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,
);
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┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ 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: ………………………………… ViscousFormulationBassiRebay1 │
│ 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 │
│ maximum #cells: ……………………………………… 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 Advective: ………………………………………… Returns{Float64}(1.0) │
│ CFL Diffusive: ………………………………………… 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: 8.22000000e-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: 502.504 MiB
#elements: 256
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: 6.0621e+01 s
#timesteps: 20 │ Δt: 1.2500e-02 │ sim. time: 2.5000e-01 (16.667%) │ run time: 6.0748e+01 s
#timesteps: 30 │ Δt: 1.2500e-02 │ sim. time: 3.7500e-01 (25.000%) │ run time: 6.0869e+01 s
#timesteps: 40 │ Δt: 1.2500e-02 │ sim. time: 5.0000e-01 (33.333%) │ run time: 6.0998e+01 s
#timesteps: 50 │ Δt: 1.2500e-02 │ sim. time: 6.2500e-01 (41.667%) │ run time: 6.1122e+01 s
#timesteps: 60 │ Δt: 1.2500e-02 │ sim. time: 7.5000e-01 (50.000%) │ run time: 6.1255e+01 s
#timesteps: 70 │ Δt: 1.2500e-02 │ sim. time: 8.7500e-01 (58.333%) │ run time: 6.1395e+01 s
#timesteps: 80 │ Δt: 1.2500e-02 │ sim. time: 1.0000e+00 (66.667%) │ run time: 6.1539e+01 s
#timesteps: 90 │ Δt: 1.2500e-02 │ sim. time: 1.1250e+00 (75.000%) │ run time: 6.1693e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 100 run time: 6.18519952e+01 s
Δt: 1.25000000e-02 └── GC time: 7.02762678e-01 s (1.136%)
sim. time: 1.25000000e+00 (83.333%) time/DOF/rhs!: 7.39232136e-08 s
PID: 3.77506770e-05 s
#DOFs per field: 4096 alloc'd memory: 529.408 MiB
#elements: 256
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: 6.2012e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 120 run time: 6.21902065e+01 s
Δt: 1.25000000e-02 └── GC time: 7.16976786e-01 s (1.153%)
sim. time: 1.50000000e+00 (100.000%) time/DOF/rhs!: 7.34283131e-08 s
PID: 1.02873485e-06 s
#DOFs per field: 4096 alloc'd memory: 548.035 MiB
#elements: 256
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: 62.2s / 1.9% 4.22GiB / 0.2%
Section ncalls time %tot avg alloc %tot avg
───────────────────────────────────────────────────────────────────────────────────────
parabolic rhs! 5.59k 1.14s 95.8% 204μs 9.00KiB 0.1% 1.65B
calculate gradient 5.59k 503ms 42.1% 89.9μs 3.33KiB 0.0% 0.61B
volume integral 5.59k 315ms 26.4% 56.3μs 0.00B 0.0% 0.00B
Jacobian 5.59k 55.7ms 4.7% 10.0μs 0.00B 0.0% 0.00B
surface integral 5.59k 39.8ms 3.3% 7.11μs 0.00B 0.0% 0.00B
interface flux 5.59k 38.3ms 3.2% 6.85μs 0.00B 0.0% 0.00B
prolong2interfaces 5.59k 34.5ms 2.9% 6.17μs 0.00B 0.0% 0.00B
reset gradients 5.59k 12.8ms 1.1% 2.29μs 0.00B 0.0% 0.00B
~calculate gradient~ 5.59k 5.46ms 0.5% 977ns 3.33KiB 0.0% 0.61B
prolong2mortars 5.59k 475μs 0.0% 84.9ns 0.00B 0.0% 0.00B
prolong2boundaries 5.59k 397μs 0.0% 71.0ns 0.00B 0.0% 0.00B
mortar flux 5.59k 354μs 0.0% 63.2ns 0.00B 0.0% 0.00B
boundary flux 5.59k 163μs 0.0% 29.2ns 0.00B 0.0% 0.00B
volume integral 5.59k 341ms 28.5% 60.9μs 0.00B 0.0% 0.00B
calculate viscous fluxes 5.59k 109ms 9.2% 19.6μs 0.00B 0.0% 0.00B
interface flux 5.59k 38.6ms 3.2% 6.90μs 0.00B 0.0% 0.00B
transform variables 5.59k 37.2ms 3.1% 6.65μs 0.00B 0.0% 0.00B
surface integral 5.59k 36.3ms 3.0% 6.48μs 0.00B 0.0% 0.00B
prolong2interfaces 5.59k 34.0ms 2.8% 6.07μs 0.00B 0.0% 0.00B
Jacobian 5.59k 28.6ms 2.4% 5.12μs 0.00B 0.0% 0.00B
~parabolic rhs!~ 5.59k 7.88ms 0.7% 1.41μs 5.67KiB 0.1% 1.04B
reset ∂u/∂t 5.59k 6.54ms 0.5% 1.17μs 0.00B 0.0% 0.00B
prolong2mortars 5.59k 493μs 0.0% 88.0ns 0.00B 0.0% 0.00B
prolong2boundaries 5.59k 351μs 0.0% 62.8ns 0.00B 0.0% 0.00B
mortar flux 5.59k 314μs 0.0% 56.1ns 0.00B 0.0% 0.00B
boundary flux 5.59k 168μs 0.0% 30.1ns 0.00B 0.0% 0.00B
source terms parabolic 5.59k 163μs 0.0% 29.2ns 0.00B 0.0% 0.00B
rhs! 480 46.8ms 3.9% 97.5μs 4.78KiB 0.1% 10.2B
volume integral 480 31.6ms 2.6% 65.9μs 0.00B 0.0% 0.00B
interface flux 480 3.85ms 0.3% 8.01μs 0.00B 0.0% 0.00B
surface integral 480 3.64ms 0.3% 7.59μs 0.00B 0.0% 0.00B
prolong2interfaces 480 3.31ms 0.3% 6.89μs 0.00B 0.0% 0.00B
Jacobian 480 3.23ms 0.3% 6.72μs 0.00B 0.0% 0.00B
~rhs!~ 480 582μs 0.0% 1.21μs 4.78KiB 0.1% 10.2B
reset ∂u/∂t 480 367μs 0.0% 765ns 0.00B 0.0% 0.00B
mortar flux 480 65.5μs 0.0% 137ns 0.00B 0.0% 0.00B
prolong2mortars 480 50.1μs 0.0% 104ns 0.00B 0.0% 0.00B
prolong2boundaries 480 27.0μs 0.0% 56.3ns 0.00B 0.0% 0.00B
boundary flux 480 14.2μs 0.0% 29.6ns 0.00B 0.0% 0.00B
source terms 480 14.0μs 0.0% 29.1ns 0.00B 0.0% 0.00B
analyze solution 3 3.53ms 0.3% 1.18ms 7.24MiB 99.6% 2.41MiB
calculate dt 121 158μs 0.0% 1.31μs 17.0KiB 0.2% 144B
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