On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three-dimensional wave equations

2015 ◽  
Vol 105 (2) ◽  
pp. 83-110 ◽  
Author(s):  
Elyas Shivanian
Keyword(s):  
Convergence Analysis ◽  
Wave Equations ◽  
Three Dimensional ◽  
Radial Point Interpolation ◽  
Point Interpolation ◽  
Dimensional Wave ◽  
Analysis Stability

MESHFREE ELASTODYNAMIC ANALYSIS OF THREE-DIMENSIONAL SOLIDS USING RADIAL POINT INTERPOLATION METHOD

2011 ◽  
Vol 02 (01) ◽  
pp. 83-95 ◽  
Author(s):  
KYOKO HASEGAWA ◽  
SUSUMU NAKATA ◽  
SATOSHI TANAKA
Keyword(s):  
Stiffness Matrix ◽  
Interpolation Method ◽  
Three Dimensional ◽  
Time Dependent ◽  
Partial Differential ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Matrix Construction

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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