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 = 0.5)
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.ARS222(); # ARS111, ARS222, ARS443
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}(0.5) │
│ CFL Diffusive: ………………………………………… Returns{Float64}(0.0) │
│ Interval: ……………………………………………………… 1 │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ Time integration │
│ ════════════════ │
│ Start time: ………………………………………………… 0.0 │
│ Final time: ………………………………………………… 1.5 │
│ time integrator: …………………………………… ARS222 │
│ adaptive: ……………………………………………………… false │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ Environment information │
│ ═══════════════════════ │
│ #threads: ……………………………………………………… 1 │
│ threading backend: ……………………………… static │
│ LoopVectorization: ……………………………… disabled │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 0 run time: 3.49508457e-01 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: 1163.905 MiB
#elements: 256
Variable: scalar
L2 error: 3.94120825e-06
Linf error: 1.23670425e-05
∑∂S/∂U ⋅ Uₜ : -1.23370054e-01
────────────────────────────────────────────────────────────────────────────────────────────────────
┌ Warning: TODO forward zero-set of memorycopy used memset rather than runtime type
│ Caused by:
│ Stacktrace:
│ [1] copy
│ @ ./array.jl:350
│ [2] unaliascopy
│ @ ./abstractarray.jl:1516
│ [3] unalias
│ @ ./abstractarray.jl:1500
│ [4] broadcast_unalias
│ @ ./broadcast.jl:946
│ [5] preprocess
│ @ ./broadcast.jl:953
│ [6] preprocess_args
│ @ ./broadcast.jl:956
│ [7] preprocess_args
│ @ ./broadcast.jl:955
│ [8] preprocess
│ @ ./broadcast.jl:952
│ [9] preprocess_args
│ @ ./broadcast.jl:956
│ [10] preprocess_args
│ @ ./broadcast.jl:955
│ [11] preprocess
│ @ ./broadcast.jl:952
│ [12] preprocess_args
│ @ ./broadcast.jl:955
│ [13] preprocess
│ @ ./broadcast.jl:952
│ [14] override_bc_copyto!
│ @ ~/.julia/packages/Enzyme/C5rSn/src/compiler/interpreter.jl:818
│ [15] copyto!
│ @ ./broadcast.jl:925
│ [16] materialize!
│ @ ./broadcast.jl:883
│ [17] materialize!
│ @ ./broadcast.jl:880
│ [18] RKIMEX
│ @ ~/work/Ariadne.jl/Ariadne.jl/libs/Theseus/src/imex/imex.jl:33
└ @ Enzyme.Compiler ~/.julia/packages/Enzyme/C5rSn/src/rules/llvmrules.jl:812
┌ Warning: TODO forward zero-set of memorycopy used memset rather than runtime type
│ Caused by:
│ Stacktrace:
│ [1] copy
│ @ ./array.jl:350
│ [2] unaliascopy
│ @ ./abstractarray.jl:1516
│ [3] unalias
│ @ ./abstractarray.jl:1500
│ [4] broadcast_unalias
│ @ ./broadcast.jl:946
│ [5] preprocess
│ @ ./broadcast.jl:953
│ [6] preprocess_args
│ @ ./broadcast.jl:956
│ [7] preprocess_args
│ @ ./broadcast.jl:955
│ [8] preprocess
│ @ ./broadcast.jl:952
│ [9] preprocess_args
│ @ ./broadcast.jl:956
│ [10] preprocess_args
│ @ ./broadcast.jl:955
│ [11] preprocess
│ @ ./broadcast.jl:952
│ [12] override_bc_copyto!
│ @ ~/.julia/packages/Enzyme/C5rSn/src/compiler/interpreter.jl:818
│ [13] copyto!
│ @ ./broadcast.jl:925
│ [14] materialize!
│ @ ./broadcast.jl:883
│ [15] materialize!
