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,
);
████████╗██████╗ ██╗██╗ ██╗██╗
╚══██╔══╝██╔══██╗██║╚██╗██╔╝██║
██║ ██████╔╝██║ ╚███╔╝ ██║
██║ ██╔══██╗██║ ██╔██╗ ██║
██║ ██║ ██║██║██╔╝ ██╗██║
╚═╝ ╚═╝ ╚═╝╚═╝╚═╝ ╚═╝╚═╝
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ 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 │
│ 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: 3.70333638e-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: 1070.122 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/xxXAx/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/xxXAx/src/rules/llvmrules.jl:806
┌ 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/xxXAx/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/xxXAx/src/rules/llvmrules.jl:806
#timesteps: 10 │ Δt: 6.2500e-03 │ sim. time: 6.2500e-02 (4.167%) │ run time: 5.3106e+01 s
#timesteps: 20 │ Δt: 6.2500e-03 │ sim. time: 1.2500e-01 (8.333%) │ run time: 5.3372e+01 s
#timesteps: 30 │ Δt: 6.2500e-03 │ sim. time: 1.8750e-01 (12.500%) │ run time: 5.3423e+01 s
#timesteps: 40 │ Δt: 6.2500e-03 │ sim. time: 2.5000e-01 (16.667%) │ run time: 5.3461e+01 s
#timesteps: 50 │ Δt: 6.2500e-03 │ sim. time: 3.1250e-01 (20.833%) │ run time: 5.3500e+01 s
#timesteps: 60 │ Δt: 6.2500e-03 │ sim. time: 3.7500e-01 (25.000%) │ run time: 5.3539e+01 s
#timesteps: 70 │ Δt: 6.2500e-03 │ sim. time: 4.3750e-01 (29.167%) │ run time: 5.3578e+01 s
#timesteps: 80 │ Δt: 6.2500e-03 │ sim. time: 5.0000e-01 (33.333%) │ run time: 5.3616e+01 s
#timesteps: 90 │ Δt: 6.2500e-03 │ sim. time: 5.6250e-01 (37.500%) │ run time: 5.3655e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 100 run time: 5.40655800e+01 s
Δt: 6.25000000e-03 └── GC time: 1.03940246e+00 s (1.922%)
sim. time: 6.25000000e-01 (41.667%) time/DOF/rhs!: 7.56484617e-08 s
PID: 4.36963132e-05 s
#DOFs per field: 4096 alloc'd memory: 527.614 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: 5.3734e+01 s
#timesteps: 120 │ Δt: 6.2500e-03 │ sim. time: 7.5000e-01 (50.000%) │ run time: 5.3772e+01 s
#timesteps: 130 │ Δt: 6.2500e-03 │ sim. time: 8.1250e-01 (54.167%) │ run time: 5.3811e+01 s
#timesteps: 140 │ Δt: 6.2500e-03 │ sim. time: 8.7500e-01 (58.333%) │ run time: 5.3850e+01 s
#timesteps: 150 │ Δt: 6.2500e-03 │ sim. time: 9.3750e-01 (62.500%) │ run time: 5.3889e+01 s
#timesteps: 160 │ Δt: 6.2500e-03 │ sim. time: 1.0000e+00 (66.667%) │ run time: 5.3927e+01 s
#timesteps: 170 │ Δt: 6.2500e-03 │ sim. time: 1.0625e+00 (70.833%) │ run time: 5.3966e+01 s
#timesteps: 180 │ Δt: 6.2500e-03 │ sim. time: 1.1250e+00 (75.000%) │ run time: 5.4005e+01 s
#timesteps: 190 │ Δt: 6.2500e-03 │ sim. time: 1.1875e+00 (79.167%) │ run time: 5.4043e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 200 run time: 5.44538411e+01 s
Δt: 6.25000000e-03 └── GC time: 1.07086479e+00 s (1.967%)
sim. time: 1.25000000e+00 (83.333%) time/DOF/rhs!: 7.54628501e-08 s
PID: 3.15107701e-07 s
#DOFs per field: 4096 alloc'd memory: 515.340 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: 5.4122e+01 s
#timesteps: 220 │ Δt: 6.2500e-03 │ sim. time: 1.3750e+00 (91.667%) │ run time: 5.4161e+01 s
