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Published 20 hours ago • verified publisher icon SciML

`discretize` errrors when a subset of equations have no time derivatives

Open musoke opened this issue 4 months ago • 5 comments

Describe the bug 🐞

I am attempting to solve a system of two PDEs. One of them is hyperbolic, the other is elliptic.

MethodOfLines.discretize reports that a variable is missing from the elliptic equation. It doesn't error for a similar system and boundary conditions when there is no hyperbolic equation.

Expected behavior

I expect that MethodOfLines is able to use boundary conditions that are valid for an elliptic PDE alone when it is combined with a hyperbolic equation.

Minimal Reproducible Example 👇

This code reproduces the error in a fresh environment:

using Pkg
Pkg.activate(temp=true)
Pkg.add(["ModelingToolkit", "MethodOfLines", "DomainSets", "NonlinearSolve"])

using ModelingToolkit, MethodOfLines, DomainSets, NonlinearSolve

# Parameters, variables, and derivatives
@parameters t r
@variables ϕ(..) V(..)

Dt = Differential(t);
Dtt = Differential(t)^2;
Drr = Differential(r)^2;

# Space and time domains
max_t = 1.0e-1
max_r = 1.0e0
domains = [t ∈ Interval(0.0, max_t), r ∈ Interval(0.0, max_r)]

# PDEs
eq = [
    # Hyperbolic
    Dtt(ϕ(t, r)) ~ Drr(ϕ(t, r)) + V(t, r),
    # Elliptic
    Drr(V(t, r)) ~ - ϕ(t, r),
]

bcs = [
    # Initial conditions
    ϕ(0, r) ~ exp(-r^2),
    Dt(ϕ(0, r)) ~ 0.0,
    # Potential on boundary
    V(t, max_r) ~ 1,
]

# PDE system
@named pdesys = PDESystem(eq, bcs, domains, [t, r], [ϕ(t, r), V(t, r)])   # Fixed missing V(t, r) in edit

dr = 0.1

# The next line fails with
# AssertionError: Boundary condition V(t, 1.0) ~ 1 is not on a boundary of the domain, or is not a valid boundary condition
discretization = MOLFiniteDifference([r => dr], t);

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

# Solve
sol = solve(prob, RadauIIA3(), saveat=max_t/10);

@assert SciMLBase.successful_retcode(sol)

Error & Stacktrace ⚠️

The system of equations is:
Equation[-(V(t))[1] + Differential(t)(Differential(t)((ϕ(t))[1])) - 199.99999999999997(ϕ(t))[1] + 499.99999999999994(ϕ(t))[2] - 399.99999999999994(ϕ(t))[3] + 99.99999999999999(ϕ(t))[4] ~ 0, -(V(t))[2] + Differential(t)(Differential(t)((ϕ(t))[2])) - 99.99999999999999(ϕ(t))[1] + 199.99999999999997(ϕ(t))[2] - 99.99999999999999(ϕ(t))[3] ~ 0, -(V(t))[3] + Differential(t)(Differential(t)((ϕ(t))[3])) - 99.99999999999999(ϕ(t))[2] + 199.99999999999997(ϕ(t))[3] - 99.99999999999999(ϕ(t))[4] ~ 0, -(V(t))[4] + Differential(t)(Differential(t)((ϕ(t))[4])) - 99.99999999999999(ϕ(t))[3] + 199.99999999999997(ϕ(t))[4] - 99.99999999999999(ϕ(t))[5] ~ 0, -(V(t))[5] + Differential(t)(Differential(t)((ϕ(t))[5])) - 99.99999999999999(ϕ(t))[4] + 199.99999999999997(ϕ(t))[5] - 99.99999999999999(ϕ(t))[6] ~ 0, -(V(t))[6] + Differential(t)(Differential(t)((ϕ(t))[6])) - 99.99999999999999(ϕ(t))[5] + 199.99999999999997(ϕ(t))[6] - 99.99999999999999(ϕ(t))[7] ~ 0, -(V(t))[7] + Differential(t)(Differential(t)((ϕ(t))[7])) - 99.99999999999999(ϕ(t))[6] + 199.99999999999997(ϕ(t))[7] - 99.99999999999999(ϕ(t))[8] ~ 0, -(V(t))[8] + Differential(t)(Differential(t)((ϕ(t))[8])) - 99.99999999999999(ϕ(t))[7] + 199.99999999999997(ϕ(t))[8] - 99.99999999999999(ϕ(t))[9] ~ 0, -(V(t))[9] + Differential(t)(Differential(t)((ϕ(t))[9])) - 99.99999999999999(ϕ(t))[10] - 99.99999999999999(ϕ(t))[8] + 199.99999999999997(ϕ(t))[9] ~ 0, -(V(t))[10] + Differential(t)(Differential(t)((ϕ(t))[10])) + 199.99999999999997(ϕ(t))[10] - 99.99999999999999(ϕ(t))[11] - 99.99999999999999(ϕ(t))[9] ~ 0, -(V(t))[11] + Differential(t)(Differential(t)((ϕ(t))[11])) + 499.99999999999994(ϕ(t))[10] - 199.99999999999997(ϕ(t))[11] + 99.99999999999999(ϕ(t))[8] - 399.99999999999994(ϕ(t))[9] ~ 0, 199.99999999999997(V(t))[1] - 499.99999999999994(V(t))[2] + 399.99999999999994(V(t))[3] - 99.99999999999999(V(t))[4] + (ϕ(t))[1] ~ 0, 99.99999999999999(V(t))[1] - 199.99999999999997(V(t))[2] + 99.99999999999999(V(t))[3] + (ϕ(t))[2] ~ 0, 99.99999999999999(V(t))[2] - 199.99999999999997(V(t))[3] + 99.99999999999999(V(t))[4] + (ϕ(t))[3] ~ 0, 99.99999999999999(V(t))[3] - 199.99999999999997(V(t))[4] + 99.99999999999999(V(t))[5] + (ϕ(t))[4] ~ 0, 99.99999999999999(V(t))[4] - 199.99999999999997(V(t))[5] + 99.99999999999999(V(t))[6] + (ϕ(t))[5] ~ 0, 99.99999999999999(V(t))[5] - 199.99999999999997(V(t))[6] + 99.99999999999999(V(t))[7] + (ϕ(t))[6] ~ 0, 99.99999999999999(V(t))[6] - 199.99999999999997(V(t))[7] + 99.99999999999999(V(t))[8] + (ϕ(t))[7] ~ 0, 99.99999999999999(V(t))[7] - 199.99999999999997(V(t))[8] + 99.99999999999999(V(t))[9] + (ϕ(t))[8] ~ 0, 99.99999999999999(V(t))[10] + 99.99999999999999(V(t))[8] - 199.99999999999997(V(t))[9] + (ϕ(t))[9] ~ 0, -199.99999999999997(V(t))[10] + 99.99999999999999(V(t))[11] + 99.99999999999999(V(t))[9] + (ϕ(t))[10] ~ 0, (V(t))[11] ~ 1]

