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: ……………………………………………… 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}(0.5) │
│ CFL Parabolic: ……………………………………………………… 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: 3.71971073e-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: 818.847 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: 6.2500e-03 │ sim. time: 6.2500e-02 (4.167%) │ run time: 4.2280e+01 s
#timesteps: 20 │ Δt: 6.2500e-03 │ sim. time: 1.2500e-01 (8.333%) │ run time: 4.2493e+01 s
#timesteps: 30 │ Δt: 6.2500e-03 │ sim. time: 1.8750e-01 (12.500%) │ run time: 4.2543e+01 s
#timesteps: 40 │ Δt: 6.2500e-03 │ sim. time: 2.5000e-01 (16.667%) │ run time: 4.2579e+01 s
#timesteps: 50 │ Δt: 6.2500e-03 │ sim. time: 3.1250e-01 (20.833%) │ run time: 4.2616e+01 s
#timesteps: 60 │ Δt: 6.2500e-03 │ sim. time: 3.7500e-01 (25.000%) │ run time: 4.2651e+01 s
#timesteps: 70 │ Δt: 6.2500e-03 │ sim. time: 4.3750e-01 (29.167%) │ run time: 4.2685e+01 s
#timesteps: 80 │ Δt: 6.2500e-03 │ sim. time: 5.0000e-01 (33.333%) │ run time: 4.2721e+01 s
#timesteps: 90 │ Δt: 6.2500e-03 │ sim. time: 5.6250e-01 (37.500%) │ run time: 4.2757e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 100 run time: 4.31659236e+01 s
Δt: 6.25000000e-03 └── GC time: 4.58687770e-01 s (1.063%)
sim. time: 6.25000000e-01 (41.667%) time/DOF/rhs!: 7.44711578e-08 s
PID: 3.48248719e-05 s
#DOFs per field: 4096 alloc'd memory: 855.942 MiB
#elements: 256 device memory: 0.000 MiB
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: 4.2830e+01 s
#timesteps: 120 │ Δt: 6.2500e-03 │ sim. time: 7.5000e-01 (50.000%) │ run time: 4.2866e+01 s
#timesteps: 130 │ Δt: 6.2500e-03 │ sim. time: 8.1250e-01 (54.167%) │ run time: 4.2899e+01 s
#timesteps: 140 │ Δt: 6.2500e-03 │ sim. time: 8.7500e-01 (58.333%) │ run time: 4.2935e+01 s
#timesteps: 150 │ Δt: 6.2500e-03 │ sim. time: 9.3750e-01 (62.500%) │ run time: 4.2971e+01 s
#timesteps: 160 │ Δt: 6.2500e-03 │ sim. time: 1.0000e+00 (66.667%) │ run time: 4.3006e+01 s
#timesteps: 170 │ Δt: 6.2500e-03 │ sim. time: 1.0625e+00 (70.833%) │ run time: 4.3042e+01 s
#timesteps: 180 │ Δt: 6.2500e-03 │ sim. time: 1.1250e+00 (75.000%) │ run time: 4.3075e+01 s
#timesteps: 190 │ Δt: 6.2500e-03 │ sim. time: 1.1875e+00 (79.167%) │ run time: 4.3111e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 200 run time: 4.35202532e+01 s
Δt: 6.25000000e-03 └── GC time: 4.79281248e-01 s (1.101%)
sim. time: 1.25000000e+00 (83.333%) time/DOF/rhs!: 7.41913091e-08 s
PID: 2.87482127e-07 s
#DOFs per field: 4096 alloc'd memory: 873.229 MiB
#elements: 256 device memory: 0.000 MiB
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: 4.3184e+01 s
#timesteps: 220 │ Δt: 6.2500e-03 │ sim. time: 1.3750e+00 (91.667%) │ run time: 4.3220e+01 s
#timesteps: 230 │ Δt: 6.2500e-03 │ sim. time: 1.4375e+00 (95.833%) │ run time: 4.3256e+01 s
────────────────────────────────────────────────────────────────────────────────────────────────────
