Add exercise 4

Cette révision appartient à :
nssc_kuen 2022-06-06 12:51:05 +02:00
Parent 3c77a2e57b
révision 392cc3fead
20 fichiers modifiés avec 61430 ajouts et 36 suppressions

12
Exercise_04/Parameters.jl Fichier normal
Voir le fichier

@ -0,0 +1,12 @@
module Parameters
export k, hz, L, q, T, e, elₘ
k = 429.
hz = 0.0005
L = 0.01
q = 2000000.
T = 293.
c = 10.
elₘ = [41,42,43,44,45,46,47,59,60,61,62,63,77,78,79,95]
end

5
Exercise_04/README Fichier normal
Voir le fichier

@ -0,0 +1,5 @@
FEM solver
- programmed in julia
- run using `julia run.jl`
- this generates output txt files in ./txt/ and plots in ./plots/ for all 5 variants

104
Exercise_04/fem.jl Fichier normal
Voir le fichier

@ -0,0 +1,104 @@
module FEM
export Node, Element, stiffness, tri_tiles, gradient, center, normalize, p
include("./Parameters.jl")
using GeometryBasics
using GeometryBasics.LinearAlgebra
struct Node
x::Float64
y::Float64
index::UInt
end
p(n::Node) = Point2f(n.x, n.y)
struct Element
nodes::Vector{Node}
a::Vector{Float64}
b::Vector{Float64}
c::Vector{Float64}
Δ::Float64
function Element(n::Vector{Node})
xs = map(nd->nd.x,n)
ys = map(nd->nd.y,n)
a = cross(xs, ys)
b = cross(ys, ones(3))
c = cross(ones(3), xs)
Δ = dot(xs,b) / 2
new(n,a,b,c,Δ)
end
end
function stiffness(e::Element)::Matrix{Float64}
# tensor product
Hₑ = e.b .* e.b'
Hₑ += e.c .* e.c'
Hₑ *= Parameters.hz*Parameters.k/4e.Δ
return Hₑ
end
function tri_tiles(L::Float64, divisions::Int, trapezoidal::Bool=false, biased::Bool=false, ring::Bool=false)::Tuple{Vector{Node}, Vector{Element}}
nodes = Matrix{Node}(undef, divisions+1, divisions+1)
i = 1
for y in 0:divisions
for x in 0:divisions
xₑ = L*x/divisions
yₑ = L*y/divisions
if biased
B = yₑ/2Parameters.L
xₑ = xₑ*(xₑ*B/Parameters.L - B + 1)
end
if trapezoidal
xₑ *= 1 - 0.5*(y/divisions)
end
if ring
r = Parameters.L*(1 + x/divisions)
θ = (π/4)*(y/divisions)
xₑ = r*cos(θ)
yₑ = r*sin(θ)
xₑ -= Parameters.L
end
nodes[x+1,y+1] = Node(xₑ,yₑ,i)
i += 1
end
end
elements = []
for y in 1:divisions
for x in 1:divisions
# lower/upper triangle
push!(elements, Element([nodes[x,y], nodes[x+1,y], nodes[x,y+1]]))
push!(elements, Element([nodes[x+1,y+1], nodes[x,y+1], nodes[x+1,y]]))
end
end
return vec(nodes), elements
end
function gradient(e::Element, T::Vector{Float64})::Vec2f
return Vec2f([
e.b[1] e.b[2] e.b[3] ;
e.c[1] e.c[2] e.c[3]
] * [
T[e.nodes[1].index]
T[e.nodes[2].index]
T[e.nodes[3].index]
] / 2e.Δ)
end
center(e::Element)::Point2f = Point2f(sum([n.x for n in e.nodes])/3.0, sum([n.y for n in e.nodes])/3.0)
normalize(v::Vec2f)::Vec2f = v / sqrt(v[1]^2 + v[2]^2)
end

0
Exercise_04/plots/.keep Fichier normal
Voir le fichier

BIN
Exercise_04/plots/baseline.png (Stocké avec Git LFS) Fichier normal

Fichier binaire non affiché.

BIN
Exercise_04/plots/variation1.png (Stocké avec Git LFS) Fichier normal

Fichier binaire non affiché.

BIN
Exercise_04/plots/variation2.png (Stocké avec Git LFS) Fichier normal

Fichier binaire non affiché.

BIN
Exercise_04/plots/variation3.png (Stocké avec Git LFS) Fichier normal

Fichier binaire non affiché.

BIN
Exercise_04/plots/variation4_div.png (Stocké avec Git LFS) Fichier normal

Fichier binaire non affiché.

BIN
Exercise_04/plots/variation4_mul.png (Stocké avec Git LFS) Fichier normal

Fichier binaire non affiché.

