An improved pseudospectral meshless radial point interpolation (PSMRPI) method for 3D wave equation with variable coefficients

2018 ◽  
Vol 35 (4) ◽  
pp. 1159-1171 ◽  
Author(s):  
Elyas Shivanian ◽  
Malihe Shaban
Keyword(s):  
Wave Equation ◽  
Variable Coefficients ◽  
Radial Point Interpolation ◽  
Point Interpolation

scholarly journals PERFORMANCE OF RADIAL POINT INTERPOLATION METHOD IN SOLVING KINEMATIC WAVE EQUATION FOR HYDROLOGIC MODELLING

2020 ◽  
Vol 82 (3) ◽  
Author(s):  
H. Hirol ◽  
M. A. Mohd Noor ◽  
M. Z. Abd Jamil ◽  
M. H. Mokhtaram ◽  
E. H. Kasiman ◽  
...  
Keyword(s):  
Wave Equation ◽  
Interpolation Method ◽  
Kinematic Wave ◽  
Weighted Residual Method ◽  
Time Step ◽  
Radial Point Interpolation Method ◽  
Kinematic Wave Equation ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

This paper presents the solution of the kinematic wave equation using a meshless radial point interpolation method (RPIM). The partial differential equation is discretized using a Galerkin weighted residual method employing RPIM shape functions. A forward difference scheme is used for temporal discretization, while the direct substitution method is employed to solve the nonlinear system at each time step. The formulation is validated against solutions from conventional numerical techniques and physical observation. In all cases, excellent agreements are achieved and hence the validation of the proposed formulation. Optimum values of the multi-quadrics shape parameters were then determined before the assessment of the performance of the method. Based on the convergence rate, it has been shown that the proposed method performs better than the finite difference method and equivalent to the finite element method. This highlights the potential of RPIM as an alternative method for hydrologic modeling.

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.

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