Mercurial > repos > public > sbplib_julia

annotate examples/wave_eq.jl @ 876:4f3924293894 laplace_benchmarks

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Add examples and benchmarks folders
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 27 Jan 2022 11:00:31 +0100
parents wave_eq.jl@7e9ebd572deb
children
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874
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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1 using Sbplib.Grids, Sbplib.SbpOperators, Sbplib.LazyTensors, Sbplib.RegionIndices
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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2 using OrdinaryDiffEq, Plots, Printf, Base.Threads
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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3
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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4 function apply_tm!(f,u,tm,ind)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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5 for I in ind
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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6 @inbounds f[I] = (tm*u)[I]
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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7 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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8 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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9
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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10 function apply_tm_all_regions!(f,u,tm,rinds)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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11 apply_tm!(f,u,tm,rinds[1])
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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12 apply_tm!(f,u,tm,rinds[2])
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13 apply_tm!(f,u,tm,rinds[3])
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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14 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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15
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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16 region_indices(L, N, ::Lower) = map(x->Index{Lower}(x),1:closure_size(L))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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17 region_indices(L, N, ::Interior) = map(x->Index{Interior}(x),closure_size(L)+1:N-closure_size(L))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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18 region_indices(L, N, ::Upper) = map(x->Index{Upper}(x),N-closure_size(L)+1:N)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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19
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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20 function get_region_indices(L,N)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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21 ind_lower = region_indices(L, N, Lower())
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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22 ind_interior = region_indices(L, N, Interior())
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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23 ind_upper = region_indices(L, N, Upper())
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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24 return (ind_lower, ind_interior, ind_upper)
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25 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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26
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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27 function wave_eq_sim(alg,T,CFL)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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28 # Domain
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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29 N = 101
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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30 g = EquidistantGrid(N,0.,1.)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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31 dx = min(spacing(g)...)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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32
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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33 # Spatial discretization
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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34 Δ = Laplace(g,sbp_operators_path()*"standard_diagonal.toml"; order=4)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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35 (id_l, id_r) = boundary_identifiers(g)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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36 SAT_l = boundary_condition(Δ,id_l,NeumannBC())
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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37 SAT_r = boundary_condition(Δ,id_r,NeumannBC())
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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38 tm = (Δ + SAT_l + SAT_r)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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39
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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40 # RHS function
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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41 rinds = get_region_indices(Δ,N)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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42 function f(du,u,p,t)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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43 du[1:N] .= u[N+1:end]
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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44 apply_tm_all_regions!(view(du,N+1:2*N), view(u,1:N), tm, rinds)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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45 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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46 # Initial condition
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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47 sigma = 0.1
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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48 ic_u = x->1/(sigma*sqrt(2*pi))*exp(-1/2*((x-0.5)^2/sigma^2))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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49 ic_u_t = x->0
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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50 w0 = [evalOn(g,ic_u);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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51 evalOn(g,ic_u_t)]
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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52 # Setup ODE and solve
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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53 tspan = (0.,T)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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54 prob = ODEProblem(f,w0,tspan)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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55 sol = solve(prob, alg, dt=CFL*dx, saveat=0.05)
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56
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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57 # Plotting
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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58 x = [x[1] for x in points(g)]
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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59 anim = @animate for i ∈ eachindex(sol.t)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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60 u_i = sol.u[i]
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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61 plot(x, u_i[1:N], ylims = (0,4), lw=3,ls=:dash,label="",title=@sprintf("u at t = %.3f", sol.t[i]))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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62 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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63 gif(anim, "wave.gif", fps = 15)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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64 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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65
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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66 wave_eq_sim(CarpenterKennedy2N54(),1.,0.25)
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