A New Meshless Collocation Method for Partial Differential Equations : New method for the solution of PDEs

Mohammad Kamruzzaman

ISBN 10: 3844301992 / ISBN 13: 9783844301991

Published by LAP LAMBERT Academic Publishing, 2011

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - A collocation meshless method is developed for the numerical solution of Partial Differential Equations (PDEs) on the scattered point distribution. The meshless shape functions are constructed on a group of selected nodes (stencil) arbitrarily distributed in a local support domain by means of a polynomial interpolation. This shape function formulation possesses the Kronecker delta function property, and hence many numerical treatments are as simple as those of the Finite Element Method (FEM). Nearest neighbor algorithm is used for the support domain nodes collection and a search algorithm based on the Gauss-Jordan pivot method is applied to select a suitable stencil for the construction of the shape functions and their derivatives. This search technique is subject to a monitoring procedure which selects appropriate stencil in order to keep the condition number of the resulting linear systems small. Various meshless collocation schemes for the solution of elliptic, parabolic and hyperbolic PDEs are investigated for the proposed method. Different types of PDEs are studied as test cases and all of the computational results are examined.

Seller Inventory # 9783844301991

Bibliographic Details

• Title: A New Meshless Collocation Method for Partial Differential Equations : New method for the solution of PDEs
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2011
• Language: English
• ISBN 10: 3844301992
• ISBN 13: 9783844301991
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 7D millimeters 220 millimeters width by 150 millimeters height by 7 millimeters depth
• Weight: 179 grams

About this title

Synopsis

A collocation meshless method is developed for the numerical solution of Partial Differential Equations (PDEs) on the scattered point distribution. The meshless shape functions are constructed on a group of selected nodes (stencil) arbitrarily distributed in a local support domain by means of a polynomial interpolation. This shape function formulation possesses the Kronecker delta function property, and hence many numerical treatments are as simple as those of the Finite Element Method (FEM). Nearest neighbor algorithm is used for the support domain nodes collection and a search algorithm based on the Gauss-Jordan pivot method is applied to select a suitable stencil for the construction of the shape functions and their derivatives. This search technique is subject to a monitoring procedure which selects appropriate stencil in order to keep the condition number of the resulting linear systems small. Various meshless collocation schemes for the solution of elliptic, parabolic and hyperbolic PDEs are investigated for the proposed method. Different types of PDEs are studied as test cases and all of the computational results are examined.

About the Author

Born in 1978 at Dhaka, Bangladesh. Currently working as a Research Assistant at IAG, University of Stuttgart. To be appeared for Dr.-Ing degree in 2011. Graduation from Shahjalal University of Science & Technology (SUST), Bangladesh in Applied Mathematics and MSc. degree in Computational Sciences in Engineering [CSE] from TU Braunschweig, Germany.