Analysis of the Boundary Knot Method for 3D Helmholtz-Type Equation. (13th March 2014)

• Record Type: Journal Article
• Authors: Wang, F. Z.; Zheng, K. H.
• Other Names: Cheng Yumin Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2014(2014)
• Publication Date: 2014-03-13
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2014/853252
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Numerical solutions of the boundary knot method (BKM) always perform oscillatory convergence when using a large number of boundary points in solving the Helmholtz-type problems. The main reason for this phenomenon may contribute to the severely ill-conditioned full coefficient matrix. In order to obtain admissible stable convergence results, regularization techniques and the effective condition number are employed in the process of simulating 3D Helmholtz-type problems. Numerical results are tested for the 3D Helmholtz-type equation with noisy and non-noisy boundary conditions. It is shown that the BKM in combination with the regularization techniques is able to produce stable numerical solutions.