Journal of Computational Methods 10, no. 05 (May 2013): 1350030. http://dx.doi.org/10.1142/s0219876213500308.

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In this work, meshfree techniques based on weakened weak formulations are presented for the solution of dynamic problems considering elastoplastic materials. Nonlinear internal forces are computed taking into account edge-based, cell-based, and node-based smoothed domains. T-schemes are applied for the construction of the support domains of the approximating shape functions, which are here formulated based on the radial point interpolation method. The mass matrix is also computed considering smoothed domains and their quadrature points. For the time-domain solution of the nonlinear system of equations, the Newmark/Newton–Raphson method is adopted. Numerical results illustrate the accuracy and efficiency of the discussed methodologies.

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29

Xia, Ping, and Ke Xiang Wei. "Shear Locking Analysis of Plate Bending by Using Meshless Local Radial Point Interpolation Method." Applied Mechanics and Materials 166-169 (May 2012): 2867–70. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.2867.

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The shape function of the meshless local radial point interpolation method is constructed by using the radial basis functions and possesses Kronecker delta function properties. Therefore, the essential boundary conditions can be easily imposed. Causation of shear locking occur in plate bending is analyzed. Bending problems for plate with two sides simply supported, the other two sides clamped boundary conditions, are analyzed by the meshless local radial point interpolation method. The shear locking is easier avoided in the meshless method than in the finite element method, and the measure of avoiding the shear locking are presented.

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30

Yan, Fei, Xiating Feng, and Hui Zhou. "A dual reciprocity hybrid radial boundary node method based on radial point interpolation method." Computational Mechanics 45, no. 6 (February 4, 2010): 541–52. http://dx.doi.org/10.1007/s00466-010-0469-1.

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LIU, G. R., Y. LI, K. Y. DAI, M. T. LUAN, and W. XUE. "A LINEARLY CONFORMING RADIAL POINT INTERPOLATION METHOD FOR SOLID MECHANICS PROBLEMS." International Journal of Computational Methods 03, no. 04 (December 2006): 401–28. http://dx.doi.org/10.1142/s0219876206001132.

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A linearly conforming radial point interpolation method (LC-RPIM) is presented for stress analysis of two-dimensional solids. In the LC-RPIM method, each field node is enclosed by a Voronoi polygon, and the displacement field function is approximated using RPIM shape functions of Kronecker delta function property created by simple interpolation using local nodes and radial basis functions augmented with linear polynomials to guarantee linear consistency. The system equations are then derived using the Galerkin weak form and nodal integration techniques, and the essential boundary conditions are imposed directly as in the finite element method. The LC-RPIM method is verified via various numerical examples and an extensive comparison study is conducted with the conventional RPIM, analytical approach and FEM. It is found that the presented LC-RPIM is more stable, more accurate in stress and more efficient than the conventional RPIM.

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32

Li, Xiaolin, Jialin Zhu, and Shougui Zhang. "A hybrid radial boundary node method based on radial basis point interpolation." Engineering Analysis with Boundary Elements 33, no. 11 (November 2009): 1273–83. http://dx.doi.org/10.1016/j.enganabound.2009.06.003.

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33

Imanian, Hanifeh, Hamidreza Shirkhani, Abdolmajid Mohammadian, Juan Hiedra Hiedra Cobo, and Pierre Payeur. "Spatial Interpolation of Soil Temperature and Water Content in the Land-Water Interface Using Artificial Intelligence." Water 15, no. 3 (January 25, 2023): 473. http://dx.doi.org/10.3390/w15030473.

