<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
the	O
singular	B-Algorithm
boundary	I-Algorithm
method	I-Algorithm
(	O
SBM	O
)	O
belongs	O
to	O
a	O
family	O
of	O
meshless	B-Algorithm
boundary	O
collocation	B-Algorithm
techniques	I-Algorithm
which	O
include	O
the	O
method	B-Algorithm
of	I-Algorithm
fundamental	I-Algorithm
solutions	I-Algorithm
(	O
MFS	O
)	O
,	O
boundary	B-Algorithm
knot	I-Algorithm
method	I-Algorithm
(	O
BKM	O
)	O
,	O
regularized	B-Algorithm
meshless	I-Algorithm
method	I-Algorithm
(	O
RMM	O
)	O
,	O
boundary	B-Algorithm
particle	I-Algorithm
method	I-Algorithm
(	O
BPM	O
)	O
,	O
modified	O
MFS	O
,	O
and	O
so	O
on	O
.	O
</s>
<s>
This	O
family	O
of	O
strong-form	O
collocation	B-Algorithm
methods	I-Algorithm
is	O
designed	O
to	O
avoid	O
singular	O
numerical	O
integration	O
and	O
mesh	O
generation	O
in	O
the	O
traditional	O
boundary	B-Algorithm
element	I-Algorithm
method	I-Algorithm
(	O
BEM	O
)	O
in	O
the	O
numerical	B-General_Concept
solution	I-General_Concept
of	O
boundary	O
value	O
problems	O
with	O
boundary	O
nodes	O
,	O
in	O
which	O
a	O
fundamental	O
solution	O
of	O
the	O
governing	O
equation	O
is	O
explicitly	O
known	O
.	O
</s>
<s>
The	O
salient	O
feature	O
of	O
the	O
SBM	O
is	O
to	O
overcome	O
the	O
fictitious	O
boundary	O
in	O
the	O
method	B-Algorithm
of	I-Algorithm
fundamental	I-Algorithm
solution	I-Algorithm
,	O
while	O
keeping	O
all	O
merits	O
of	O
the	O
latter	O
.	O
</s>
<s>
meshless	B-Algorithm
.	O
</s>
<s>
The	O
numerical	O
integration	O
of	O
singular	O
or	O
nearly	O
singular	O
kernels	O
could	O
be	O
otherwise	O
troublesome	O
,	O
expensive	O
,	O
and	O
complicated	O
,	O
as	O
in	O
the	O
case	O
,	O
for	O
example	O
,	O
the	O
boundary	B-Algorithm
element	I-Algorithm
method	I-Algorithm
;	O
</s>
<s>
to	O
overcome	O
the	O
perplexing	O
fictitious	O
boundary	O
in	O
the	O
method	B-Algorithm
of	I-Algorithm
fundamental	I-Algorithm
solutions	I-Algorithm
(	O
see	O
Figs	O
.	O
</s>
<s>
In	O
comparison	O
,	O
the	O
method	B-Algorithm
of	I-Algorithm
fundamental	I-Algorithm
solutions	I-Algorithm
requires	O
a	O
fictitious	O
boundary	O
for	O
placing	O
the	O
source	O
points	O
to	O
avoid	O
the	O
singularity	O
of	O
fundamental	O
solution	O
.	O
</s>
<s>
Like	O
all	O
the	O
other	O
boundary-type	O
numerical	B-General_Concept
methods	I-General_Concept
,	O
also	O
it	O
is	O
observed	O
that	O
the	O
SBM	O
encounters	O
a	O
dramatic	O
drop	O
of	O
solution	O
accuracy	O
at	O
the	O
region	O
nearby	O
boundary	O
.	O
</s>
<s>
The	O
fast	B-Algorithm
multipole	I-Algorithm
method	I-Algorithm
(	O
FMM	O
)	O
can	O
reduce	O
both	O
CPU	O
time	O
and	O
memory	O
requirement	O
from	O
O(N2 )	O
to	O
O(N )	O
or	O
O(NlogN )	O
.	O
</s>
