A new wavelet multigrid method for the numerical solution of elliptic type differential equations

In this paper, we present a new wavelet multigrid method for the numerical solution of elliptic type differential equations based on Daubechies (db4) high pass and low pass filter coefficients with modified intergrid operators. The proposed method is the robust technique for faster convergence with...

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Main Authors: S.C. Shiralashetti, M.H. Kantli, A.B. Deshi
Format: Article
Language:English
Published: Elsevier 2018-03-01
Series:Alexandria Engineering Journal
Online Access:http://www.sciencedirect.com/science/article/pii/S1110016816303398
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author S.C. Shiralashetti
M.H. Kantli
A.B. Deshi
author_facet S.C. Shiralashetti
M.H. Kantli
A.B. Deshi
author_sort S.C. Shiralashetti
collection DOAJ
description In this paper, we present a new wavelet multigrid method for the numerical solution of elliptic type differential equations based on Daubechies (db4) high pass and low pass filter coefficients with modified intergrid operators. The proposed method is the robust technique for faster convergence with less computational cost which is justified through the error analysis and condition number of a system in comparison with integrated-RBF technique based on Galerkin formulation (Mai-Duy and Tran-Cong, 2009) and finite difference method. Some of the illustrative problems are presented to demonstrate the attractiveness of the proposed technique. Keywords: Wavelet multigrid, Daubechies filters, Elliptic differential equations, Condition number
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spelling doaj.art-b568072171d3410f8c7db15f2dc44ded2022-12-21T18:31:08ZengElsevierAlexandria Engineering Journal1110-01682018-03-01571203209A new wavelet multigrid method for the numerical solution of elliptic type differential equationsS.C. Shiralashetti0M.H. Kantli1A.B. Deshi2Corresponding author. Fax: +91 836 347884.; Department of Mathematics, Karnatak University, Dharwad 580003, IndiaDepartment of Mathematics, Karnatak University, Dharwad 580003, IndiaDepartment of Mathematics, Karnatak University, Dharwad 580003, IndiaIn this paper, we present a new wavelet multigrid method for the numerical solution of elliptic type differential equations based on Daubechies (db4) high pass and low pass filter coefficients with modified intergrid operators. The proposed method is the robust technique for faster convergence with less computational cost which is justified through the error analysis and condition number of a system in comparison with integrated-RBF technique based on Galerkin formulation (Mai-Duy and Tran-Cong, 2009) and finite difference method. Some of the illustrative problems are presented to demonstrate the attractiveness of the proposed technique. Keywords: Wavelet multigrid, Daubechies filters, Elliptic differential equations, Condition numberhttp://www.sciencedirect.com/science/article/pii/S1110016816303398
spellingShingle S.C. Shiralashetti
M.H. Kantli
A.B. Deshi
A new wavelet multigrid method for the numerical solution of elliptic type differential equations
Alexandria Engineering Journal
title A new wavelet multigrid method for the numerical solution of elliptic type differential equations
title_full A new wavelet multigrid method for the numerical solution of elliptic type differential equations
title_fullStr A new wavelet multigrid method for the numerical solution of elliptic type differential equations
title_full_unstemmed A new wavelet multigrid method for the numerical solution of elliptic type differential equations
title_short A new wavelet multigrid method for the numerical solution of elliptic type differential equations
title_sort new wavelet multigrid method for the numerical solution of elliptic type differential equations
url http://www.sciencedirect.com/science/article/pii/S1110016816303398
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