2D Nonlinear Poisson equation with boundary reaction

module NonlinearPoisson2D_BoundaryReaction

using Printf
using TwoPointFluxFVM
const Node=TwoPointFluxFVM.Node
const Edge=TwoPointFluxFVM.Edge

if isinteractive()
    using PyPlot
end


mutable struct Physics
    breaction::Function
    flux::Function
    source::Function
    storage::Function
    eps::Float64
    k::Float64
    Physics()=new()
end






function main(;n=10,pyplot=false,verbose=false)
    h=1.0/convert(Float64,n)
    X=collect(0.0:h:1.0)
    Y=collect(0.0:h:1.0)
    
    geom=TwoPointFluxFVM.Grid(X,Y)

    
    physics=Physics()
    physics.eps=1.0e-2
    physics.k=1.0
    
    physics.breaction=function(physics,node,f,u)
        if  node.region==2
            f[1]=physics.k*(u[1]-u[2])
            f[2]=physics.k*(u[2]-u[1])
        else
            f[1]=0        
            f[2]=0
        end
    end
    
    physics.flux=function(physics,edge,f,uk,ul)
        f[1]=physics.eps*(uk[1]-ul[1])
        f[2]=physics.eps*(uk[2]-ul[2])
    end 
    
    physics.source=function(physics,node,f)
        x1=node.coord[1]-0.5
        x2=node.coord[2]-0.5
        f[1]=exp(-20*(x1^2+x2^2))
    end 
    
    physics.storage=function(physics,node, f,u)
        f[1]=u[1]
        f[2]=u[2]
    end

    
    sys=TwoPointFluxFVM.System(geom,physics,2)
    add_species(sys,1,[1])
    add_species(sys,2,[1])

    
    inival=unknowns(sys)
    inival.=0.0
    
    
    control=TwoPointFluxFVM.NewtonControl()
    control.verbose=verbose
    control.tol_linear=1.0e-5
    control.max_lureuse=0
    tstep=0.01
    time=0.0
    istep=0
    u25=0
    while time<1
        time=time+tstep
        U=solve(sys,inival,control=control,tstep=tstep)
        inival.=U
        # for i in eachindex(U)
        #     inival[i]=U[i]
        # end
        if verbose
            @printf("time=%g\n",time)
        end

        tstep*=1.0
        istep=istep+1
        u25=U[25]
        if pyplot && istep%10 == 0
            if verbose
                @printf("max1=%g max2=%g\n",maximum(U[1,:]),maximum(U[2,:]))
            end
            PyPlot.clf()
            subplot(211)
            contourf(X,Y,reshape(U[1,:],length(X),length(Y)), cmap=ColorMap("hot"), vmin=0.0, vmax=0.6)
            colorbar()
            subplot(212)
            contourf(X,Y,reshape(U[2,:],length(X),length(Y)), cmap=ColorMap("hot"), vmin=0.0, vmax=0.02)
            colorbar()

            pause(1.0e-10)
        end
    end
    return u25
end
end