39
Exercise_04/print_HTP.jl Fichier normal
Voir le fichier

@ -0,0 +1,39 @@
using Fmt
function print_HTP(H::Matrix{Float64}, T::Vector{Float64}, P::Vector{Float64}, filename="output.txt")
# Print matrices to .txt-file (name of file = filename).
# H... overall assembled stiffness matrix
# T... nodal temperature vector
# P... nodal force vector
# Make sure, that your system of equations is sorted by
# ascending node numbers, i.e., N1 N2 ... N100.
open(filename, "w") do io
write(io, "Stiffness matrix H: \n")
for row in H
for col in row
outline = f"{$col:+8.4e},"
write(io, f"{$outline:11s}")
end
write(io, "\n")
end
write(io, "Temperature T: \n")
for row in T
for col in row
outline = f"{$col:+8.4e},"
write(io, f"{$outline:11s} \n")
end
end
write(io, "Force vector P: \n")
for row in P
for col in row
outline = f"{$col:+8.4e},"
write(io, f"{$outline:11s} \n")
end
end
end
end

Voir le fichier

@ -1,36 +0,0 @@
def print_HTP(H, T, P, filename="output.txt"):
"""
Print matrices to .txt-file (name of file = filename).
H... overall assembled stiffness matrix
T... nodal temperature vector
P... nodal force vector
Make sure, that your system of equations is sorted by
ascending node numbers, i.e., N1 N2 ... N100.
"""
F = open(filename, 'w')
F.write("Stiffness matrix H: \n")
for row in H:
for col in row:
outline = "{0:+8.4e},".format(col)
F.write("{0:11s}".format(str(outline)))
F.write("\n")
F.write("Temperature T: \n")
for row in T:
for col in row:
outline = "{0:+8.4e},".format(col)
F.write("{0:11s} \n".format(str(outline)))
F.write("Force vector P: \n")
for row in P:
for col in row:
outline = "{0:+8.4e},".format(col)
F.write("{0:11s} \n".format(str(outline)))
F.close()
return None

94
Exercise_04/run.jl Fichier normal
Voir le fichier

@ -0,0 +1,94 @@
include("./fem.jl")
include("./Parameters.jl")
include("./print_HTP.jl")
using .FEM
using GLMakie
using Makie.GeometryBasics
@enum Variation BASIC V1 V2 V3 V4_div V4_mul
function solve(name::String, variation::Variation)
div = 9
H = zeros(Float64,(div+1)^2, (div+1)^2)
(nodes, elements) = tri_tiles(Parameters.L, div, variation==V1, variation==V2, variation==V3)
for (index, el) in enumerate(elements)
Hₑ = stiffness(el)
if variation == V4_div && index in Parameters.elₘ
Hₑ /= Parameters.c
elseif variation == V4_mul && index in Parameters.elₘ
Hₑ *= Parameters.c
end
for i in 1:3
for j in 1:3
H[el.nodes[i].index, el.nodes[j].index] += Hₑ[i,j]
end
end
end
P = zeros(Float64, 90)
# impose neumann conditions on top edge
# adapted from https://mathoverflow.net/questions/5085/how-to-apply-neuman-boundary-condition-to-finite-element-method-problems
# maybe check if this actually makes sense
nᵧ = -Parameters.q / Parameters.k
# skip=2 since only every second element has a edge along the bottom: ◺◹
for ∂_el in elements[1:2:18]
n1 = ∂_el.nodes[1]
n2 = ∂_el.nodes[2]
l = abs(n2.x - n1.x)
P[n1.index] += nᵧ*l/2
P[n2.index] += nᵧ*l/2
end
rhs = P - H[1:90,91:100]*fill(Parameters.T, 10,1)
T = vec(H[1:90,1:90]\rhs)
append!(T, fill(Parameters.T, 10))
reaction_forces = H[91:100,:]*T
centers = center.(elements)
gradients = map(el -> gradient(el, T), elements)
flux = gradients .* -1
norm = maximum(map(g-> sqrt(g[1]^2 + g[2]^2), gradients))/(Parameters.L/div)*2.5
gradients ./= norm
flux ./= norm
set_theme!(theme_black())
f = Figure(resolution = (1536, 1024))
tris = map(e->Polygon([p(e.nodes[1]), p(e.nodes[2]), p(e.nodes[3])]), elements)
poly(f[1, 1], tris, color=:transparent, linestyle=:solid, strokewidth=0.8, strokecolor=:white, transparency=true)
xs = map(n->n.x, nodes)
ys = map(n->n.y, nodes)
xs = reshape(xs, (div+1, div+1))
ys = reshape(ys, (div+1, div+1))
Ts = reshape(T, (div+1, div+1))
surface(f[2, 1], xs, ys, Ts, colormap=:matter, axis=(type=Axis3,))
contour(f[1:2,2:3], map(n->n.x,nodes), map(n->n.y,nodes), T, levels=16, colormap=:matter)
arrows!(f[1:2,2:3], centers, gradients, arrowcolor=:red, linecolor=:red)
arrows!(f[1:2,2:3], centers, flux, arrowcolor=:blue, linecolor=:blue)
save("plots/$name.png", current_figure())
print_HTP(H, T, P, "txt/htp_$name.txt")
end
solve("baseline", BASIC)
solve("variation1", V1)
solve("variation2", V2)
solve("variation3", V3)
solve("variation4_div", V4_div)
solve("variation4_mul", V4_mul)

0
Exercise_04/txt/.keep Fichier normal
Voir le fichier

10193
Exercise_04/txt/htp_baseline.txt Fichier normal

Fichier diff supprimé car celui-ci est trop grand Voir la Diff

10193
Exercise_04/txt/htp_variation1.txt Fichier normal

Fichier diff supprimé car celui-ci est trop grand Voir la Diff

10193
Exercise_04/txt/htp_variation2.txt Fichier normal

Fichier diff supprimé car celui-ci est trop grand Voir la Diff

10193
Exercise_04/txt/htp_variation3.txt Fichier normal

Fichier diff supprimé car celui-ci est trop grand Voir la Diff

Fichier diff supprimé car celui-ci est trop grand Voir la Diff

Fichier diff supprimé car celui-ci est trop grand Voir la Diff