│ @ ./broadcast.jl:880
│ [16] RKIMEX
│ @ ~/work/Ariadne.jl/Ariadne.jl/libs/Theseus/src/imex/imex.jl:33
└ @ Enzyme.Compiler ~/.julia/packages/Enzyme/C5rSn/src/rules/llvmrules.jl:812
#timesteps: 10 │ Δt: 6.2500e-03 │ sim. time: 6.2500e-02 (4.167%) │ run time: 5.7836e+01 s
#timesteps: 20 │ Δt: 6.2500e-03 │ sim. time: 1.2500e-01 (8.333%) │ run time: 5.8007e+01 s
#timesteps: 30 │ Δt: 6.2500e-03 │ sim. time: 1.8750e-01 (12.500%) │ run time: 5.8069e+01 s
#timesteps: 40 │ Δt: 6.2500e-03 │ sim. time: 2.5000e-01 (16.667%) │ run time: 5.8103e+01 s
#timesteps: 50 │ Δt: 6.2500e-03 │ sim. time: 3.1250e-01 (20.833%) │ run time: 5.8141e+01 s
#timesteps: 60 │ Δt: 6.2500e-03 │ sim. time: 3.7500e-01 (25.000%) │ run time: 5.8174e+01 s
#timesteps: 70 │ Δt: 6.2500e-03 │ sim. time: 4.3750e-01 (29.167%) │ run time: 5.8214e+01 s
#timesteps: 80 │ Δt: 6.2500e-03 │ sim. time: 5.0000e-01 (33.333%) │ run time: 5.8247e+01 s
#timesteps: 90 │ Δt: 6.2500e-03 │ sim. time: 5.6250e-01 (37.500%) │ run time: 5.8285e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 100 run time: 5.86689206e+01 s
Δt: 6.25000000e-03 └── GC time: 8.72812911e-01 s (1.488%)
sim. time: 6.25000000e-01 (41.667%) time/DOF/rhs!: 7.37983541e-08 s
PID: 4.74595289e-05 s
#DOFs per field: 4096 alloc'd memory: 1172.882 MiB
#elements: 256
Variable: scalar
L2 error: 3.81726799e-04
Linf error: 5.50778812e-04
∑∂S/∂U ⋅ Uₜ : -3.59099416e-02
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 110 │ Δt: 6.2500e-03 │ sim. time: 6.8750e-01 (45.833%) │ run time: 5.8357e+01 s
#timesteps: 120 │ Δt: 6.2500e-03 │ sim. time: 7.5000e-01 (50.000%) │ run time: 5.8391e+01 s
#timesteps: 130 │ Δt: 6.2500e-03 │ sim. time: 8.1250e-01 (54.167%) │ run time: 5.8424e+01 s
#timesteps: 140 │ Δt: 6.2500e-03 │ sim. time: 8.7500e-01 (58.333%) │ run time: 5.8462e+01 s
#timesteps: 150 │ Δt: 6.2500e-03 │ sim. time: 9.3750e-01 (62.500%) │ run time: 5.8496e+01 s
#timesteps: 160 │ Δt: 6.2500e-03 │ sim. time: 1.0000e+00 (66.667%) │ run time: 5.8534e+01 s
#timesteps: 170 │ Δt: 6.2500e-03 │ sim. time: 1.0625e+00 (70.833%) │ run time: 5.8567e+01 s
#timesteps: 180 │ Δt: 6.2500e-03 │ sim. time: 1.1250e+00 (75.000%) │ run time: 5.8606e+01 s
#timesteps: 190 │ Δt: 6.2500e-03 │ sim. time: 1.1875e+00 (79.167%) │ run time: 5.8639e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 200 run time: 5.90278198e+01 s
Δt: 6.25000000e-03 └── GC time: 8.97627060e-01 s (1.521%)
sim. time: 1.25000000e+00 (83.333%) time/DOF/rhs!: 7.38230588e-08 s
PID: 2.91221899e-07 s
#DOFs per field: 4096 alloc'd memory: 1142.403 MiB
#elements: 256
Variable: scalar
L2 error: 4.11963020e-04
Linf error: 5.84938377e-04
∑∂S/∂U ⋅ Uₜ : -1.04524859e-02
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 210 │ Δt: 6.2500e-03 │ sim. time: 1.3125e+00 (87.500%) │ run time: 5.8711e+01 s
#timesteps: 220 │ Δt: 6.2500e-03 │ sim. time: 1.3750e+00 (91.667%) │ run time: 5.8750e+01 s
#timesteps: 230 │ Δt: 6.2500e-03 │ sim. time: 1.4375e+00 (95.833%) │ run time: 5.8783e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 240 run time: 5.91718631e+01 s
Δt: 6.25000000e-03 └── GC time: 9.07402166e-01 s (1.534%)
sim. time: 1.50000000e+00 (100.000%) time/DOF/rhs!: 7.37148779e-08 s
PID: 2.90892360e-07 s
