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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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8cd5f7de
...
@@ -2968,27 +2968,26 @@ interpolation matrices used for high-order adaptive visualization.
...
@@ -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
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
is written as a linear combination of @var
{
d
}
basis functions
@var
{
f
}
[@var
{
j
}
], @var
{
j
}
=0, ..., @var
{
d
}
-1 (the coefficients being
@var
{
f
}
[@var
{
i
}
], @var
{
i
}
=0, ..., @var
{
d
}
-1 (the coefficients being
stored in @var
{
list-of-values
}
). Defining @var
{
f
}
[@var
{
j
}
] =
stored in @var
{
list-of-values
}
). Defining @var
{
f
}
[@var
{
i
}
] =
Sum(@var
{
i
}
=0, ..., @var
{
d
}
-1) @var
{
p
}
[@var
{
i
}
]
Sum(@var
{
j
}
=0, ..., @var
{
d
}
-1) @var
{
F
}
[@var
{
i
}
]
[@var
{
j
}
]
@var
{
F
}
[@var
{
j
}
][@var
{
i
}
]
, with @var
{
p
}
[@var
{
i
}
]
=
@var
{
p
}
[@var
{
j
}
]
, with @var
{
p
}
[@var
{
j
}
]
= @var
{
u
}^
@var
{
P
}
[@var
{
j
}
]
[0]
@var
{
u
}^
@var
{
P
}
[@var
{
i
}
][
0
] @var
{
v
}^
@var
{
P
}
[@var
{
i
}
][
1]
@var
{
v
}^
@var
{
P
}
[@var
{
j
}
][
1
] @var
{
w
}^
@var
{
P
}
[@var
{
j
}
][
2] (@var
{
u
}
,
@var
{
w
}^
@var
{
P
}
[@var
{
i
}
][2] (@var
{
u
}
, @var
{
v
}
and @var
{
w
}
being the
@var
{
v
}
and @var
{
w
}
being the coordinates in the element's parameter
coordinates in the element's parameter space), then
space), then @var
{
val-coef-matrix
}
denotes the @var
{
d
}
x @var
{
d
}
matrix
@var
{
val-
coef
-matrix
}
denotes the @var
{
d
}
x @var
{
d
}
matrix
@var
{
F
}
and
@var
{
F
}
and
@var
{
val-
exp
-matrix
}
denotes the @var
{
d
}
x @var
{
3
}
matrix
@var
{
val-exp-matrix
}
denotes the @var
{
d
}
x @var
{
3
}
matrix
@var
{
P
}
.
@var
{
P
}
.
In the same way, let us also assume that the coordinates @var
{
x
}
,
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
@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
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
functions @var
{
g
}
[@var
{
i
}
], @var
{
i
}
=0, ..., @var
{
m
}
-1 (the coefficients
being stored in @var
{
list-of-coords
}
). Defining @var
{
g
}
[@var
{
j
}
] =
being stored in @var
{
list-of-coords
}
). Defining @var
{
g
}
[@var
{
i
}
] =
Sum(@var
{
i
}
=0, ..., @var
{
m
}
-1) @var
{
q
}
[@var
{
i
}
]
Sum(@var
{
j
}
=0, ..., @var
{
m
}
-1) @var
{
G
}
[@var
{
i
}
][@var
{
j
}
]
@var
{
G
}
[@var
{
j
}
][@var
{
i
}
], with @var
{
q
}
[@var
{
i
}
] =
@var
{
q
}
[@var
{
j
}
], with @var
{
q
}
[@var
{
j
}
] = @var
{
u
}^
@var
{
Q
}
[@var
{
j
}
][0]
@var
{
u
}^
@var
{
Q
}
[@var
{
i
}
][0] @var
{
v
}^
@var
{
Q
}
[@var
{
i
}
][1]
@var
{
v
}^
@var
{
Q
}
[@var
{
j
}
][1] @var
{
w
}^
@var
{
Q
}
[@var
{
j
}
][2], then
@var
{
w
}^
@var
{
Q
}
[@var
{
i
}
][2], then @var
{
val-coef-matrix
}
denotes the
@var
{
val-coef-matrix
}
denotes the @var
{
m
}
x @var
{
m
}
matrix @var
{
G
}
and
@var
{
m
}
x @var
{
m
}
matrix @var
{
G
}
and @var
{
val-exp-matrix
}
denotes the
@var
{
val-exp-matrix
}
denotes the @var
{
m
}
x @var
{
3
}
matrix @var
{
Q
}
.
@var
{
m
}
x @var
{
3
}
matrix @var
{
Q
}
.
Here are for example the interpolation matrices for a first order
Here are for example the interpolation matrices for a first order
quadrangle:
quadrangle:
...
...
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