Based on the assumption that solutions from different methods should be the same, the relationship among weakly singular, strongly singular and hypersingular matrices associated with symmetric Galerkin boundary element method (SGBEM) is derived in this paper. Hypersingularity is avoided through matrix manipulations so that only weakly and strongly singularities need to be solved. Compared with the advantages brought about by symmetry, the additional computation caused by matrix manipulations is not so important in many cases, especially for time-domain problems or when one wants to couple BEM with other symmetric schemes. Simplicity is the advantage of the current method over the traditional SGBEM. Both steady-state and time-domain potential problems have been studied, and two numerical examples are included to show the effectiveness and accuracy of the present formulation.

1.
Sirtori
,
S.
,
1979
, “
General Stress Analysis Method by Means of Integral Equations and Boundary Elements
,”
Meccanica
,
14
, pp.
210
218
.
2.
Bonnet
,
M.
,
Maier
,
G.
, and
Polizzotto
,
C.
,
1998
, “
Symmetric Galerkin Boundary Element Methods
,”
Appl. Mech. Rev.
,
51
(
11
), pp.
669
704
.
3.
Carini
,
A.
,
Diligent
,
M.
,
Maranesi
,
P.
, and
Zanella
,
M.
,
1999
, “
Analytical Integrations for Two-Dimensional Elastic Analysis by the Symmetric Galerkin Boundary Element Method
,”
Comput. Mech.
,
23
, pp.
308
323
.
4.
Krishnasamy, G., Rizzo, F. J., and Rudolphi, T. J., 1991, “Hypersingular Boundary Integral Equations: Their Occurrence, Interpretation, Regularization and Computation,” Developments in Boundary Element Methods, Vol. 7, P. K. Banerjee, and S. Kobayashi, eds., Elsevier Applied Science Publishers, New York.
5.
Dominguez
,
J.
,
Ariza
,
M. P.
, and
Gallego
,
R.
,
2000
, “
Flux and Traction Boundary Elements without Hypersingular or Strongly Singular Integrals
,”
Int. J. Numer. Methods Eng.
,
48
, pp.
111
135
.
6.
Tanaka
,
M.
,
Sladek
,
V.
, and
Sladek
,
J.
,
1994
, “
Regularization Techniques Applied to Boundary Element Methods
,”
Appl. Mech. Rev.
,
47
(
10
), pp.
457
499
.
7.
Hadamard, J., 1923, Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Yale University Press, New Haven, CT.
8.
Monegato
,
G.
,
1994
, “
The Numerical Evaluation of Hypersingular Integrals
,”
J. Comput. Appl. Math.
,
50
, pp.
9
31
.
9.
Aimi
,
A.
,
Carini
,
A.
,
Diligenti
,
M.
, and
Monegato
,
G.
,
1998
, “
Numerical Integration Schemes for Evaluation of (Hyper) singular Integrals in 2D BEM
,”
Comput. Mech.
,
22
, pp.
1
11
.
10.
Gray
,
L. J.
,
Martha
,
L. F.
, and
Ingraffea
,
A. R.
,
1990
, “
Hypersingular Integrals in Boundary Element Fracture Analysis
,”
Int. J. Numer. Methods Eng.
,
29
, pp.
1135
1158
.
11.
Guiggiani
,
M.
,
1994
, “
Hypersingular Formulation for Boundary Stress Evaluation
,”
Eng. Anal. Boundary Elem.
,
13
, pp.
169
179
.
12.
Guiggiani
,
M.
,
1995
, “
Hypersingular Boundary Integral Equations Have an Additional Free Term
,”
Comput. Mech.
,
16
, pp.
245
248
.
13.
Gallego
,
R.
, and
Dominguez
,
J.
,
1996
, “
Hypersingular BEM for Transient Elastodynamics
,”
Int. J. Numer. Methods Eng.
,
39
, pp.
1681
1705
.
14.
Carini
,
A.
,
Diligenti
,
M.
, and
Salvadori
,
A.
,
1999
, “
Implementation of a Symmetric Boundary Element Method in Transient Heat Conduction with Semi-Analytical Integrations
,”
Int. J. Numer. Methods Eng.
,
46
, pp.
1819
1843
.
15.
Yu
,
G. Y.
,
Mansur
,
W. J.
,
Carrer
,
J. A. M.
, and
Gong
,
L.
,
2000
, “
Stability of Galerkin and Collocation Time Domain Boundary Element Methods as Applied to Scalar Wave Equation
,”
Comput. Struct.
,
74
, pp.
495
506
.
16.
Mansur, W. J., 1983, “A Time-Stepping Technique to Solve Wave Propagation Problems Using the Boundary Element Method,” Ph.D. thesis, University of Southampton.
17.
Yu
,
G. Y.
,
Mansur
,
W. J.
,
Carrer
,
J. A. M.
, and
Gong
,
L.
,
1998
, “
A Linear θ Method Applied to 2D Time-Domain BEM
,”
Commun. Numer. Methods Eng.
,
14
(
12
), pp.
1171
1180
.
18.
Mansur
,
W. J.
,
Yu
,
G. Y.
,
Carrer
,
J. A. M.
,
Lie
,
S. T.
, and
Siquiera
,
E. F. N.
,
2000
, “
The θ Scheme for Time-Domain BEM/FEM Coupling Applied to the 2-D Scalar Wave Equation
,”
Commun. Numer. Methods Eng.
,
16
, pp.
439
448
.
You do not currently have access to this content.