ArgumentError: SymbolicUtils.BasicSymbolic{Real}[(V(t))[10]] are missing from the variable map.

Stacktrace:
  [1] throw_missingvars(vars::Vector{SymbolicUtils.BasicSymbolic{Real}})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/Gpzyo/src/variables.jl:122
  [2] _varmap_to_vars(varmap::Dict{Any, Any}, varlist::Vector{SymbolicUtils.BasicSymbolic{Real}}; defaults::Dict{Any, Any}, check::Bool, toterm::typeof(ModelingToolkit.default_toterm))
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/Gpzyo/src/variables.jl:116
  [3] varmap_to_vars(varmap::Vector{Pair}, varlist::Vector{SymbolicUtils.BasicSymbolic{Real}}; defaults::Dict{Any, Any}, check::Bool, toterm::Function, promotetoconcrete::Nothing, tofloat::Bool, use_union::Bool)
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/Gpzyo/src/variables.jl:85
  [4] get_u0_p(sys::ODESystem, u0map::Vector{Pair}, parammap::SciMLBase.NullParameters; use_union::Bool, tofloat::Bool, symbolic_u0::Bool)
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/Gpzyo/src/systems/diffeqs/abstractodesystem.jl:786
  [5] get_u0_p
    @ ~/.julia/packages/ModelingToolkit/Gpzyo/src/systems/diffeqs/abstractodesystem.jl:768 [inlined]
  [6] process_DEProblem(constructor::Type, sys::ODESystem, u0map::Vector{Pair}, parammap::SciMLBase.NullParameters; implicit_dae::Bool, du0map::Nothing, version::Nothing, tgrad::Bool, jac::Bool, checkbounds::Bool, sparse::Bool, simplify::Bool, linenumbers::Bool, parallel::Symbolics.SerialForm, eval_expression::Bool, use_union::Bool, tofloat::Bool, symbolic_u0::Bool, u0_constructor::typeof(identity), kwargs::@Kwargs{t::Float64, has_difference::Bool, check_length::Bool})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/Gpzyo/src/systems/diffeqs/abstractodesystem.jl:811
  [7] (ODEProblem{true, SciMLBase.AutoSpecialize})(sys::ODESystem, u0map::Vector{Pair}, tspan::Tuple{Float64, Float64}, parammap::SciMLBase.NullParameters; callback::Nothing, check_length::Bool, kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/Gpzyo/src/systems/diffeqs/abstractodesystem.jl:936
  [8] ODEProblem
    @ ~/.julia/packages/ModelingToolkit/Gpzyo/src/systems/diffeqs/abstractodesystem.jl:929 [inlined]
  [9] (ODEProblem{true, SciMLBase.AutoSpecialize})(sys::ODESystem, u0map::Vector{Pair}, tspan::Tuple{Float64, Float64})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/Gpzyo/src/systems/diffeqs/abstractodesystem.jl:929
 [10] (ODEProblem{true})(::ODESystem, ::Vector{Pair}, ::Vararg{Any}; kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/Gpzyo/src/systems/diffeqs/abstractodesystem.jl:916
 [11] (ODEProblem{true})(::ODESystem, ::Vector{Pair}, ::Vararg{Any})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/Gpzyo/src/systems/diffeqs/abstractodesystem.jl:915
 [12] ODEProblem(::ODESystem, ::Vector{Pair}, ::Vararg{Any}; kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/Gpzyo/src/systems/diffeqs/abstractodesystem.jl:912
 [13] ODEProblem(::ODESystem, ::Vector{Pair}, ::Vararg{Any})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/Gpzyo/src/systems/diffeqs/abstractodesystem.jl:911
 [14] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}; analytic::Nothing, kwargs::@Kwargs{})
    @ PDEBase ~/.julia/packages/PDEBase/Aqj4G/src/discretization_state.jl:74
 [15] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
    @ PDEBase ~/.julia/packages/PDEBase/Aqj4G/src/discretization_state.jl:55
 [16] top-level scope
    @ In[1]:43