#DOFs per field: 4096 alloc'd memory: 1131.554 MiB
#elements: 256
Variable: scalar
L2 error: 3.86247716e-04
Linf error: 5.47814220e-04
∑∂S/∂U ⋅ Uₜ : -6.38001271e-03
────────────────────────────────────────────────────────────────────────────────────────────────────
────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl simulation finished. Final time: 1.5 Time steps: 240 (accepted), 240 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────
───────────────────────────────────────────────────────────────────────────────────────
Trixi.jl Time Allocations
─────────────────────── ────────────────────────
Tot / % measured: 59.2s / 1.1% 4.86GiB / 0.2%
Section ncalls time %tot avg alloc %tot avg
───────────────────────────────────────────────────────────────────────────────────────
parabolic rhs! 2.65k 556ms 88.7% 210μs 9.00KiB 0.1% 3.48B
calculate gradient 2.65k 247ms 39.5% 93.4μs 3.33KiB 0.0% 1.29B
volume integral 2.65k 154ms 24.6% 58.2μs 0.00B 0.0% 0.00B
Jacobian 2.65k 28.6ms 4.6% 10.8μs 0.00B 0.0% 0.00B
surface integral 2.65k 19.6ms 3.1% 7.42μs 0.00B 0.0% 0.00B
prolong2interfaces 2.65k 18.4ms 2.9% 6.95μs 0.00B 0.0% 0.00B
interface flux 2.65k 17.9ms 2.8% 6.74μs 0.00B 0.0% 0.00B
reset gradients 2.65k 5.11ms 0.8% 1.93μs 0.00B 0.0% 0.00B
~calculate gradient~ 2.65k 2.95ms 0.5% 1.11μs 3.33KiB 0.0% 1.29B
prolong2mortars 2.65k 328μs 0.1% 124ns 0.00B 0.0% 0.00B
prolong2boundaries 2.65k 272μs 0.0% 103ns 0.00B 0.0% 0.00B
mortar flux 2.65k 228μs 0.0% 86.3ns 0.00B 0.0% 0.00B
boundary flux 2.65k 83.2μs 0.0% 31.4ns 0.00B 0.0% 0.00B
volume integral 2.65k 164ms 26.2% 61.9μs 0.00B 0.0% 0.00B
calculate viscous fluxes 2.65k 50.8ms 8.1% 19.2μs 0.00B 0.0% 0.00B
surface integral 2.65k 19.9ms 3.2% 7.51μs 0.00B 0.0% 0.00B
interface flux 2.65k 17.5ms 2.8% 6.60μs 0.00B 0.0% 0.00B
transform variables 2.65k 17.2ms 2.7% 6.49μs 0.00B 0.0% 0.00B
prolong2interfaces 2.65k 16.6ms 2.6% 6.27μs 0.00B 0.0% 0.00B
Jacobian 2.65k 14.6ms 2.3% 5.50μs 0.00B 0.0% 0.00B
~parabolic rhs!~ 2.65k 4.38ms 0.7% 1.65μs 5.67KiB 0.1% 2.19B
reset ∂u/∂t 2.65k 2.62ms 0.4% 988ns 0.00B 0.0% 0.00B
prolong2mortars 2.65k 274μs 0.0% 103ns 0.00B 0.0% 0.00B
mortar flux 2.65k 259μs 0.0% 97.9ns 0.00B 0.0% 0.00B
prolong2boundaries 2.65k 245μs 0.0% 92.4ns 0.00B 0.0% 0.00B
source terms parabolic 2.65k 96.9μs 0.0% 36.6ns 0.00B 0.0% 0.00B
boundary flux 2.65k 82.8μs 0.0% 31.3ns 0.00B 0.0% 0.00B
rhs! 720 66.2ms 10.6% 92.0μs 4.78KiB 0.0% 6.80B
volume integral 720 42.5ms 6.8% 59.0μs 0.00B 0.0% 0.00B
surface integral 720 6.21ms 1.0% 8.62μs 0.00B 0.0% 0.00B
interface flux 720 5.99ms 1.0% 8.32μs 0.00B 0.0% 0.00B
prolong2interfaces 720 5.24ms 0.8% 7.27μs 0.00B 0.0% 0.00B
Jacobian 720 4.62ms 0.7% 6.41μs 0.00B 0.0% 0.00B
~rhs!~ 720 882μs 0.1% 1.23μs 4.78KiB 0.0% 6.80B
reset ∂u/∂t 720 553μs 0.1% 769ns 0.00B 0.0% 0.00B
prolong2boundaries 720 81.5μs 0.0% 113ns 0.00B 0.0% 0.00B
prolong2mortars 720 68.5μs 0.0% 95.2ns 0.00B 0.0% 0.00B
mortar flux 720 51.9μs 0.0% 72.1ns 0.00B 0.0% 0.00B
boundary flux 720 22.9μs 0.0% 31.7ns 0.00B 0.0% 0.00B
source terms 720 22.3μs 0.0% 30.9ns 0.00B 0.0% 0.00B
analyze solution 4 4.29ms 0.7% 1.07ms 9.65MiB 99.5% 2.41MiB
calculate dt 241 173μs 0.0% 718ns 33.9KiB 0.3% 144B
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