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The distributed measured data in large regions and remote locations, along with a need to estimate climatic data for point sites where no data have been recorded, has encouraged the implementation of spatial interpolation techniques. Recently, the increasing use of artificial intelligence has become a promising alternative to conventional deterministic algorithms for spatial interpolation. The present study aims to evaluate some machine learning-based algorithms against conventional strategies for interpolating soil temperature data from a region in southeast Canada with an area of 1000 km by 550 km. The radial basis function neural networks (RBFN) and the deep learning approach were used to estimate soil temperature along a railroad after the spline deterministic spatial interpolation method failed to interpolate gridded soil temperature data on the desired locations. The spline method showed weaknesses in interpolating soil temperature data in areas with sudden changes. This limitation did not improve even by increasing the spline nonlinearity. Although both radial basis function neural networks and the deep learning approach had successful performances in interpolating soil temperature data even in sharp transition areas, deep learning outperformed the former method with a normalized RMSE of 9.0% against 16.2% and an R-squared of 89.2% against 53.8%. This finding was confirmed in the same investigation on soil water content.

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34

Nguyen, Nha Thanh, Tinh Quoc Bui, and Thien Tich Truong. "Extended Radial Point Interpolation Method for crack analysis in orthotropic media." Science and Technology Development Journal 18, no. 2 (June 30, 2015): 5–13. http://dx.doi.org/10.32508/stdj.v18i2.1066.

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Orthotropic materials are particular type of anisotropic materials; In contrast with isotropic materials, their properties depend on the direction in which they are measured. Orthotropic composite materials and their structures have been extensively used in a wide range of engineering applications. Studies on their physical behaviors under in-work loading conditions are essential. In this present, we apply an extended meshfree radial point interpolation method (XRPIM) for analyzing crack behaviour in 2D orthotropic materials models. The thin plate spline (TPS) radial basis function (RBF) is used for constructing the RPIM shape functions. Typical advantages of using RBF are the satisfaction of the Kronecker’s delta property and the high-order continuity. To calculate the stress intensity factors (SIFs), Interaction integral method with orthotropic auxiliary fields are used. Numerical examples are performed to show the accuracy of the approach; the results are compared with available refered results. Our numerical experiments have shown a very good performance of the present method.

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35

Belinha, Jorge, and Miguel Aires. "Elastoplastic Analysis of Plates with Radial Point Interpolation Meshless Methods." Applied Sciences 12, no. 24 (December 14, 2022): 12842. http://dx.doi.org/10.3390/app122412842.

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For both linear and nonlinear analysis, finite element method (FEM) software packages, whether commercial or in-house, have contributed significantly to ease the analysis of simple and complex structures with various working conditions. However, the literature offers other discretization techniques equally accurate, which show a higher meshing flexibility, such as meshless methods. Thus, in this work, the radial point interpolation meshless method (RPIM) is used to obtain the required variable fields for a nonlinear elastostatic analysis. This work focuses its attention on the nonlinear analysis of two benchmark plate-bending problems. The plate is analysed as a 3D solid and, in order to obtain the nonlinear solution, modified versions of the Newton–Raphson method are revisited and applied. The material elastoplastic behaviour is predicted assuming the von Mises yield surface and isotropic hardening. The nonlinear algorithm is discussed in detail. The analysis of the two benchmark plate examples allows us to understand that the RPIM version explored is accurate and allows to achieve smooth variable fields, being a solid alternative to FEM.

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Sánchez-Arce, I. J., L. D. C. Ramalho, D. C. Gonçalves, R. D. S. G. Campilho, and J. Belinha. "Hyperelasticity and the radial point interpolation method via the Ogden model." Engineering Analysis with Boundary Elements 145 (December 2022): 25–33. http://dx.doi.org/10.1016/j.enganabound.2022.08.035.

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Afsari, Arman. "Mixed basis function for radial point interpolation meshless method in electromagnetics." Journal of Electromagnetic Waves and Applications 29, no. 6 (April 2015): 786–97. http://dx.doi.org/10.1080/09205071.2015.1024336.

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Yang, Shunchuan, Zhizhang Chen, Yiqiang Yu, and Sergey Ponomarenko. "On the Numerical Dispersion of the Radial Point Interpolation Meshless Method." IEEE Microwave and Wireless Components Letters 24, no. 10 (October 2014): 653–55. http://dx.doi.org/10.1109/lmwc.2014.2340696.

