TY - EJOU
AU - Wang, F.Z.
TI - Applicability of the Boundary Particle Method
T2 - Computer Modeling in Engineering \& Sciences
PY - 2011
VL - 80
IS - 3&4
SN - 1526-1506
AB - In this paper, we consider the boundary particle method (BPM) which is excellent in solving inhomogeneous partial differential equations in terms of solution accuracy and simplicity. In order to investigate the applicability of the BPM, we examine the relationship between its solution accuracy and the effective condition number. We show that the effective condition number, which estimates system stability with the right-hand side vector taken into account, is inversely proportional to the root mean square error in the numerical approximation. Moreover, for noisy-boundary cases, we find that the BPM can not yield reasonable results, for more noise added to the right-hand side vector, by using Gaussian elimination. Thus, to solve effectively the discrete ill-conditioned coefficient matrix, we adopt three regularization techniques under two different regularization parameter choices. Numerical results indicate that the generalized cross-validation choice rule for the damped singular value decomposition regularization strategy performs the best.
KW - Effective condition number
KW - noisy-boundary
KW - inhomogeneous
KW - regularization technique
KW - regularization parameter
DO - 10.3970/cmes.2011.080.201