MethodError with getmetadata

[PeterARBork]

Describe the bug 🐞

There seems to be an error when calling getmetadata somewhere with a Pair instead of Num.

(Background: The minimal example below begins to simulate an advection-diffusion problem but with parameters D, v, and C0 as @parameters, while simulation domain length L for example is not an @parameter).

Expected behavior

Expected the library to produce a discretization, but it failed.

Minimal Reproducible Example 👇

using ModelingToolkit, MethodOfLines, DomainSets

@parameters t x
@parameters D, v, C0
@variables c(..)
Dt = Differential(t)
Dx = Differential(x)
Dxx = Differential(x)^2

p = (
    D = 0.5,
    C0 = 1.0,
    v = 0.1,
    T = 1.0,
    L = 1.0,
)
@unpack L, T, C0 = p
dx = 0.01
order = 2

# 1D PDE and boundary conditions
eq = [
    Dt(c(t, x)) ~ D * Dxx(c(t, x))
]
bcs = [
    c(0, x) ~ C0 * exp(-(x .- L/2).^2),
    Dx(c(t, 0)) ~ (v/D) * c(t, 0),
    Dx(c(t, L)) ~ (v/D) * c(t, L)
]

# Space and time domains
domains = [
    t ∈ Interval(0.0, T),
    x ∈ Interval(0.0, L),
]

# PDE system
@named pdesys = PDESystem(
    eq, bcs, domains,
    [t, x], [c(t, x),],
    [D=>p.D, v=>p.v,],
)

discretization = MOLFiniteDifference([x => dx], t, approx_order=order)

# Convert the PDE problem into an ODE problem
prob = discretize(pdesys, discretization)

Error & Stacktrace ⚠️

2-element Vector{Num}:
 t
 x

3-element Vector{Num}:
  D
  v
 C0

1-element Vector{Symbolics.CallWithMetadata{SymbolicUtils.FnType{Tuple, Real}, Base.ImmutableDict{DataType, Any}}}:
 c⋆

Differential(t)

Differential(x)

Differential(x) ∘ Differential(x)

(D = 0.5, C0 = 1.0, v = 0.1, T = 1.0, L = 1.0)

(D = 0.5, C0 = 1.0, v = 0.1, T = 1.0, L = 1.0)

0.01

2

1-element Vector{Equation}:
 Differential(t)(c(t, x)) ~ D*Differential(x)(Differential(x)(c(t, x)))

3-element Vector{Equation}:
 c(0, x) ~ exp(-((-0.5 + x)^2))
 Differential(x)(c(t, 0)) ~ (v*c(t, 0)) / D
 Differential(x)(c(t, 1.0)) ~ (v*c(t, 1.0)) / D

2-element Vector{Symbolics.VarDomainPairing}:
 Symbolics.VarDomainPairing(t, 0.0 .. 1.0)
 Symbolics.VarDomainPairing(x, 0.0 .. 1.0)

PDESystem
Equations: Equation[Differential(t)(c(t, x)) ~ D*Differential(x)(Differential(x)(c(t, x)))]
Boundary Conditions: Equation[c(0, x) ~ exp(-((-0.5 + x)^2)), Differential(x)(c(t, 0)) ~ (v*c(t, 0)) / D, Differential(x)(c(t, 1.0)) ~ (v*c(t, 1.0)) / D]
Domain: Symbolics.VarDomainPairing[Symbolics.VarDomainPairing(t, 0.0 .. 1.0), Symbolics.VarDomainPairing(x, 0.0 .. 1.0)]
Dependent Variables: Num[c(t, x)]
Independent Variables: Num[t, x]
Parameters: Pair{Num, Float64}[D => 0.5, v => 0.1]
Default Parameter ValuesDict{Any, Any}()

MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}(Dict{Num, Float64}(x => 0.01), t, 2, UpwindScheme(1), MethodOfLines.CenterAlignedGrid(), true, false, MethodOfLines.ScalarizedDiscretization(), true, Any[], Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}())

The system of equations is:

Discretization failed, please post an issue on https://github.com/SciML/MethodOfLines.jl with the failing code and system at low point count.