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Chen, Xiaojie, Zhizhang Chen, Yiqiang Yu, and Donglin Su. "An Unconditionally Stable Radial Point Interpolation Meshless Method With Laguerre Polynomials." IEEE Transactions on Antennas and Propagation 59, no. 10 (October 2011): 3756–63. http://dx.doi.org/10.1109/tap.2011.2163769.

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Wang, J. G., Bingyin Zhang, and T. Nogami. "Wave-induced seabed response analysis by radial point interpolation meshless method." Ocean Engineering 31, no. 1 (January 2004): 21–42. http://dx.doi.org/10.1016/s0029-8018(03)00112-4.

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You, Xiangyu, Qiang Gui, Qifan Zhang, Yingbin Chai, and Wei Li. "Meshfree simulations of acoustic problems by a radial point interpolation method." Ocean Engineering 218 (December 2020): 108202. http://dx.doi.org/10.1016/j.oceaneng.2020.108202.

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Wang, J. G., G. R. Liu, and P. Lin. "Numerical analysis of Biot's consolidation process by radial point interpolation method." International Journal of Solids and Structures 39, no. 6 (March 2002): 1557–73. http://dx.doi.org/10.1016/s0020-7683(02)00005-7.

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Qian, Xiaoxiang, Huina Yuan, Mozhen Zhou, and Bingyin Zhang. "A general 3D contact smoothing method based on radial point interpolation." Journal of Computational and Applied Mathematics 257 (February 2014): 1–13. http://dx.doi.org/10.1016/j.cam.2013.08.014.

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Azevedo, J. M. C., J. Belinha, L. M. J. S. Dinis, and R. M. Natal Jorge. "Crack path prediction using the natural neighbour radial point interpolation method." Engineering Analysis with Boundary Elements 59 (October 2015): 144–58. http://dx.doi.org/10.1016/j.enganabound.2015.06.001.

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Nakata, Susumu, Yu Takeda, Norihisa Fujita, and Soichiro Ikuno. "Parallel Algorithm for Meshfree Radial Point Interpolation Method on Graphics Hardware." IEEE Transactions on Magnetics 47, no. 5 (May 2011): 1206–9. http://dx.doi.org/10.1109/tmag.2010.2091110.

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Dehghan, Mehdi, and Mina Haghjoo-Saniji. "The local radial point interpolation meshless method for solving Maxwell equations." Engineering with Computers 33, no. 4 (March 25, 2017): 897–918. http://dx.doi.org/10.1007/s00366-017-0505-2.

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Liu, G. R., G. Y. Zhang, Y. T. Gu, and Y. Y. Wang. "A meshfree radial point interpolation method (RPIM) for three-dimensional solids." Computational Mechanics 36, no. 6 (August 10, 2005): 421–30. http://dx.doi.org/10.1007/s00466-005-0657-6.

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Zhao, X., G. R. Liu, K. Y. Dai, Z. H. Zhong, G. Y. Li, and X. Han. "A linearly conforming radial point interpolation method (LC-RPIM) for shells." Computational Mechanics 43, no. 3 (July 4, 2008): 403–13. http://dx.doi.org/10.1007/s00466-008-0313-z.

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Afsari, Arman, Akram Chehrazi, and Masoud Movahhedi. "Toward a computational multiresolution analysis for radial point interpolation meshless method." International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 28, no. 1 (March 10, 2014): 1–20. http://dx.doi.org/10.1002/jnm.1977.

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Cui, Xiangyang, Guirong Liu, and Guangyao Li. "A smoothed Hermite radial point interpolation method for thin plate analysis." Archive of Applied Mechanics 81, no. 1 (November 4, 2009): 1–18. http://dx.doi.org/10.1007/s00419-009-0392-0.

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