#timesteps: 230 │ Δt: 6.2500e-03 │ sim. time: 1.4375e+00 (95.833%) │ run time: 5.4200e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 240 run time: 5.46097130e+01 s
Δt: 6.25000000e-03 └── GC time: 1.08344281e+00 s (1.984%)
sim. time: 1.50000000e+00 (100.000%) time/DOF/rhs!: 7.54728763e-08 s
PID: 3.14963560e-07 s
#DOFs per field: 4096 alloc'd memory: 510.451 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: 54.7s / 1.2% 3.20GiB / 0.3%
Section ncalls time %tot avg alloc %tot avg
───────────────────────────────────────────────────────────────────────────────────────
parabolic rhs! 2.65k 558ms 88.1% 211μs 8.70KiB 0.1% 3.37B
calculate gradient 2.65k 249ms 39.4% 94.2μs 3.33KiB 0.0% 1.29B
volume integral 2.65k 158ms 24.9% 59.7μs 0.00B 0.0% 0.00B
Jacobian 2.65k 28.9ms 4.6% 10.9μs 0.00B 0.0% 0.00B
surface integral 2.65k 19.6ms 3.1% 7.40μs 0.00B 0.0% 0.00B
interface flux 2.65k 17.8ms 2.8% 6.73μs 0.00B 0.0% 0.00B
prolong2interfaces 2.65k 16.8ms 2.7% 6.36μs 0.00B 0.0% 0.00B
reset gradients 2.65k 4.97ms 0.8% 1.88μs 0.00B 0.0% 0.00B
~calculate gradient~ 2.65k 2.50ms 0.4% 943ns 3.33KiB 0.0% 1.29B
prolong2mortars 2.65k 225μs 0.0% 85.1ns 0.00B 0.0% 0.00B
prolong2boundaries 2.65k 222μs 0.0% 83.8ns 0.00B 0.0% 0.00B
mortar flux 2.65k 157μs 0.0% 59.2ns 0.00B 0.0% 0.00B
boundary flux 2.65k 77.7μs 0.0% 29.4ns 0.00B 0.0% 0.00B
volume integral 2.65k 168ms 26.5% 63.4μs 0.00B 0.0% 0.00B
calculate viscous fluxes 2.65k 50.6ms 8.0% 19.1μs 0.00B 0.0% 0.00B
transform variables 2.65k 18.0ms 2.8% 6.78μs 0.00B 0.0% 0.00B
surface integral 2.65k 17.8ms 2.8% 6.73μs 0.00B 0.0% 0.00B
interface flux 2.65k 17.5ms 2.8% 6.62μs 0.00B 0.0% 0.00B
prolong2interfaces 2.65k 16.0ms 2.5% 6.03μs 0.00B 0.0% 0.00B
Jacobian 2.65k 14.5ms 2.3% 5.47μs 0.00B 0.0% 0.00B
~parabolic rhs!~ 2.65k 3.51ms 0.6% 1.32μs 5.38KiB 0.1% 2.08B
reset ∂u/∂t 2.65k 2.56ms 0.4% 967ns 0.00B 0.0% 0.00B
prolong2mortars 2.65k 218μs 0.0% 82.5ns 0.00B 0.0% 0.00B
prolong2boundaries 2.65k 194μs 0.0% 73.4ns 0.00B 0.0% 0.00B
mortar flux 2.65k 169μs 0.0% 63.9ns 0.00B 0.0% 0.00B
boundary flux 2.65k 76.8μs 0.0% 29.0ns 0.00B 0.0% 0.00B
rhs! 720 70.7ms 11.2% 98.2μs 4.78KiB 0.0% 6.80B
volume integral 720 47.9ms 7.6% 66.6μs 0.00B 0.0% 0.00B
interface flux 720 5.82ms 0.9% 8.08μs 0.00B 0.0% 0.00B
surface integral 720 5.49ms 0.9% 7.63μs 0.00B 0.0% 0.00B
prolong2interfaces 720 4.99ms 0.8% 6.94μs 0.00B 0.0% 0.00B
Jacobian 720 4.88ms 0.8% 6.78μs 0.00B 0.0% 0.00B
~rhs!~ 720 810μs 0.1% 1.13μs 4.78KiB 0.0% 6.80B
reset ∂u/∂t 720 509μs 0.1% 707ns 0.00B 0.0% 0.00B
prolong2mortars 720 72.6μs 0.0% 101ns 0.00B 0.0% 0.00B
prolong2boundaries 720 59.4μs 0.0% 82.5ns 0.00B 0.0% 0.00B
mortar flux 720 41.7μs 0.0% 58.0ns 0.00B 0.0% 0.00B
source terms 720 34.7μs 0.0% 48.2ns 0.00B 0.0% 0.00B
boundary flux 720 22.1μs 0.0% 30.7ns 0.00B 0.0% 0.00B
analyze solution 4 4.38ms 0.7% 1.09ms 9.65MiB 99.5% 2.41MiB
calculate dt 241 157μs 0.0% 652ns 33.9KiB 0.3% 144B
───────────────────────────────────────────────────────────────────────────────────────This page was generated using Literate.jl.