Hermite-Lagrange Two-Point Interpolation Via Peano Kernels

1989 ◽  
Vol 16 (3-4) ◽  
pp. 253-260
Author(s):  
Burkhard Lenze ◽  
Franz Locher
Keyword(s):  
Point Interpolation ◽  
Peano Kernels

A cell-based smoothed point interpolation method (CS-PIM) for 2D thermoelastic problems

2017 ◽  
Vol 27 (6) ◽  
pp. 1249-1265 ◽  
Author(s):  
Yijun Liu ◽  
Guiyong Zhang ◽  
Huan Lu ◽  
Zhi Zong
Keyword(s):  
Thermal Stresses ◽  
Interpolation Method ◽  
Content Type ◽  
Novel Approach ◽  
Convergence Results ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Thermoelastic Problems ◽  
Gradient Smoothing ◽  
Practical Implications

Purpose Due to the strong reliance on element quality, there exist some inherent shortcomings of the traditional finite element method (FEM). The model of FEM behaves overly stiff, and the solutions of automated generated linear elements are generally of poor accuracy about especially gradient results. The proposed cell-based smoothed point interpolation method (CS-PIM) aims to improve the results accuracy of the thermoelastic problems via properly softening the overly-stiff stiffness. Design/methodology/approach This novel approach is based on the newly developed G space and weakened weak (w2) formulation, and of which shape functions are created using the point interpolation method and the cell-based gradient smoothing operation is conducted based on the linear triangular background cells. Findings Owing to the property of softened stiffness, the present method can generally achieve better accuracy and higher convergence results (especially for the temperature gradient and thermal stress solutions) than the FEM does by using the simplest linear triangular background cells, which has been examined by extensive numerical studies. Practical implications The CS-PIM is capable of producing more accurate results of temperature gradients as well as thermal stresses with the automated generated and unstructured background cells, which make it a better candidate for solving practical thermoelastic problems. Originality/value It is the first time that the novel CS-PIM was further developed for solving thermoelastic problems, which shows its tremendous potential for practical implications.

A point interpolation algorithm resulting from weighted linear regression

2021 ◽  
Vol 50 ◽  
pp. 101304
Author(s):  
Leonardo Ramos Emmendorfer ◽  
Graçaliz Pereira Dimuro
Keyword(s):  
Linear Regression ◽  
Interpolation Algorithm ◽  
Weighted Linear Regression ◽  
Point Interpolation

scholarly journals Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2288
Author(s):  
Hongming Luo ◽  
Guanhua Sun
Keyword(s):  
Structural Dynamics ◽  
Interpolation Method ◽  
Mass Matrix ◽  
Time Integration ◽  
Partition Of Unity ◽  
Implicit Time ◽  
Lumped Mass ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Consistent Mass Matrix

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

scholarly journals An Effective Interface Tracking Method for Simulating the Extrudate Swell Phenomenon

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1305
Author(s):  
Ahmad Fakhari ◽  
Željko Tukovic ◽  
Olga Sousa Carneiro ◽  
Célio Fernandes
Keyword(s):  
Interpolation Method ◽  
Polymer Processing ◽  
Free Surface Flows ◽  
Interface Tracking ◽  
Extrudate Swell ◽  
Support Design ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Flowing Material ◽  
Processing Techniques

The extrudate swell, i.e., the geometrical modifications that take place when the flowing material leaves the confined flow inside a channel and moves freely without the restrictions that are promoted by the walls, is a relevant phenomenon in several polymer processing techniques. For instance, in profile extrusion, the extrudate cross-section is subjected to a number of distortions that are motivated by the swell, which are very difficult to anticipate, especially for complex geometries. As happens in many industrial processes, numerical modelling might provide useful information to support design tasks, i.e., to allow for identifying the best strategy to compensate the changes promoted by the extrudate swell. This study reports the development of an improved interface tracking algorithm that employs the least-squares volume-to-point interpolation method for the grid movement. The formulation is enriched further with the consistent second-order time-accurate non-iterative Pressure-Implicit with Splitting of Operators (PISO) algorithm, which allows for efficiently simulating free-surface flows. The accuracy and robustness of the proposed solver is illustrated through the simulation of the steady planar and asymmetric extrudate swell flows of Newtonian fluids. The role of inertia on the extrudate swell is studied, and the results that are obtained with the newly improved solver show good agreement with reference data that are found in the scientific literature.

scholarly journals Comparison and Evaluation of Different Pit-Filling Methods for Generating High Resolution Canopy Height Model Using UAV Laser Scanning Data

2021 ◽  
Vol 13 (12) ◽  
pp. 2239
Author(s):  
Ying Quan ◽  
Mingze Li ◽  
Yuanshuo Hao ◽  
Bin Wang
Keyword(s):  
High Resolution ◽  
Laser Scanning ◽  
Evaluation Framework ◽  
Canopy Height ◽  
Filter Method ◽  
Individual Tree ◽  
Significant Difference ◽  
Point Interpolation ◽  
Canopy Height Model ◽  
Height Model

