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: 3.45897246e-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: 1062.656 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: 5.9164e+01 s
#timesteps: 20 │ Δt: 6.2500e-03 │ sim. time: 1.2500e-01 (8.333%) │ run time: 5.9379e+01 s
#timesteps: 30 │ Δt: 6.2500e-03 │ sim. time: 1.8750e-01 (12.500%) │ run time: 5.9416e+01 s
#timesteps: 40 │ Δt: 6.2500e-03 │ sim. time: 2.5000e-01 (16.667%) │ run time: 5.9479e+01 s
#timesteps: 50 │ Δt: 6.2500e-03 │ sim. time: 3.1250e-01 (20.833%) │ run time: 5.9515e+01 s
#timesteps: 60 │ Δt: 6.2500e-03 │ sim. time: 3.7500e-01 (25.000%) │ run time: 5.9558e+01 s
#timesteps: 70 │ Δt: 6.2500e-03 │ sim. time: 4.3750e-01 (29.167%) │ run time: 5.9599e+01 s
#timesteps: 80 │ Δt: 6.2500e-03 │ sim. time: 5.0000e-01 (33.333%) │ run time: 5.9636e+01 s
#timesteps: 90 │ Δt: 6.2500e-03 │ sim. time: 5.6250e-01 (37.500%) │ run time: 5.9677e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 100 run time: 6.00604033e+01 s
Δt: 6.25000000e-03 └── GC time: 1.01896353e+00 s (1.697%)
sim. time: 6.25000000e-01 (41.667%) time/DOF/rhs!: 6.91708245e-08 s
PID: 4.85949045e-05 s
#DOFs per field: 4096 alloc'd memory: 1029.938 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: 5.9756e+01 s
#timesteps: 120 │ Δt: 6.2500e-03 │ sim. time: 7.5000e-01 (50.000%) │ run time: 5.9792e+01 s
#timesteps: 130 │ Δt: 6.2500e-03 │ sim. time: 8.1250e-01 (54.167%) │ run time: 5.9834e+01 s
#timesteps: 140 │ Δt: 6.2500e-03 │ sim. time: 8.7500e-01 (58.333%) │ run time: 5.9871e+01 s
#timesteps: 150 │ Δt: 6.2500e-03 │ sim. time: 9.3750e-01 (62.500%) │ run time: 5.9913e+01 s
#timesteps: 160 │ Δt: 6.2500e-03 │ sim. time: 1.0000e+00 (66.667%) │ run time: 5.9949e+01 s
#timesteps: 170 │ Δt: 6.2500e-03 │ sim. time: 1.0625e+00 (70.833%) │ run time: 5.9991e+01 s
#timesteps: 180 │ Δt: 6.2500e-03 │ sim. time: 1.1250e+00 (75.000%) │ run time: 6.0027e+01 s
#timesteps: 190 │ Δt: 6.2500e-03 │ sim. time: 1.1875e+00 (79.167%) │ run time: 6.0069e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 200 run time: 6.04518167e+01 s
Δt: 6.25000000e-03 └── GC time: 1.04638984e+00 s (1.731%)
sim. time: 1.25000000e+00 (83.333%) time/DOF/rhs!: 6.88401028e-08 s
PID: 3.17696930e-07 s
#DOFs per field: 4096 alloc'd memory: 1054.129 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: 6.0148e+01 s
#timesteps: 220 │ Δt: 6.2500e-03 │ sim. time: 1.3750e+00 (91.667%) │ run time: 6.0184e+01 s
#timesteps: 230 │ Δt: 6.2500e-03 │ sim. time: 1.4375e+00 (95.833%) │ run time: 6.0226e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 240 run time: 6.06146283e+01 s
Δt: 6.25000000e-03 └── GC time: 1.06281237e+00 s (1.753%)
sim. time: 1.50000000e+00 (100.000%) time/DOF/rhs!: 6.89644066e-08 s