ERROR: MethodError: no method matching getmetadata(::Pair{Num, Float64}, ::Type{ModelingToolkit.VariableGuess}, ::Nothing)
The function `getmetadata` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  getmetadata(::SymbolicUtils.Symbolic, ::Any, ::Any)
   @ SymbolicUtils ~/.julia/packages/SymbolicUtils/jf8aQ/src/types.jl:658
  getmetadata(::Num, ::Any)
   @ Symbolics ~/.julia/packages/Symbolics/GYV9b/src/Symbolics.jl:188
  getmetadata(::Complex{Num}, ::Any)
   @ Symbolics ~/.julia/packages/Symbolics/GYV9b/src/Symbolics.jl:188
  ...

Stacktrace:
  [1] getguess(x::Pair{Num, Float64})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/89pF2/src/variables.jl:516
  [2] (::ModelingToolkit.var"#776#789")(st::Pair{Num, Float64})
    @ ModelingToolkit ./none:0
  [3] iterate
    @ ./generator.jl:48 [inlined]
  [4] collect
    @ ./array.jl:780 [inlined]
  [5] ODESystem(deqs::Vector{…}, iv::Num, dvs::Vector{…}, ps::Vector{…}; controls::Vector{…}, observed::Vector{…}, systems::Vector{…}, tspan::Nothing, name::Symbol, description::String, default_u0::Dict{…}, default_p::Dict{…}, defaults::Dict{…}, guesses::Dict{…}, initializesystem::Nothing, initialization_eqs::Vector{…}, schedule::Nothing, connector_type::Nothing, preface::Nothing, continuous_events::Nothing, discrete_events::Nothing, parameter_dependencies::Vector{…}, checks::Bool, metadata::MethodOfLines.MOLMetadata{…}, gui_metadata::Nothing, is_dde::Nothing)
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/89pF2/src/systems/diffeqs/odesystem.jl:265
  [6] generate_system(disc_state::PDEBase.EquationState, s::MethodOfLines.DiscreteSpace{…}, u0::Vector{…}, tspan::Tuple{…}, metadata::MethodOfLines.MOLMetadata{…}, disc::MOLFiniteDifference{…})
    @ PDEBase ~/.julia/packages/PDEBase/VVGPP/src/discretization_state.jl:40
  [7] symbolic_discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{…})
    @ PDEBase ~/.julia/packages/PDEBase/VVGPP/src/symbolic_discretize.jl:89
  [8] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{…}; analytic::Nothing, kwargs::@Kwargs{})
    @ PDEBase ~/.julia/packages/PDEBase/VVGPP/src/discretization_state.jl:57
  [9] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{…})
    @ PDEBase ~/.julia/packages/PDEBase/VVGPP/src/discretization_state.jl:54
 [10] top-level scope
    @ ~/Documents/GitHub/divergentMRIflow/scripts/getmetadataproblem.jl:47
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `~/Documents/GitHub/divergentMRIflow/Project.toml`
  [99985d1d] AbstractGPs v0.5.21
  [336ed68f] CSV v0.10.15
  [5b8099bc] DomainSets v0.7.14
  [b964fa9f] LaTeXStrings v1.4.0
  [94925ecb] MethodOfLines v0.11.7
  [961ee093] ModelingToolkit v9.51.0
  [1dea7af3] OrdinaryDiffEq v6.90.1
  [d96e819e] Parameters v0.12.3
  [91a5bcdd] Plots v1.40.9
  [10745b16] Statistics v1.11.1
  [fce5fe82] Turing v0.35.2

• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

Status `~/Documents/GitHub/divergentMRIflow/Manifest-v1.11.toml`
  [47edcb42] ADTypes v1.10.0
  [621f4979] AbstractFFTs v1.5.0
  [99985d1d] AbstractGPs v0.5.21
  [80f14c24] AbstractMCMC v5.6.0
  [7a57a42e] AbstractPPL v0.9.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.38
  [79e6a3ab] Adapt v4.1.1
  [0bf59076] AdvancedHMC v0.6.4
  [5b7e9947] AdvancedMH v0.8.4
  [576499cb] AdvancedPS v0.6.0
  [b5ca4192] AdvancedVI v0.2.10
  [66dad0bd] AliasTables v1.1.3
  [dce04be8] ArgCheck v2.3.0
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.17.1
  [4c555306] ArrayLayouts v1.10.4
  [a9b6321e] Atomix v0.1.0
  [13072b0f] AxisAlgorithms v1.1.0
  [39de3d68] AxisArrays v0.4.7
  [198e06fe] BangBang v0.4.3
  [9718e550] Baselet v0.1.1
  [e2ed5e7c] Bijections v0.1.9
  [76274a88] Bijectors v0.14.0
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.1.1
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [336ed68f] CSV v0.10.15
  [082447d4] ChainRules v1.72.1
  [d360d2e6] ChainRulesCore v1.25.0
  [9e997f8a] ChangesOfVariables v0.1.9
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [944b1d66] CodecZlib v0.7.6
  [35d6a980] ColorSchemes v3.27.1
  [3da002f7] ColorTypes v0.12.0
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.0
  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.15
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [f0e56b4a] ConcurrentUtilities v2.4.2
  [88cd18e8] ConsoleProgressMonitor v0.1.2
  [187b0558] ConstructionBase v1.5.8
  [d38c429a] Contour v0.6.3
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [244e2a9f] DefineSingletons v0.1.2
  [8bb1440f] DelimitedFiles v1.9.1
  [b429d917] DensityInterface v0.4.0
  [2b5f629d] DiffEqBase v6.160.0
⌃ [459566f4] DiffEqCallbacks v4.1.0
  [77a26b50] DiffEqNoiseProcess v5.23.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.6.22
  [8d63f2c5] DispatchDoctor v0.4.17
  [b4f34e82] Distances v0.10.12
  [31c24e10] Distributions v0.25.113
  [ced4e74d] DistributionsAD v0.6.57
  [ffbed154] DocStringExtensions v0.9.3
  [5b8099bc] DomainSets v0.7.14
  [366bfd00] DynamicPPL v0.30.5
  [7c1d4256] DynamicPolynomials v0.6.0
  [06fc5a27] DynamicQuantities v1.3.0
  [cad2338a] EllipticalSliceSampling v2.0.0
  [4e289a0a] EnumX v1.0.4
⌃ [f151be2c] EnzymeCore v0.7.8
  [460bff9d] ExceptionUnwrapping v0.1.10
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
⌅ [6b7a57c9] Expronicon v0.8.5
  [c87230d0] FFMPEG v0.4.2
  [7a1cc6ca] FFTW v1.8.0
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.4
  [a4df4552] FastPower v1.1.1
  [48062228] FilePathsBase v0.9.22
  [1a297f60] FillArrays v1.13.0
  [64ca27bc] FindFirstFunctions v1.4.1
  [6a86dc24] FiniteDiff v2.26.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.38
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
⌅ [d9f16b24] Functors v0.4.12
⌅ [46192b85] GPUArraysCore v0.1.6
  [28b8d3ca] GR v0.73.8
  [c145ed77] GenericSchur v0.5.4
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.12.0
  [42e2da0e] Grisu v1.0.2
  [cd3eb016] HTTP v1.10.10
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [34004b35] HypergeometricFunctions v0.3.25
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [22cec73e] InitialValues v0.3.1
  [842dd82b] InlineStrings v1.4.2
  [505f98c9] InplaceOps v0.3.0
  [18e54dd8] IntegerMathUtils v0.1.2
  [a98d9a8b] Interpolations v0.15.1
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.17
  [41ab1584] InvertedIndices v1.3.0
  [92d709cd] IrrationalConstants v0.2.2
  [c8e1da08] IterTools v1.10.0
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.8
  [692b3bcd] JLLWrappers v1.6.1
  [682c06a0] JSON v0.21.4
  [98e50ef6] JuliaFormatter v1.0.62
  [ccbc3e58] JumpProcesses v9.14.0
  [ef3ab10e] KLU v0.6.0
  [63c18a36] KernelAbstractions v0.9.29
  [5ab0869b] KernelDensity v0.6.9
  [ec8451be] KernelFunctions v0.10.64
  [ba0b0d4f] Krylov v0.9.8
  [5be7bae1] LBFGSB v0.4.1
  [929cbde3] LLVM v9.1.3
  [8ac3fa9e] LRUCache v1.6.1
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.5
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.2.2
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.0
  [6f1fad26] Libtask v0.8.8
