Using an implicit-explicit (IMEX) Runge-Kutta solver based on Ariadne with Trixi.jl
using Trixi
using Theseus
using CairoMakieNotes: You must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl.
LocalPreferences.jl
[Trixi]
loop_vectorization = false
backend = "static"@assert Trixi._PREFERENCE_THREADING !== :polyester
@assert !Trixi._PREFERENCE_LOOPVECTORIZATIONFirst call to load callbacks
trixi_include(@__MODULE__, joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_diffusion.jl"), sol = nothing);
stepsize_callback = StepsizeCallback(cfl = 1.0)
callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback)
trixi_include(@__MODULE__, joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_diffusion.jl"), sol = nothing, callbacks = callbacks);
###############################################################################[ Info: You just called `trixi_include`. Julia may now compile the code, please be patient.
[ Info: You just called `trixi_include`. Julia may now compile the code, please be patient.run the simulation
sol = solve(
ode,
Theseus.SSP3433();
dt = 0.01, # solve needs some value here but it will be overwritten by the stepsize_callback
ode_default_options()..., callback = callbacks,
krylov_algo = :gmres,
);
████████╗██████╗ ██╗██╗ ██╗██╗
╚══██╔══╝██╔══██╗██║╚██╗██╔╝██║
██║ ██████╔╝██║ ╚███╔╝ ██║
██║ ██╔══██╗██║ ██╔██╗ ██║
██║ ██║ ██║██║██╔╝ ██╗██║
╚═╝ ╚═╝ ╚═╝╚═╝╚═╝ ╚═╝╚═╝
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ SemidiscretizationHyperbolicParabolic │
│ ═════════════════════════════════════ │
│ #spatial dimensions: ……………………………………… 2 │
│ mesh: ……………………………………………………………………………… TreeMesh{2, Trixi.SerialTree{2, Float64}} with length 341 │
│ hyperbolic equations: …………………………………… LinearScalarAdvectionEquation2D │
│ parabolic equations: ……………………………………… LaplaceDiffusion2D │
│ initial condition: …………………………………………… initial_condition_diffusive_convergence_test │
│ source terms: ………………………………………………………… nothing │
│ source terms parabolic: ……………………………… nothing │
│ solver: ………………………………………………………………………… DG │
│ parabolic solver: ……………………………………………… ParabolicFormulationBassiRebay1 │
│ total #DOFs per field: ………………………………… 4096 │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ TreeMesh{2, Trixi.SerialTree{2, Float64}} │
│ ═════════════════════════════════════════ │
│ center: ………………………………………………………………………… [0.0, 0.0] │
│ length: ………………………………………………………………………… 2.0 │
│ periodicity: …………………………………………………………… (true, true) │
│ current #cells: …………………………………………………… 341 │
│ #leaf-cells: …………………………………………………………… 256 │
│ current capacity: ……………………………………………… 30000 │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ LinearScalarAdvectionEquation2D │
│ ═══════════════════════════════ │
│ #variables: ……………………………………………………………… 1 │
│ │ variable 1: ………………………………………………………… scalar │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ DG{Float64} │
│ ═══════════ │
│ basis: …………………………………………………………………………… LobattoLegendreBasis{Float64}(polydeg=3) │
│ mortar: ………………………………………………………………………… LobattoLegendreMortarL2{Float64}(polydeg=3) │
│ surface integral: ……………………………………………… SurfaceIntegralWeakForm │
│ │ surface flux: …………………………………………………… FluxLaxFriedrichs(max_abs_speed) │
│ volume integral: ………………………………………………… VolumeIntegralWeakForm │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ AnalysisCallback │