As a common form of light detection and ranging (LiDAR) in forestry applications, the canopy height model (CHM) provides the elevation distribution of aboveground vegetation. A CHM is traditionally generated by interpolating all the first LiDAR echoes. However, the first echo cannot accurately represent the canopy surface, and the resulting large amount of noise (data pits) also reduce the CHM quality. Although previous studies concentrate on many pit-filling methods, the applicability of these methods in high-resolution unmanned aerial vehicle laser scanning (UAVLS)-derived CHMs has not been revealed. This study selected eight widely used, recently developed, representative pit-filling methods, namely first-echo interpolation, smooth filtering (mean, medium and Gaussian), highest point interpolation, pit-free algorithm, spike-free algorithm and graph-based progressive morphological filtering (GPMF). A comprehensive evaluation framework was implemented, including a quantitative evaluation using simulation data and an additional application evaluation using UAVLS data. The results indicated that the spike-free algorithm and GPMF had excellent visual performances and were closest to the real canopy surface (root mean square error (RMSE) of simulated data were 0.1578 m and 0.1093 m, respectively; RMSE of UAVLS data were 0.3179 m and 0.4379 m, respectively). Compared with the first-echo method, the accuracies of the spike-free algorithm and GPMF improved by approximately 23% and 22%, respectively. The pit-free algorithm and highest point interpolation method also have advantages in high-resolution CHM generation. The global smooth filter method based on the first-echo CHM reduced the average canopy height by approximately 7.73%. Coniferous forests require more pit-filling than broad-leaved forests and mixed forests. Although the results of individual tree applications indicated that there was no significant difference between these methods except the median filter method, pit-filling is still of great significance for generating high-resolution CHMs. This study provides guidance for using high-resolution UAVLS in forestry applications.

Radial point interpolation collocation method based approximation for 2D fractional equation models

2021 ◽  
Vol 97 ◽  
pp. 153-161
Author(s):  
Qingxia Liu ◽  
Pinghui Zhuang ◽  
Fawang Liu ◽  
Minling Zheng ◽  
Shanzhen Chen
Keyword(s):  
Collocation Method ◽  
Radial Point Interpolation ◽  
Point Interpolation ◽  
Fractional Equation

Simulation of the viscoplastic extrusion process using the radial point interpolation meshless method

2021 ◽  
pp. 146442072098858
Author(s):  
ROSS Costa ◽  
J Belinha ◽  
RM Natal Jorge ◽  
DES Rodrigues
Keyword(s):  
Meshless Method ◽  
Fused Deposition Modeling ◽  
Interpolation Method ◽  
Extrusion Process ◽  
Fused Deposition ◽  
Radial Point Interpolation ◽  
Large Growth ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Deposition Modeling

Additive manufacturing is an emergent technology, which witnessed a large growth demanded by the consumer market. Despite this growth, the technology needs scientific regulation and guidelines to be reliable and consistent to the point that is feasible to be used as a source of manufactured end-products. One of the processes that has seen the most significant development is the fused deposition modeling, more commonly known as 3D printing. The motivation to better understand this process makes the study of extrusion of materials important. In this work, the radial point interpolation method, a meshless method, is applied to the study of extrusion of viscoplastic materials, using the formulation originally intended for the finite element method, the flow formulation. This formulation is based on the reasoning that solid materials under those conditions behave like non-Newtonian fluids. The time stepped analysis follows the Lagrangian approach taking advantage of the easy remeshing inherent to meshless methods. To validate the newly developed numerical tool, tests are conducted with numerical examples obtained from the literature for the extrusion of aluminum, which is a more common problem. Thus, after the performed validation, the algorithm can easily be adapted to simulate the extrusion of polymers in fused deposition modeling processes.

MESHFREE CELL-BASED SMOOTHED POINT INTERPOLATION METHOD USING ISOPARAMETRIC PIM SHAPE FUNCTIONS AND CONDENSED RPIM SHAPE FUNCTIONS

2011 ◽  
Vol 08 (04) ◽  
pp. 705-730 ◽  
Author(s):  
G. Y. ZHANG ◽  
G. R. LIU
Keyword(s):  
Computational Efficiency ◽  
Interpolation Method ◽  
Shape Functions ◽  
Generalized Gradient ◽  
Singularity Problem ◽  
Numerical Examples ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
System Equations ◽  
Gradient Smoothing

This paper presents two novel and effective cell-based smoothed point interpolation methods (CS-PIM) using isoparametric PIM (PIM-Iso) shape functions and condensed radial PIM (RPIM-Cd) shape functions respectively. These two types of PIM shape functions can successfully overcome the singularity problem occurred in the process of creating PIM shape functions and make the constructed CS-PIM models work well with the three-node triangular meshes. Smoothed strains are obtained by performing the generalized gradient smoothing operation over each triangular background cells, because the nodal PIM shape functions can be discontinuous. The generalized smoothed Galerkin (GS-Galerkin) weakform is used to create the discretized system equations. Some numerical examples are studied to examine various properties of the present methods in terms of accuracy, convergence, and computational efficiency.

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