  [d3d80556] LineSearches v7.3.0
⌃ [7ed4a6bd] LinearSolve v2.34.0
  [6fdf6af0] LogDensityProblems v2.1.2
  [996a588d] LogDensityProblemsAD v1.12.0
  [2ab3a3ac] LogExpFunctions v0.3.28
  [e6f89c97] LoggingExtras v1.1.0
  [bdcacae8] LoopVectorization v0.12.171
  [c7f686f2] MCMCChains v6.0.6
  [be115224] MCMCDiagnosticTools v0.3.11
  [e80e1ace] MLJModelInterface v1.11.0
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [dbb5928d] MappedArrays v0.4.2
  [bb5d69b7] MaybeInplace v0.1.4
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.2
  [94925ecb] MethodOfLines v0.11.7
  [128add7d] MicroCollections v0.2.0
  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v9.51.0
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.7
  [d8a4904e] MutableArithmetics v1.6.0
  [d41bc354] NLSolversBase v7.8.3
  [872c559c] NNlib v0.9.24
  [77ba4419] NaNMath v1.0.2
  [86f7a689] NamedArrays v0.10.3
  [c020b1a1] NaturalSort v1.0.0
⌃ [8913a72c] NonlinearSolve v3.14.0
  [6fe1bfb0] OffsetArrays v1.14.1
  [4d8831e6] OpenSSL v1.4.3
  [429524aa] Optim v1.10.0
⌃ [3bd65402] Optimisers v0.4.0
  [7f7a1694] Optimization v4.0.5
  [bca83a33] OptimizationBase v2.4.0
  [36348300] OptimizationOptimJL v0.4.1
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.90.1
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.1.0
  [6ad6398a] OrdinaryDiffEqBDF v1.1.2
  [bbf590c4] OrdinaryDiffEqCore v1.11.0
  [50262376] OrdinaryDiffEqDefault v1.1.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.2.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.1.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.2.1
  [5960d6e9] OrdinaryDiffEqFIRK v1.4.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.1.1
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.1.0
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.2.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.2.1
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.2.4
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.1.0
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.1.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.3.1
  [2d112036] OrdinaryDiffEqSDIRK v1.1.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.2.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.1.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.1.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.1.0
  [79d7bb75] OrdinaryDiffEqVerner v1.1.1
  [a7812802] PDEBase v0.1.17
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [b98c9c47] Pipe v1.3.0
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.3
  [91a5bcdd] Plots v1.40.9
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [2dfb63ee] PooledArrays v1.4.3
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.24
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [08abe8d2] PrettyTables v2.4.0
  [27ebfcd6] Primes v0.5.6
  [33c8b6b6] ProgressLogging v0.1.4
  [92933f4c] ProgressMeter v1.10.2
  [43287f4e] PtrArrays v1.2.1
  [1fd47b50] QuadGK v2.11.1
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.6.0
  [b3c3ace0] RangeArrays v0.3.2
  [c84ed2f1] Ratios v0.4.5
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [731186ca] RecursiveArrayTools v3.27.3
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.8.0
  [f2b01f46] Roots v2.2.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
⌅ [26aad666] SSMProblems v0.1.1
  [0bca4576] SciMLBase v2.62.0
  [c0aeaf25] SciMLOperators v0.3.12
  [53ae85a6] SciMLStructures v1.5.0
  [30f210dd] ScientificTypesBase v3.0.0
  [6c6a2e73] Scratch v1.2.1
  [91c51154] SentinelArrays v1.4.7
  [efcf1570] Setfield v1.1.1
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
⌅ [727e6d20] SimpleNonlinearSolve v1.12.3
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [9f842d2f] SparseConnectivityTracer v0.6.8
  [47a9eef4] SparseDiffTools v2.23.0
  [dc90abb0] SparseInverseSubset v0.1.2
  [0a514795] SparseMatrixColorings v0.4.10
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [171d559e] SplittablesBase v0.1.15
  [860ef19b] StableRNGs v1.0.2
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.8
  [1e83bf80] StaticArraysCore v1.4.3
  [64bff920] StatisticalTraits v3.4.0