Environment (please complete the following information):

  • Output of using Pkg; Pkg.status() 
Status `/tmp/jl_z366gV/Project.toml`
⌅ [5b8099bc] DomainSets v0.6.7
  [94925ecb] MethodOfLines v0.10.7
  [961ee093] ModelingToolkit v8.75.0
  [8913a72c] NonlinearSolve v3.6.0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`
  • Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST) 
Status `/tmp/jl_z366gV/Manifest.toml`
  [47edcb42] ADTypes v0.2.6
  [1520ce14] AbstractTrees v0.4.5
  [79e6a3ab] Adapt v4.0.1
⌅ [ec485272] ArnoldiMethod v0.2.0
  [4fba245c] ArrayInterface v7.7.1
  [4c555306] ArrayLayouts v1.6.0
⌃ [13072b0f] AxisAlgorithms v1.0.1
  [e2ed5e7c] Bijections v0.1.6
  [62783981] BitTwiddlingConvenienceFunctions v0.1.5
  [2a0fbf3d] CPUSummary v0.2.4
  [00ebfdb7] CSTParser v3.4.1
  [49dc2e85] Calculus v0.5.1
  [d360d2e6] ChainRulesCore v1.22.0
  [fb6a15b2] CloseOpenIntervals v0.1.12
  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.12
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.0
  [34da2185] Compat v4.13.0
  [b152e2b5] CompositeTypes v0.1.3
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.4
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.17
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.147.0
  [459566f4] DiffEqCallbacks v2.37.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [b4f34e82] Distances v0.10.11
  [31c24e10] Distributions v0.25.107
  [ffbed154] DocStringExtensions v0.9.3
⌅ [5b8099bc] DomainSets v0.6.7
  [fa6b7ba4] DualNumbers v0.6.8
  [7c1d4256] DynamicPolynomials v0.5.5
  [4e289a0a] EnumX v1.0.4
  [f151be2c] EnzymeCore v0.6.5
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
  [7034ab61] FastBroadcast v0.2.8
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.1
  [1a297f60] FillArrays v1.9.3
  [6a86dc24] FiniteDiff v2.22.0
  [59287772] Formatting v0.4.2
  [f6369f11] ForwardDiff v0.10.36
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.7
  [46192b85] GPUArraysCore v0.1.6
  [c145ed77] GenericSchur v0.5.3
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.9.0
  [3e5b6fbb] HostCPUFeatures v0.1.16
  [34004b35] HypergeometricFunctions v0.3.23
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.4
⌅ [a98d9a8b] Interpolations v0.14.0
  [8197267c] IntervalSets v0.7.10
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.5.0
  [682c06a0] JSON v0.21.4
  [98e50ef6] JuliaFormatter v1.0.50
  [ccbc3e58] JumpProcesses v9.10.1
  [ef3ab10e] KLU v0.5.0
  [ba0b0d4f] Krylov v0.9.5
  [b964fa9f] LaTeXStrings v1.3.1
  [2ee39098] LabelledArrays v1.15.1
  [984bce1d] LambertW v0.4.6
  [23fbe1c1] Latexify v0.16.1
  [10f19ff3] LayoutPointers v0.1.15
  [50d2b5c4] Lazy v0.15.1
  [5078a376] LazyArrays v1.8.3
  [d3d80556] LineSearches v7.2.0
  [7ed4a6bd] LinearSolve v2.23.4
  [2ab3a3ac] LogExpFunctions v0.3.27
  [bdcacae8] LoopVectorization v0.12.166
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [a3b82374] MatrixFactorizations v2.1.0
  [bb5d69b7] MaybeInplace v0.1.1
  [94925ecb] MethodOfLines v0.10.7
  [e1d29d7a] Missings v1.1.0
  [961ee093] ModelingToolkit v8.75.0
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.4
  [d8a4904e] MutableArithmetics v1.4.1
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.0.2
  [8913a72c] NonlinearSolve v3.6.0
  [6fe1bfb0] OffsetArrays v1.13.0
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.71.0
  [a7812802] PDEBase v0.1.8
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.9
  [1d0040c9] PolyesterWeave v0.2.1
  [d236fae5] PreallocationTools v0.4.20