PID: 3.29143138e-07 s
#DOFs per field: 4096 alloc'd memory: 981.416 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: 60.7s / 1.0% 4.98GiB / 0.2%
Section ncalls time %tot avg alloc %tot avg
───────────────────────────────────────────────────────────────────────────────────────
parabolic rhs! 2.65k 534ms 89.5% 202μs 9.00KiB 0.1% 3.48B
calculate gradient 2.65k 241ms 40.4% 91.0μs 3.33KiB 0.0% 1.29B
volume integral 2.65k 145ms 24.2% 54.6μs 0.00B 0.0% 0.00B
Jacobian 2.65k 29.3ms 4.9% 11.1μs 0.00B 0.0% 0.00B
interface flux 2.65k 19.5ms 3.3% 7.38μs 0.00B 0.0% 0.00B
surface integral 2.65k 19.4ms 3.3% 7.32μs 0.00B 0.0% 0.00B
prolong2interfaces 2.65k 17.1ms 2.9% 6.45μs 0.00B 0.0% 0.00B
reset gradients 2.65k 7.42ms 1.2% 2.80μs 0.00B 0.0% 0.00B
~calculate gradient~ 2.65k 2.88ms 0.5% 1.09μs 3.33KiB 0.0% 1.29B
prolong2mortars 2.65k 313μs 0.1% 118ns 0.00B 0.0% 0.00B
mortar flux 2.65k 258μs 0.0% 97.4ns 0.00B 0.0% 0.00B
prolong2boundaries 2.65k 189μs 0.0% 71.3ns 0.00B 0.0% 0.00B
boundary flux 2.65k 77.8μs 0.0% 29.4ns 0.00B 0.0% 0.00B
volume integral 2.65k 150ms 25.2% 56.7μs 0.00B 0.0% 0.00B
calculate viscous fluxes 2.65k 53.6ms 9.0% 20.3μs 0.00B 0.0% 0.00B
surface integral 2.65k 17.0ms 2.8% 6.42μs 0.00B 0.0% 0.00B
interface flux 2.65k 16.9ms 2.8% 6.37μs 0.00B 0.0% 0.00B
transform variables 2.65k 16.8ms 2.8% 6.33μs 0.00B 0.0% 0.00B
prolong2interfaces 2.65k 15.4ms 2.6% 5.80μs 0.00B 0.0% 0.00B
Jacobian 2.65k 14.4ms 2.4% 5.45μs 0.00B 0.0% 0.00B
~parabolic rhs!~ 2.65k 4.12ms 0.7% 1.56μs 5.67KiB 0.1% 2.19B
reset ∂u/∂t 2.65k 3.93ms 0.7% 1.48μs 0.00B 0.0% 0.00B
prolong2mortars 2.65k 256μs 0.0% 96.6ns 0.00B 0.0% 0.00B
prolong2boundaries 2.65k 203μs 0.0% 76.6ns 0.00B 0.0% 0.00B
mortar flux 2.65k 198μs 0.0% 74.7ns 0.00B 0.0% 0.00B
boundary flux 2.65k 58.6μs 0.0% 22.1ns 0.00B 0.0% 0.00B
source terms parabolic 2.65k 56.7μs 0.0% 21.4ns 0.00B 0.0% 0.00B
rhs! 720 58.0ms 9.7% 80.6μs 4.78KiB 0.0% 6.80B
volume integral 720 36.3ms 6.1% 50.4μs 0.00B 0.0% 0.00B
interface flux 720 5.75ms 1.0% 7.99μs 0.00B 0.0% 0.00B
surface integral 720 5.08ms 0.9% 7.06μs 0.00B 0.0% 0.00B
Jacobian 720 4.66ms 0.8% 6.48μs 0.00B 0.0% 0.00B
prolong2interfaces 720 4.58ms 0.8% 6.37μs 0.00B 0.0% 0.00B
~rhs!~ 720 884μs 0.1% 1.23μs 4.78KiB 0.0% 6.80B
reset ∂u/∂t 720 602μs 0.1% 836ns 0.00B 0.0% 0.00B
prolong2mortars 720 55.3μs 0.0% 76.8ns 0.00B 0.0% 0.00B
prolong2boundaries 720 47.0μs 0.0% 65.2ns 0.00B 0.0% 0.00B
mortar flux 720 44.1μs 0.0% 61.3ns 0.00B 0.0% 0.00B
boundary flux 720 18.1μs 0.0% 25.2ns 0.00B 0.0% 0.00B
source terms 720 17.0μs 0.0% 23.6ns 0.00B 0.0% 0.00B
analyze solution 4 4.19ms 0.7% 1.05ms 9.65MiB 99.5% 2.41MiB
calculate dt 241 412μs 0.1% 1.71μs 33.9KiB 0.3% 144B
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