Types and functions

struct VlasovSolution1D1V

Data structure that stores the solution of the Vlasov problem of one dimension in both physical space and phase space.

• values::Vector{Matrix{Float64}}

• times::Vector{Float64}

• energy::Vector{Float64}

• saveat::Float64

advection!(fp, fi, mesh, interp, v, dt)

advection!(f, grid, v, dt; p)

Advect the distribution function f with velocity v along first f dimension with a time step dt. Interpolation method uses bspline periodic of order 5 by default. Real type version.

advection!(f, grid, v, dt; p)

Advect the distribution function f with velocity v along first f dimension with a time step dt. Interpolation method uses bspline periodic of order 5 by default. Complex type version.

advection_x!(f, adv, e, v, dt)

advection_v!(fᵗ, adv, e, dt)

solve(problem, stepper, dt, nsteps)

solve(problem, stepper, dt, nsteps)

compute_e(f)

compute Ex using that -ik*Ex = rho

compute_rho(f)

Compute charge density ρ(x,t) = ∫ f(x,v,t) dv

two_stream_instability!(f; eps, xi, v0)

struct Fourier <: VlasovSolvers.AbstractMethod

• kx::Vector{Float64}

• kv::Vector{Float64}

struct BSLLagrange <: VlasovSolvers.AbstractMethod

• order::Int64

• interp::SemiLagrangian.Lagrange

bspline(p, j, x)

Return the value at x in [0,1] of the B-spline with integer nodes of degree p with support starting at j. Implemented recursively using the De Boor's Algorithm

\[B_{i,0}(x) := \left\{ \begin{matrix} 1 & \mathrm{if} \quad t_i ≤ x < t_{i+1} \\ 0 & \mathrm{otherwise} \end{matrix} \right.\]

\[B_{i,p}(x) := \frac{x - t_i}{t_{i+p} - t_i} B_{i,p-1}(x) + \frac{t_{i+p+1} - x}{t_{i+p+1} - t_{i+1}} B_{i+1,p-1}(x).\]