  [aea7be01] PrecompileTools v1.2.0
  [21216c6a] Preferences v1.4.1
  [1fd47b50] QuadGK v2.9.4
  [e6cf234a] RandomNumbers v1.5.3
  [c84ed2f1] Ratios v0.4.5
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.9.0
  [f2c3362d] RecursiveFactorization v0.2.21
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [79098fc4] Rmath v0.7.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.12
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.42
  [0bca4576] SciMLBase v2.26.1
  [c0aeaf25] SciMLOperators v0.3.7
  [efcf1570] Setfield v1.1.1
  [727e6d20] SimpleNonlinearSolve v1.5.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [47a9eef4] SparseDiffTools v2.17.0
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.3.1
  [aedffcd0] Static v0.8.10
  [0d7ed370] StaticArrayInterface v1.5.0
  [90137ffa] StaticArrays v1.9.3
  [1e83bf80] StaticArraysCore v1.4.2
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.2
  [4c63d2b9] StatsFuns v1.3.1
  [7792a7ef] StrideArraysCore v0.5.2
  [2efcf032] SymbolicIndexingInterface v0.3.7
  [d1185830] SymbolicUtils v1.5.0
  [0c5d862f] Symbolics v5.20.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.11.1
  [8ea1fca8] TermInterface v0.3.3
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.23
  [0796e94c] Tokenize v0.5.28
  [d5829a12] TriangularSolve v0.1.20
  [410a4b4d] Tricks v0.1.8
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1986cc42] Unitful v1.19.0
  [a7c27f48] Unityper v0.1.6
  [3d5dd08c] VectorizationBase v0.21.65
  [19fa3120] VertexSafeGraphs v0.2.0
⌅ [efce3f68] WoodburyMatrices v0.5.6
  [1d5cc7b8] IntelOpenMP_jll v2024.0.2+0
  [856f044c] MKL_jll v2024.0.0+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [f50d1b31] Rmath_jll v0.4.0+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.0+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [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 1.10.1
Commit 7790d6f0641 (2024-02-13 20:41 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × 11th Gen Intel(R) Core(TM) i7-11850H @ 2.50GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, tigerlake)
Threads: 16 default, 0 interactive, 8 GC (on 16 virtual cores)
Environment:
  LD_LIBRARY_PATH = /snap/alacritty/70/usr/lib/x86_64-linux-gnu:/snap/alacritty/70/lib/x86_64-linux-gnu:/snap/alacritty/70/usr/lib/x86_64-linux-gnu/dri
  JULIA_NUM_THREADS = auto

Additional context

The following very similar system is solved without issue.

using Pkg
Pkg.activate(temp=true)
Pkg.add(["OrdinaryDiffEq", "ModelingToolkit", "MethodOfLines", "DomainSets", "DifferentialEquations", "NonlinearSolve"])

using OrdinaryDiffEq, ModelingToolkit, MethodOfLines, DomainSets, DifferentialEquations, NonlinearSolve

# Parameters, variables, and derivatives
@parameters t r
@variables ϕ(..)

Drr = Differential(r)^2;

# Space and time domains
max_r = 1.0e0
domains_space = [r ∈ Interval(0.0, max_r)]

ϕfixed(r) = sign(-r + 0.1) + 1
eq_space = [
    Drr(V(r)) ~ - ϕfixed(r)^2,
]

bcs_space = [
    V(max_r) ~ 1,
]

# PDE system
@named pdesys_space = PDESystem(eq_space, bcs_space, domains_space, [r], [V(r)])

# Method of lines discretization
dr = 0.1
discretization_space = MOLFiniteDifference([r => dr], nothing);

# Convert the PDE problem into an ODE problem
prob_space = discretize(pdesys_space, discretization_space);

sol_space = NonlinearSolve.solve(prob_space, NewtonRaphson())
@assert SciMLBase.successful_retcode(sol_space)
sol_space.retcode

It has output

ReturnCode.Success = 1

musoke avatar Feb 21 '24 20:02 musoke