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# Balaje K Balaje

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Last active Nov 24, 2021
A Julia script to solve a Hamilton Jacobi Equation using the Rouy and Tourin Scheme.
View PlotSolution.jl
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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),
Last active Oct 22, 2021
Last active Aug 20, 2021
Interpolation Algorithm in Gridap
View blog-script.jl
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Created Jul 29, 2021
Mixed DG method for Biharmonic equation using FreeFem
View mixed_dg_freefem.cpp
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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.;
Last active Aug 14, 2021
Julia program to verify the convergence rate of mixed DG method for biharmonic equation
View dgmethod.jl
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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)
Last active Jul 9, 2021
Complex Plots with UnicodePlots.jl
View phaseportrait_unicode.jl
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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)
Last active Jul 2, 2021
SymbolicUtils Test
View ruletest.jl
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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
Created Mar 28, 2021
Julia code to extract the coefficients of the heat equation.
View poisson.jl
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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
Last active Jul 24, 2016
View ff++.cpp
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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.