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@Balaje
Balaje / PlotSolution.jl
Last active Nov 24, 2021
A Julia script to solve a Hamilton Jacobi Equation using the Rouy and Tourin Scheme.
View PlotSolution.jl
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),
@Balaje
Balaje / blog-script.jl
Last active Aug 20, 2021
Interpolation Algorithm in Gridap
View blog-script.jl
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 / mixed_dg_freefem.cpp
Created Jul 29, 2021
Mixed DG method for Biharmonic equation using FreeFem
View mixed_dg_freefem.cpp
/* 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
Balaje / dgmethod.jl
Last active Aug 14, 2021
Julia program to verify the convergence rate of mixed DG method for biharmonic equation
View dgmethod.jl
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
Balaje / phaseportrait_unicode.jl
Last active Jul 9, 2021
Complex Plots with UnicodePlots.jl
View phaseportrait_unicode.jl
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
Balaje / ruletest.jl
Last active Jul 2, 2021
SymbolicUtils Test
View ruletest.jl
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
Balaje / poisson.jl
Created Mar 28, 2021
Julia code to extract the coefficients of the heat equation.
View poisson.jl
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
View ff++.cpp
/* 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.