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/* Solve the poisson problem | |
on a circle with homogeneous boundary conditions | |
and f = x*y | |
NOTE : The extension .cpp is used only | |
for illustration in github gists as | |
syntax highlighting is not available for FreeFEM++. | |
The actual extension for FreeFEM++ is .edp. | |
If you want to run the file, download it as ff++.edp and run it. |
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using ModelingToolkit | |
@parameters x y z | |
@variables u(..) # Need to choose u but user can pass the argument | |
Dx=Differential(x) | |
Dy=Differential(y) | |
Dz=Differential(z) | |
Dxx=Differential(x)^2 |
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using ModelingToolkit | |
using SymbolicUtils | |
@syms w x y z | |
# Rule using exp | |
rexp=@rule exp(~~xs) => ~~xs | |
A=rexp(exp(10*sin(w)+exp(z))) # Returns 10*sin(w)+exp(z) | |
# Rule using Differential |
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using UnicodePlots | |
using ComplexPhasePortrait | |
nx = 1000 | |
x = range(-1, stop=1, length=nx) | |
Z = x' .+ reverse(x)*im | |
f = z -> (z - 0.5im)^2 * (z + 0.5+0.5im)/z | |
fz = f.(Z) |
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using Gridap | |
using Plots | |
using Gridap: ∇ | |
using Gridap: Δ | |
using LinearAlgebra | |
using Gridap: mean | |
# Define the manufactured solution | |
u(x) = 1000*(x[1]^4*(1-x[1])^4*x[2]^4*(1-x[2])^4*x[3]^4*(1-x[3])^4) |
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/* Program to solve the Biharmonic equation | |
\Delta^2 u = f(x,y) in \Omega | |
with u = \Grad u.n = 0 on boundary | |
*/ | |
include "getARGV.idp" | |
load "Element_P3dc" | |
load "Element_P4dc" | |
load "Element_P4" | |
verbosity = 0.; |
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using Pkg | |
Pkg.add("Gridap") | |
Pkg.add("StaticArrays") | |
Pkg.add("Random") | |
using Gridap | |
using Gridap.Algebra | |
using Gridap.CellData | |
using Gridap.Fields | |
using Gridap.Arrays |
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function PlotSolution(fontsize) | |
fig = Figure(fontsize=fontsize, resolution=(1000,700)) | |
ax1 = GLMakie.Axis(fig[1, 1]); | |
ax2 = GLMakie.Axis3(fig[1, 2]); | |
ax3 = GLMakie.Axis3(fig[2, 1]); | |
ax4 = GLMakie.Axis3(fig[2, 2]); | |
image!(ax1, x, y, collect(imrotate(img,π/2))) | |
GLMakie.surface!(ax2, x[2:end-1], y[2:end-1], -0.8*U[2:end-1,2:end-1], | |
colormap=(:gray,:gray), |