Interpolating wavelets

2016 ◽  
Author(s):  
Yuval Weiss ◽  
Dominique Mouliere-Reiser ◽  
Alex Malkin ◽  
Nimrod Grinberg ◽  
Anat Canning
Keyword(s):  
Interpolating Wavelets

An adaptive wavelet collocation method for the optimal heat source problem

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mahmood Khaksar-e Oshagh ◽  
Mostafa Abbaszadeh ◽  
Esmail Babolian ◽  
Hossein Pourbashash
Keyword(s):  
Heat Source ◽  
Numerical Technique ◽  
State Function ◽  
Adaptive Wavelet ◽  
Content Type ◽  
Optimal Heat ◽  
Wavelet Collocation Method ◽  
Collocation Approach ◽  
Interpolating Wavelets ◽  
Accurate Numerical Solution

Purpose This paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP). Design/methodology/approach The main aim of this paper is to present an adaptive collocation approach based on the interpolating wavelets to solve an OCP for finding optimal heat source, in a two-dimensional domain. This problem arises when the domain is heated by microwaves or by electromagnetic induction. Findings This paper shows that combination of interpolating wavelet basis and finite difference method makes an accurate structure to design adaptive algorithm for such problems which usually have non-smooth solution. Originality/value The proposed numerical technique is flexible for different OCP governed by a partial differential equation with box constraint over the control or the state function.

scholarly journals A construction of interpolating wavelets on invariant sets

1999 ◽  
Vol 68 (228) ◽  
pp. 1569-1588 ◽  
Author(s):  
Zhongying Chen ◽  
Charles A. Micchelli ◽  
Yuesheng Xu
Keyword(s):  
Invariant Sets ◽  
Interpolating Wavelets

Construction of nearly orthogonal interpolating wavelets

1999 ◽  
Vol 79 (3) ◽  
pp. 289-300 ◽  
Author(s):  
Peng-Lang Shui ◽  
Zheng Bao
Keyword(s):  
Interpolating Wavelets

WAVELET-BASED ADAPTIVE COLLOCATION METHOD FOR THE RESOLUTION OF NONLINEAR PDEs

2007 ◽  
Vol 05 (06) ◽  
pp. 957-973 ◽  
Author(s):  
A. KARAMI ◽  
H. R. KARIMI ◽  
B. MOSHIRI ◽  
P. JABEDAR MARALANI
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Multiresolution Analysis ◽  
Chemical Engineering ◽  
Nonlinear Pdes ◽  
Dynamic Processes ◽  
Partial Differential ◽  
Numeric Solution ◽  
Interpolating Wavelets

Theoretical modeling of dynamic processes in chemical engineering often implies the numeric solution of one or more partial differential equations. The complexity of such problems is increased when the solutions exhibit sharp moving fronts. An efficient adaptive multiresolution numerical method is described for solving systems of partial differential equations. This method is based on multiresolution analysis and interpolating wavelets, that dynamically adapts the collocation grid so that higher resolution is automatically attributed to domain regions where sharp features are present. Space derivatives were computed in an irregular grid by cubic splines method. The effectiveness of the method is demonstrated with some relevant examples in a chemical engineering context.

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