Discrete differential operators on irregular nodes (DDIN)

A previous research made an integral mathematical contribution for obtaining local function interpolation using neighboring nodal values of the solution function. Subsequent researchers developed mesh‐free methods for Finite Element Method (FEM). This principle can also be used to obtain discrete di...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2011-12, Vol.88 (12), p.1323-1343
Main Author: Isshiki, H.
Format: Article
Language:English
Subjects:
Differential equations
discrete differential operator
Exact sciences and technology
Finite difference method
Finite element method
Interpolation
irregular nodes
local function interpolation
Mathematical analysis
Mathematical models
Mathematics
mesh-free method
Methods of scientific computing (including symbolic computation, algebraic computation)
MPS
Numerical analysis. Scientific computation
Operators
RCM
Sciences and techniques of general use
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Summary:A previous research made an integral mathematical contribution for obtaining local function interpolation using neighboring nodal values of the solution function. Subsequent researchers developed mesh‐free methods for Finite Element Method (FEM). This principle can also be used to obtain discrete differential operators on irregular nodes. They may be successfully applied to Finite Difference method, Moving Particle Semi‐implicit (MPS) method and Random Collocation Method (RCM). In this paper, we obtain discrete differential operators on irregular nodes and successfully apply them to solve differential equations using the RCM. We also discuss mathematical aspects of the MPS method. Copyright © 2011 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
1097-0207
DOI:10.1002/nme.3225