│ ════════════════ │
│ interval: …………………………………………………………………… 100 │
│ analyzer: …………………………………………………………………… LobattoLegendreAnalyzer{Float64}(polydeg=6) │
│ │ error 1: ………………………………………………………………… l2_error │
│ │ error 2: ………………………………………………………………… linf_error │
│ │ integral 1: ………………………………………………………… entropy_timederivative │
│ save analysis to file: ………………………………… no │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ AliveCallback │
│ ═════════════ │
│ interval: …………………………………………………………………… 10 │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ StepsizeCallback │
│ ════════════════ │
│ CFL Hyperbolic: …………………………………………………… Returns{Float64}(1.0) │
│ CFL Parabolic: ……………………………………………………… Returns{Float64}(0.0) │
│ Interval: …………………………………………………………………… 1 │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ Time integration │
│ ════════════════ │
│ Start time: ……………………………………………………………… 0.0 │
│ Final time: ……………………………………………………………… 1.5 │
│ time integrator: ………………………………………………… SSP3433 │
│ adaptive: …………………………………………………………………… false │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ Environment information │
│ ═══════════════════════ │
│ #threads: …………………………………………………………………… 1 │
│ threading backend: …………………………………………… static │
│ LoopVectorization: …………………………………………… disabled │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 0 run time: 6.91000000e-07 s
Δt: 1.00000000e-02 └── GC time: 0.00000000e+00 s (0.000%)
sim. time: 0.00000000e+00 (0.000%) time/DOF/rhs!: NaN s
PID: Inf s
#DOFs per field: 4096 alloc'd memory: 930.199 MiB
#elements: 256 device memory: 0.000 MiB
Variable: scalar
L2 error: 3.94120825e-06
Linf error: 1.23670425e-05
∑∂S/∂U ⋅ Uₜ : -1.23370054e-01
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 10 │ Δt: 1.2500e-02 │ sim. time: 1.2500e-01 (8.333%) │ run time: 4.1013e+01 s
#timesteps: 20 │ Δt: 1.2500e-02 │ sim. time: 2.5000e-01 (16.667%) │ run time: 4.1130e+01 s
#timesteps: 30 │ Δt: 1.2500e-02 │ sim. time: 3.7500e-01 (25.000%) │ run time: 4.1244e+01 s
#timesteps: 40 │ Δt: 1.2500e-02 │ sim. time: 5.0000e-01 (33.333%) │ run time: 4.1363e+01 s
#timesteps: 50 │ Δt: 1.2500e-02 │ sim. time: 6.2500e-01 (41.667%) │ run time: 4.1479e+01 s
#timesteps: 60 │ Δt: 1.2500e-02 │ sim. time: 7.5000e-01 (50.000%) │ run time: 4.1601e+01 s
#timesteps: 70 │ Δt: 1.2500e-02 │ sim. time: 8.7500e-01 (58.333%) │ run time: 4.1730e+01 s
#timesteps: 80 │ Δt: 1.2500e-02 │ sim. time: 1.0000e+00 (66.667%) │ run time: 4.1861e+01 s
#timesteps: 90 │ Δt: 1.2500e-02 │ sim. time: 1.1250e+00 (75.000%) │ run time: 4.2001e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 100 run time: 4.21450107e+01 s
Δt: 1.25000000e-02 └── GC time: 3.37824780e-01 s (0.802%)
sim. time: 1.25000000e+00 (83.333%) time/DOF/rhs!: 7.33259618e-08 s
PID: 2.57226507e-05 s
#DOFs per field: 4096 alloc'd memory: 865.411 MiB
#elements: 256 device memory: 0.000 MiB
Variable: scalar
L2 error: 4.05753105e-05
Linf error: 8.89682358e-05
∑∂S/∂U ⋅ Uₜ : -1.04542977e-02
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 110 │ Δt: 1.2500e-02 │ sim. time: 1.3750e+00 (91.667%) │ run time: 4.2296e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 120 run time: 4.24640372e+01 s
Δt: 1.25000000e-02 └── GC time: 3.46993672e-01 s (0.817%)
sim. time: 1.50000000e+00 (100.000%) time/DOF/rhs!: 7.31030181e-08 s