Simulation running 'LinearScalarAdvectionEquation2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
#timesteps: 240 run time: 4.36619660e+01 s
Δt: 6.25000000e-03 └── GC time: 4.86980797e-01 s (1.115%)
sim. time: 1.50000000e+00 (100.000%) time/DOF/rhs!: 7.41072960e-08 s
PID: 2.86083124e-07 s
#DOFs per field: 4096 alloc'd memory: 893.119 MiB
#elements: 256 device memory: 0.000 MiB
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: 43.7s / 1.4% 3.23GiB / 0.3%
Section ncalls time %tot avg alloc %tot avg
─────────────────────────────────────────────────────────────────────────────────────────
parabolic rhs! 2.65k 548ms 87.7% 207μs 9.00KiB 0.1% 3.48B
calculate gradient 2.65k 243ms 38.9% 91.9μs 3.33KiB 0.0% 1.29B
volume integral 2.65k 153ms 24.4% 57.6μs 0.00B 0.0% 0.00B
Jacobian 2.65k 29.0ms 4.6% 10.9μs 0.00B 0.0% 0.00B
surface integral 2.65k 19.7ms 3.2% 7.45μs 0.00B 0.0% 0.00B
interface flux 2.65k 17.3ms 2.8% 6.55μs 0.00B 0.0% 0.00B
prolong2interfaces 2.65k 16.5ms 2.6% 6.25μs 0.00B 0.0% 0.00B
reset gradients 2.65k 4.96ms 0.8% 1.87μs 0.00B 0.0% 0.00B
~calculate gradient~ 2.65k 2.63ms 0.4% 993ns 3.33KiB 0.0% 1.29B
prolong2mortars 2.65k 238μs 0.0% 89.8ns 0.00B 0.0% 0.00B
prolong2boundaries 2.65k 182μs 0.0% 68.9ns 0.00B 0.0% 0.00B
mortar flux 2.65k 155μs 0.0% 58.4ns 0.00B 0.0% 0.00B
boundary flux 2.65k 82.6μs 0.0% 31.2ns 0.00B 0.0% 0.00B
volume integral 2.65k 166ms 26.5% 62.7μs 0.00B 0.0% 0.00B
calculate parabolic fluxes 2.65k 49.6ms 7.9% 18.7μs 0.00B 0.0% 0.00B
transform variables 2.65k 17.2ms 2.8% 6.50μs 0.00B 0.0% 0.00B
interface flux 2.65k 17.2ms 2.7% 6.48μs 0.00B 0.0% 0.00B
surface integral 2.65k 16.6ms 2.6% 6.25μs 0.00B 0.0% 0.00B
prolong2interfaces 2.65k 16.2ms 2.6% 6.14μs 0.00B 0.0% 0.00B
Jacobian 2.65k 15.0ms 2.4% 5.65μs 0.00B 0.0% 0.00B
~parabolic rhs!~ 2.65k 3.96ms 0.6% 1.49μs 5.67KiB 0.1% 2.19B
reset ∂u/∂t 2.65k 2.58ms 0.4% 976ns 0.00B 0.0% 0.00B
prolong2mortars 2.65k 181μs 0.0% 68.4ns 0.00B 0.0% 0.00B
prolong2boundaries 2.65k 160μs 0.0% 60.4ns 0.00B 0.0% 0.00B
mortar flux 2.65k 157μs 0.0% 59.3ns 0.00B 0.0% 0.00B
boundary flux 2.65k 91.6μs 0.0% 34.6ns 0.00B 0.0% 0.00B
source terms parabolic 2.65k 76.9μs 0.0% 29.0ns 0.00B 0.0% 0.00B
rhs! 720 69.7ms 11.1% 96.8μs 4.78KiB 0.0% 6.80B
volume integral 720 47.4ms 7.6% 65.8μs 0.00B 0.0% 0.00B
interface flux 720 5.72ms 0.9% 7.94μs 0.00B 0.0% 0.00B
surface integral 720 5.07ms 0.8% 7.05μs 0.00B 0.0% 0.00B
Jacobian 720 5.01ms 0.8% 6.96μs 0.00B 0.0% 0.00B
prolong2interfaces 720 4.91ms 0.8% 6.82μs 0.00B 0.0% 0.00B
~rhs!~ 720 878μs 0.1% 1.22μs 4.78KiB 0.0% 6.80B
reset ∂u/∂t 720 508μs 0.1% 705ns 0.00B 0.0% 0.00B
prolong2mortars 720 70.7μs 0.0% 98.1ns 0.00B 0.0% 0.00B
prolong2boundaries 720 44.7μs 0.0% 62.1ns 0.00B 0.0% 0.00B
boundary flux 720 42.7μs 0.0% 59.3ns 0.00B 0.0% 0.00B
mortar flux 720 38.3μs 0.0% 53.2ns 0.00B 0.0% 0.00B
source terms 720 20.8μs 0.0% 28.8ns 0.00B 0.0% 0.00B
analyze solution 4 7.04ms 1.1% 1.76ms 9.65MiB 99.5% 2.41MiB
calculate dt 241 172μs 0.0% 713ns 33.9KiB 0.3% 144B
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