Balaje

/* 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.

Balaje

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

Balaje

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

Balaje

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)

Balaje

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)

Balaje

/* 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.;

Balaje

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

Balaje

Balaje

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),