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Stephan Hilb
SemiSmoothNewton.jl
Commits
40b8a151
Commit
40b8a151
authored
Jul 12, 2021
by
Stephan Hilb
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implement newest-vertex bisection for HMesh
parent
5c46c0c8
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1 changed file
src/mesh.jl
+137
-4
137 additions, 4 deletions
src/mesh.jl
with
137 additions
and
4 deletions
src/mesh.jl
+
137
−
4
View file @
40b8a151
export
init_grid
,
save
export
init_grid
,
init_hgrid
,
save
,
refine!
,
cells
,
vertices
using
WriteVTK
using
StaticArrays
:
SVector
struct
HMesh
vertices
::
Vector
{
SVector
{
2
,
Float64
}}
cells
::
Vector
{
NTuple
{
3
,
Int
}}
end
Base
.
show
(
io
::
IO
,
::
MIME
"text/plain"
,
x
::
HMesh
)
=
print
(
"
$
(nameof(typeof(x))),
$
(ncells(x)) cells"
)
ndims_domain
(
::
HMesh
)
=
2
ndims_space
(
::
HMesh
)
=
2
nvertices_cell
(
::
HMesh
)
=
3
nvertices
(
x
::
HMesh
)
=
length
(
x
.
vertices
)
ncells
(
x
::
HMesh
)
=
length
(
x
.
cells
)
cells
(
mesh
::
HMesh
)
=
axes
(
mesh
.
cells
,
1
)
vertices
(
mesh
::
HMesh
,
cell
)
=
mesh
.
cells
[
cell
]
function
init_hgrid
(
m
::
Int
,
n
::
Int
=
m
,
v0
=
(
0.
,
0.
),
v1
=
(
1.
,
1.
))
r1
=
LinRange
(
v0
[
1
],
v1
[
1
],
m
+
1
)
r2
=
LinRange
(
v0
[
2
],
v1
[
2
],
n
+
1
)
coords
=
collect
(
Iterators
.
product
(
r1
,
r2
))
vertices
=
SVector
{
2
,
Float64
}
.
(
vec
(
coords
))
cells
=
Vector
{
NTuple
{
3
,
Int
}}()
vidx
=
LinearIndices
((
m
+
1
,
n
+
1
))
e1
=
CartesianIndex
(
1
,
0
)
e2
=
CartesianIndex
(
0
,
1
)
k
=
0
for
I
in
CartesianIndices
((
m
,
n
))
push!
(
cells
,
(
vidx
[
I
],
vidx
[
I
+
e1
],
vidx
[
I
+
e1
+
e2
]))
push!
(
cells
,
(
vidx
[
I
],
vidx
[
I
+
e1
+
e2
],
vidx
[
I
+
e2
]))
end
return
HMesh
(
vertices
,
cells
)
end
init_hgrid
(
img
::
Array
{
<:
Any
,
2
};
type
=:
vertex
)
=
type
==
:
vertex
?
init_grid
(
size
(
img
,
1
)
-
1
,
size
(
img
,
2
)
-
1
,
(
1.0
,
1.0
),
size
(
img
))
:
init_grid
(
size
(
img
,
1
),
size
(
img
,
2
),
(
0.5
,
0.5
),
size
(
img
)
.-
(
0.5
,
0.5
))
# 2d, simplex grid
struct
Mesh
vertices
::
Array
{
Float64
,
2
}
cells
::
Array
{
Int
,
2
}
end
Base
.
show
(
io
::
IO
,
::
MIME
"text/plain"
,
f
::
Mesh
)
=
print
(
"
$
(nameof(typeof(
f
))),
$
(
size(f.
cells
, 2
)) cells"
)
Base
.
show
(
io
::
IO
,
::
MIME
"text/plain"
,
x
::
Mesh
)
=
print
(
"
$
(nameof(typeof(
x
))),
$
(
n
cells
(x
)) cells"
)
ndims_domain
(
::
Mesh
)
=
2
ndims_space
(
::
Mesh
)
=
2
...
...
@@ -18,7 +61,8 @@ nvertices_cell(::Mesh) = 3
nvertices
(
x
::
Mesh
)
=
size
(
x
.
vertices
,
2
)
ncells
(
x
::
Mesh
)
=
size
(
x
.
cells
,
2
)
cells
(
x
::
Mesh
)
=
axes
(
x
.
cells
,
2
)
cells
(
mesh
::
Mesh
)
=
axes
(
mesh
.
cells
,
2
)
vertices
(
mesh
::
Mesh
,
cell
)
=
ntuple
(
i
->
mesh
.
cells
[
i
,
cell
],
nvertices_cell
(
mesh
))
#function Base.getproperty(obj::Mesh, sym::Symbol)
# if sym === :vertices
...
...
@@ -53,6 +97,95 @@ init_grid(img::Array{<:Any, 2}; type=:vertex) =
init_grid
(
size
(
img
,
1
)
-
1
,
size
(
img
,
2
)
-
1
,
(
1.0
,
1.0
),
size
(
img
))
:
init_grid
(
size
(
img
,
1
),
size
(
img
,
2
),
(
0.5
,
0.5
),
size
(
img
)
.-
(
0.5
,
0.5
))
function
refine!
