TY - JOUR
T1 - Boundary cloud method
T2 - A combined scattered point/boundary integral approach for boundary-only analysis
AU - Li, Gang
AU - Aluru, N. R.
N1 - Funding Information:
This work was supported by an NSF CAREER award to N.R. Aluru and by a grant from DARPA under agreement number F30602-98-2-0178. This support is gratefully acknowledged.
PY - 2002/3/15
Y1 - 2002/3/15
N2 - A boundary cloud method (BCM), for boundary-only analysis of partial differential equations, is presented in this paper for solving potential equations in two dimensions (2-D). The BCM combines a weighted least-squares approach for construction of interpolation functions with a boundary integral formulation for the governing equations. Given a set of scattered points on the surface of an arbitrary object, Hermite-type interpolation functions are constructed by developing a weighted least-squares approach. We also introduce truncated Hermite-type interpolation functions. The boundary integrals are evaluated by using a cell structure. We propose various schemes for evaluating the singular, nearly singular and nonsingular integrals. We also propose a true meshless approach for boundary-only analysis of potential equations. Numerical results, comparing the classical boundary element method and the BCM, are presented for several 2-D potential problems.
AB - A boundary cloud method (BCM), for boundary-only analysis of partial differential equations, is presented in this paper for solving potential equations in two dimensions (2-D). The BCM combines a weighted least-squares approach for construction of interpolation functions with a boundary integral formulation for the governing equations. Given a set of scattered points on the surface of an arbitrary object, Hermite-type interpolation functions are constructed by developing a weighted least-squares approach. We also introduce truncated Hermite-type interpolation functions. The boundary integrals are evaluated by using a cell structure. We propose various schemes for evaluating the singular, nearly singular and nonsingular integrals. We also propose a true meshless approach for boundary-only analysis of potential equations. Numerical results, comparing the classical boundary element method and the BCM, are presented for several 2-D potential problems.
KW - Boundary cloud method
KW - Boundary integral method
KW - Boundary-only analysis
KW - Hermite interpolation
KW - Meshless
KW - Scattered point interpolation
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U2 - 10.1016/S0045-7825(01)00415-7
DO - 10.1016/S0045-7825(01)00415-7
M3 - Article
AN - SCOPUS:0037087991
SN - 0045-7825
VL - 191
SP - 2337
EP - 2370
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 21-22
ER -