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.2
  [7792a7ef] StrideArraysCore v0.5.7
  [892a3eda] StringManipulation v0.4.0
⌃ [09ab397b] StructArrays v0.6.18
  [2efcf032] SymbolicIndexingInterface v0.3.35
  [19f23fe9] SymbolicLimits v0.2.2
  [d1185830] SymbolicUtils v3.7.2
  [0c5d862f] Symbolics v6.21.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v2.0.0
  [5d786b92] TerminalLoggers v0.1.7
  [1c621080] TestItems v1.0.0
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.25
  [0796e94c] Tokenize v0.5.29
  [9f7883ad] Tracker v0.2.37
  [3bb67fe8] TranscodingStreams v0.11.3
  [28d57a85] Transducers v0.4.84
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.9
  [781d530d] TruncatedStacktraces v1.4.0
  [fce5fe82] Turing v0.35.2
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.21.0
  [45397f5d] UnitfulLatexify v1.6.4
  [a7c27f48] Unityper v0.1.6
  [013be700] UnsafeAtomics v0.2.1
  [d80eeb9a] UnsafeAtomicsLLVM v0.2.1
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.71
  [19fa3120] VertexSafeGraphs v0.2.0
  [ea10d353] WeakRefStrings v1.4.2
  [efce3f68] WoodburyMatrices v1.0.0
  [76eceee3] WorkerUtilities v1.6.1
  [700de1a5] ZygoteRules v0.2.5
  [6e34b625] Bzip2_jll v1.0.8+2
  [83423d85] Cairo_jll v1.18.2+1
  [ee1fde0b] Dbus_jll v1.14.10+0
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.6.4+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [f5851436] FFTW_jll v3.3.10+1
  [a3f928ae] Fontconfig_jll v2.13.96+0
  [d7e528f0] FreeType2_jll v2.13.2+0
  [559328eb] FriBidi_jll v1.0.14+0
  [0656b61e] GLFW_jll v3.4.0+1
  [d2c73de3] GR_jll v0.73.8+0
  [78b55507] Gettext_jll v0.21.0+0
  [7746bdde] Glib_jll v2.80.5+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v8.3.1+0
  [1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
  [aacddb02] JpegTurbo_jll v3.0.4+0
  [c1c5ebd0] LAME_jll v3.100.2+0
  [88015f11] LERC_jll v4.0.0+0
  [dad2f222] LLVMExtra_jll v0.0.34+0
  [1d63c593] LLVMOpenMP_jll v18.1.7+0
  [dd4b983a] LZO_jll v2.10.2+1
  [81d17ec3] L_BFGS_B_jll v3.0.1+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.11.0+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.50.0+0
  [94ce4f54] Libiconv_jll v1.17.0+1
  [4b2f31a3] Libmount_jll v2.40.1+0
  [89763e89] Libtiff_jll v4.7.0+0
  [38a345b3] Libuuid_jll v2.40.1+0
  [856f044c] MKL_jll v2024.2.0+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v3.0.15+1
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.3+0
  [36c8627f] Pango_jll v1.54.1+0
  [30392449] Pixman_jll v0.43.4+0
  [c0090381] Qt6Base_jll v6.7.1+1
  [629bc702] Qt6Declarative_jll v6.7.1+2
  [ce943373] Qt6ShaderTools_jll v6.7.1+1
  [e99dba38] Qt6Wayland_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.5.1+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.31.0+0
  [02c8fc9c] XML2_jll v2.13.5+0
  [aed1982a] XSLT_jll v1.1.41+0
  [ffd25f8a] XZ_jll v5.6.3+0
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.6+0
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [3161d3a3] Zstd_jll v1.5.6+1
  [35ca27e7] eudev_jll v3.2.9+0
  [214eeab7] fzf_jll v0.53.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.2+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.3+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.44+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
⌅ [1270edf5] x264_jll v2021.5.5+0
⌅ [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.1+2
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

• Output of versioninfo()

Julia Version 1.11.1
Commit 8f5b7ca12ad (2024-10-16 10:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (x86_64-apple-darwin22.4.0)
  CPU: 4 × Intel(R) Core(TM) i5-6500 CPU @ 3.20GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, skylake)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 

Additional context

Add any other context about the problem here.

[rzhli]

Same problem as here， try this

[D, v],
defaults = Dict(D => p.D, v => p.v)

instead of
[D=>p.D, v=>p.v,]

But I'm wondering why your boundary conditions works fine, the problem can be discretized, while my problem failed, they are all Neumann type boundary conditions

[PeterARBork]

Thank you, problem solved!

Hope your problem will find its solution too @rzhli!