PID: 9.70270511e-07 s
#DOFs per field: 4096 alloc'd memory: 883.060 MiB
#elements: 256 device memory: 0.000 MiB
Variable: scalar
L2 error: 3.88015754e-05
Linf error: 2.33956836e-04
∑∂S/∂U ⋅ Uₜ : -6.38139917e-03
────────────────────────────────────────────────────────────────────────────────────────────────────
────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl simulation finished. Final time: 1.5 Time steps: 120 (accepted), 120 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────
─────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl Time Allocations
─────────────────────── ────────────────────────
Tot / % measured: 42.5s / 2.8% 2.88GiB / 0.2%
Section ncalls time %tot avg alloc %tot avg
─────────────────────────────────────────────────────────────────────────────────────────
parabolic rhs! 5.59k 1.13s 95.8% 202μs 9.00KiB 0.1% 1.65B
calculate gradient 5.59k 502ms 42.5% 89.7μs 3.33KiB 0.0% 0.61B
volume integral 5.59k 317ms 26.8% 56.7μs 0.00B 0.0% 0.00B
Jacobian 5.59k 56.5ms 4.8% 10.1μs 0.00B 0.0% 0.00B
surface integral 5.59k 39.9ms 3.4% 7.14μs 0.00B 0.0% 0.00B
interface flux 5.59k 36.8ms 3.1% 6.59μs 0.00B 0.0% 0.00B
prolong2interfaces 5.59k 33.9ms 2.9% 6.06μs 0.00B 0.0% 0.00B
reset gradients 5.59k 11.4ms 1.0% 2.04μs 0.00B 0.0% 0.00B
~calculate gradient~ 5.59k 5.14ms 0.4% 919ns 3.33KiB 0.0% 0.61B
prolong2mortars 5.59k 465μs 0.0% 83.1ns 0.00B 0.0% 0.00B
prolong2boundaries 5.59k 405μs 0.0% 72.4ns 0.00B 0.0% 0.00B
mortar flux 5.59k 299μs 0.0% 53.4ns 0.00B 0.0% 0.00B
boundary flux 5.59k 168μs 0.0% 30.0ns 0.00B 0.0% 0.00B
volume integral 5.59k 336ms 28.4% 60.0μs 0.00B 0.0% 0.00B
calculate parabolic fluxes 5.59k 109ms 9.2% 19.5μs 0.00B 0.0% 0.00B
transform variables 5.59k 36.9ms 3.1% 6.60μs 0.00B 0.0% 0.00B
interface flux 5.59k 36.7ms 3.1% 6.55μs 0.00B 0.0% 0.00B
prolong2interfaces 5.59k 33.8ms 2.9% 6.05μs 0.00B 0.0% 0.00B
surface integral 5.59k 33.6ms 2.8% 6.00μs 0.00B 0.0% 0.00B
Jacobian 5.59k 28.6ms 2.4% 5.11μs 0.00B 0.0% 0.00B
~parabolic rhs!~ 5.59k 7.75ms 0.7% 1.38μs 5.67KiB 0.1% 1.04B
reset ∂u/∂t 5.59k 5.98ms 0.5% 1.07μs 0.00B 0.0% 0.00B
prolong2mortars 5.59k 454μs 0.0% 81.2ns 0.00B 0.0% 0.00B
prolong2boundaries 5.59k 350μs 0.0% 62.5ns 0.00B 0.0% 0.00B
mortar flux 5.59k 340μs 0.0% 60.8ns 0.00B 0.0% 0.00B
source terms parabolic 5.59k 172μs 0.0% 30.7ns 0.00B 0.0% 0.00B
boundary flux 5.59k 163μs 0.0% 29.1ns 0.00B 0.0% 0.00B
rhs! 480 46.8ms 4.0% 97.4μs 4.78KiB 0.1% 10.2B
volume integral 480 31.9ms 2.7% 66.5μs 0.00B 0.0% 0.00B
interface flux 480 3.85ms 0.3% 8.02μs 0.00B 0.0% 0.00B
surface integral 480 3.39ms 0.3% 7.07μs 0.00B 0.0% 0.00B
prolong2interfaces 480 3.31ms 0.3% 6.90μs 0.00B 0.0% 0.00B
Jacobian 480 3.23ms 0.3% 6.72μs 0.00B 0.0% 0.00B
~rhs!~ 480 575μs 0.0% 1.20μs 4.78KiB 0.1% 10.2B
reset ∂u/∂t 480 358μs 0.0% 746ns 0.00B 0.0% 0.00B
prolong2mortars 480 45.5μs 0.0% 94.7ns 0.00B 0.0% 0.00B
prolong2boundaries 480 38.6μs 0.0% 80.4ns 0.00B 0.0% 0.00B
boundary flux 480 28.8μs 0.0% 60.1ns 0.00B 0.0% 0.00B
mortar flux 480 25.8μs 0.0% 53.7ns 0.00B 0.0% 0.00B
source terms 480 14.5μs 0.0% 30.3ns 0.00B 0.0% 0.00B
analyze solution 3 3.19ms 0.3% 1.06ms 7.24MiB 99.6% 2.41MiB
calculate dt 121 120μs 0.0% 996ns 17.0KiB 0.2% 144B
─────────────────────────────────────────────────────────────────────────────────────────This page was generated using Literate.jl.