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Larry Price
gmsh
Commits
8cd5f7de
Commit
8cd5f7de
authored
16 years ago
by
Christophe Geuzaine
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doc/texinfo/gmsh.texi
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doc/texinfo/gmsh.texi
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16
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17
View file @
8cd5f7de
...
...
@@ -2968,27 +2968,26 @@ interpolation matrices used for high-order adaptive visualization.
Let us assume that the approximation of the view's value over an element
is written as a linear combination of @var
{
d
}
basis functions
@var
{
f
}
[@var
{
j
}
], @var
{
j
}
=0, ..., @var
{
d
}
-1 (the coefficients being
stored in @var
{
list-of-values
}
). Defining @var
{
f
}
[@var
{
j
}
] =
Sum(@var
{
i
}
=0, ..., @var
{
d
}
-1) @var
{
p
}
[@var
{
i
}
]
@var
{
F
}
[@var
{
j
}
][@var
{
i
}
]
, with @var
{
p
}
[@var
{
i
}
]
=
@var
{
u
}^
@var
{
P
}
[@var
{
i
}
][
0
] @var
{
v
}^
@var
{
P
}
[@var
{
i
}
][
1]
@var
{
w
}^
@var
{
P
}
[@var
{
i
}
][2] (@var
{
u
}
, @var
{
v
}
and @var
{
w
}
being the
coordinates in the element's parameter space), then
@var
{
val-
coef
-matrix
}
denotes the @var
{
d
}
x @var
{
d
}
matrix
@var
{
F
}
and
@var
{
val-exp-matrix
}
denotes the @var
{
d
}
x @var
{
3
}
matrix
@var
{
P
}
.
@var
{
f
}
[@var
{
i
}
], @var
{
i
}
=0, ..., @var
{
d
}
-1 (the coefficients being
stored in @var
{
list-of-values
}
). Defining @var
{
f
}
[@var
{
i
}
] =
Sum(@var
{
j
}
=0, ..., @var
{
d
}
-1) @var
{
F
}
[@var
{
i
}
]
[@var
{
j
}
]
@var
{
p
}
[@var
{
j
}
]
, with @var
{
p
}
[@var
{
j
}
]
= @var
{
u
}^
@var
{
P
}
[@var
{
j
}
]
[0]
@var
{
v
}^
@var
{
P
}
[@var
{
j
}
][
1
] @var
{
w
}^
@var
{
P
}
[@var
{
j
}
][
2] (@var
{
u
}
,
@var
{
v
}
and @var
{
w
}
being the coordinates in the element's parameter
space), then @var
{
val-coef-matrix
}
denotes the @var
{
d
}
x @var
{
d
}
matrix
@var
{
F
}
and
@var
{
val-
exp
-matrix
}
denotes the @var
{
d
}
x @var
{
3
}
matrix
@var
{
P
}
.
In the same way, let us also assume that the coordinates @var
{
x
}
,
@var
{
y
}
and @var
{
z
}
of the element are obtained through a geometrical
mapping from parameter space as a linear combination of @var
{
m
}
basis
functions @var
{
g
}
[@var
{
j
}
], @var
{
j
}
=0, ..., @var
{
m
}
-1 (the coefficients
being stored in @var
{
list-of-coords
}
). Defining @var
{
g
}
[@var
{
j
}
] =
Sum(@var
{
i
}
=0, ..., @var
{
m
}
-1) @var
{
q
}
[@var
{
i
}
]
@var
{
G
}
[@var
{
j
}
][@var
{
i
}
], with @var
{
q
}
[@var
{
i
}
] =
@var
{
u
}^
@var
{
Q
}
[@var
{
i
}
][0] @var
{
v
}^
@var
{
Q
}
[@var
{
i
}
][1]
@var
{
w
}^
@var
{
Q
}
[@var
{
i
}
][2], then @var
{
val-coef-matrix
}
denotes the
@var
{
m
}
x @var
{
m
}
matrix @var
{
G
}
and @var
{
val-exp-matrix
}
denotes the
@var
{
m
}
x @var
{
3
}
matrix @var
{
Q
}
.
functions @var
{
g
}
[@var
{
i
}
], @var
{
i
}
=0, ..., @var
{
m
}
-1 (the coefficients
being stored in @var
{
list-of-coords
}
). Defining @var
{
g
}
[@var
{
i
}
] =
Sum(@var
{
j
}
=0, ..., @var
{
m
}
-1) @var
{
G
}
[@var
{
i
}
][@var
{
j
}
]
@var
{
q
}
[@var
{
j
}
], with @var
{
q
}
[@var
{
j
}
] = @var
{
u
}^
@var
{
Q
}
[@var
{
j
}
][0]
@var
{
v
}^
@var
{
Q
}
[@var
{
j
}
][1] @var
{
w
}^
@var
{
Q
}
[@var
{
j
}
][2], then
@var
{
val-coef-matrix
}
denotes the @var
{
m
}
x @var
{
m
}
matrix @var
{
G
}
and
@var
{
val-exp-matrix
}
denotes the @var
{
m
}
x @var
{
3
}
matrix @var
{
Q
}
.
Here are for example the interpolation matrices for a first order
quadrangle:
...
...
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