(
mesh
::
HMesh
,
marked_cells
::
Set
)
refined_cells
=
Set
{
Int
}()
# assemble edge -> cells map
edgemap
=
Dict
{
NTuple
{
2
,
Int
},
Vector
{
Int
}}()
for
cell
in
cells
(
mesh
)
vs
=
sort
(
SVector
(
vertices
(
mesh
,
cell
)))
e1
=
(
vs
[
1
],
vs
[
2
])
e2
=
(
vs
[
1
],
vs
[
3
])
e3
=
(
vs
[
2
],
vs
[
3
])
edgemap
[
e1
]
=
push!
(
get!
(
edgemap
,
e1
,
[]),
cell
)
edgemap
[
e2
]
=
push!
(
get!
(
edgemap
,
e2
,
[]),
cell
)
edgemap
[
e3
]
=
push!
(
get!
(
edgemap
,
e3
,
[]),
cell
)
end
function
refine_cell
(
c1
)
c2
=
-
1
# c1 -> c11 + c12
# c2 -> c21 + c22
c1_vs
=
sort
(
SVector
(
vertices
(
mesh
,
c1
)))
c2_arr
=
setdiff
(
edgemap
[(
c1_vs
[
1
],
c1_vs
[
2
])],
c1
)
if
!
isempty
(
c2_arr
)
@assert
(
length
(
c2_arr
)
==
1
)
c2
=
c2_arr
[
begin
]
c2_vs
=
sort
(
SVector
(
vertices
(
mesh
,
c2
)))
if
c1_vs
[
end
]
!=
c2_vs
[
end
]
# cannot refine `cellop` compatibly, recurse
refine_cell
(
c2
)
# refetch c2 because topology has changed
c2_arr
=
setdiff
(
edgemap
[(
c1_vs
[
1
],
c1_vs
[
2
])],
c1
)
@assert
(
!
isempty
(
c2_arr
))
c2
=
c2_arr
[
begin
]
c2_vs
=
sort
(
SVector
(
vertices
(
mesh
,
c2
)))
end
# c2 exists and compatibility is guaranteed
@assert
(
c1_vs
[
1
:
2
]
==
c2_vs
[
1
:
2
])
end
# create bisection vertex
xbisect
=
(
mesh
.
vertices
[
c1_vs
[
1
]]
+
mesh
.
vertices
[
c1_vs
[
2
]])
/
2
push!
(
mesh
.
vertices
,
xbisect
)
vbisect
=
lastindex
(
mesh
.
vertices
)
push!
(
mesh
.
cells
,
Tuple
(
sort
(
replace
(
c1_vs
,
c1_vs
[
1
]
=>
vbisect
))))
c3
=
lastindex
(
mesh
.
cells
)
replace!
(
edgemap
[
NTuple
{
2
}(
setdiff
(
c1_vs
,
c1_vs
[
1
]))],
c1
=>
c3
)
push!
(
mesh
.
cells
,
Tuple
(
sort
(
replace
(
c1_vs
,
c1_vs
[
2
]
=>
vbisect
))))
c4
=
lastindex
(
mesh
.
cells
)
replace!
(
edgemap
[
NTuple
{
2
}(
setdiff
(
c1_vs
,
c1_vs
[
2
]))],
c1
=>
c4
)
# flip is correct
edgemap
[(
c1_vs
[
1
],
vbisect
)]
=
[
c4
]
edgemap
[(
c1_vs
[
2
],
vbisect
)]
=
[
c3
]
edgemap
[(
c1_vs
[
3
],
vbisect
)]
=
[
c3
,
c4
]
delete!
(
marked_cells
,
c1
)
push!
(
refined_cells
,
c1
)
if
c2
>
0
push!
(
mesh
.
cells
,
Tuple
(
sort
(
replace
(
c2_vs
,
c1_vs
[
1
]
=>
vbisect
))))
# c1_vs is correct
c5
=
lastindex
(
mesh
.
cells
)
replace!
(
edgemap
[
NTuple
{
2
}(
setdiff
(
c2_vs
,
c1_vs
[
1
]))],
c1
=>
c5
)
push!
(
mesh
.
cells
,
Tuple
(
sort
(
replace
(
c2_vs
,
c1_vs
[
2
]
=>
vbisect
))))
# c1_vs is correct
c6
=
lastindex
(
mesh
.
cells
)
replace!
(
edgemap
[
NTuple
{
2
}(
setdiff
(
c2_vs
,
c1_vs
[
2
]))],
c1
=>
c6
)
# flip is correct
push!
(
edgemap
[(
c1_vs
[
1
],
vbisect
)],
c6
)
push!
(
edgemap
[(
c1_vs
[
2
],
vbisect
)],
c5
)
edgemap
[(
c1_vs
[
3
],
vbisect
)]
=
[
c5
,
c6
]
delete!
(
marked_cells
,
c2
)
push!
(
refined_cells
,
c1
)
end
end
while
!
isempty
(
marked_cells
)
refine_cell
(
first
(
marked_cells
))
end
deleteat!
(
mesh
.
cells
,
sort
(
collect
(
refined_cells
)))
return
mesh
end
#function cell_contains(mesh, cell, v)
# geo = mesh.vertices[:, mesh.cells[:, cell]]
# J = jacobian(x -> geo * [1 - x[1] - x[2], x[1], x[2]], [0., 0.])
...
...
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