Merge pull request #2450 from Shreyas-Ekanathan/master

Implement Part 1 Of Adaptive Radau Method

Author: ChrisRackauckas

lib/OrdinaryDiffEqFIRK/Project.toml

@@ -6,15 +6,20 @@ version = "1.1.1"
 [deps]
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FastBroadcast = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
+GenericLinearAlgebra = "14197337-ba66-59df-a3e3-ca00e7dcff7a"
+GenericSchur = "c145ed77-6b09-5dd9-b285-bf645a82121e"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 MuladdMacro = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221"
 OrdinaryDiffEqCore = "bbf590c4-e513-4bbe-9b18-05decba2e5d8"
 OrdinaryDiffEqDifferentiation = "4302a76b-040a-498a-8c04-15b101fed76b"
 OrdinaryDiffEqNonlinearSolve = "127b3ac7-2247-4354-8eb6-78cf4e7c58e8"
+Polynomials = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+RootedTrees = "47965b36-3f3e-11e9-0dcf-4570dfd42a8c"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 
 [compat]
 DiffEqBase = "6.152.2"

lib/OrdinaryDiffEqFIRK/src/OrdinaryDiffEqFIRK.jl

@@ -18,6 +18,7 @@ import OrdinaryDiffEqCore: alg_order, calculate_residuals!,
                            get_current_adaptive_order, get_fsalfirstlast,
                            isfirk, generic_solver_docstring
 using MuladdMacro, DiffEqBase, RecursiveArrayTools
+using Polynomials, GenericLinearAlgebra, GenericSchur
 using SciMLOperators: AbstractSciMLOperator
 using LinearAlgebra: I, UniformScaling, mul!, lu
 import LinearSolve
@@ -42,6 +43,6 @@ include("firk_tableaus.jl")
 include("firk_perform_step.jl")
 include("integrator_interface.jl")
 
-export RadauIIA3, RadauIIA5, RadauIIA9
+export RadauIIA3, RadauIIA5, RadauIIA9, AdaptiveRadau
 
 end

lib/OrdinaryDiffEqFIRK/src/alg_utils.jl

@@ -3,10 +3,12 @@ qmax_default(alg::Union{RadauIIA3, RadauIIA5, RadauIIA9}) = 8
 alg_order(alg::RadauIIA3) = 3
 alg_order(alg::RadauIIA5) = 5
 alg_order(alg::RadauIIA9) = 9
+alg_order(alg::AdaptiveRadau) = 5
 
 isfirk(alg::RadauIIA3) = true
 isfirk(alg::RadauIIA5) = true
 isfirk(alg::RadauIIA9) = true
+isfirk(alg::AdaptiveRadau) = true
 
 alg_adaptive_order(alg::RadauIIA3) = 1
 alg_adaptive_order(alg::RadauIIA5) = 3

lib/OrdinaryDiffEqFIRK/src/algorithms.jl

@@ -150,3 +150,42 @@ function RadauIIA9(; chunk_size = Val{0}(), autodiff = Val{true}(),
         controller,
         step_limiter!)
 end
+
+struct AdaptiveRadau{CS, AD, F, P, FDT, ST, CJ, Tol, C1, C2, StepLimiter} <:
+    OrdinaryDiffEqNewtonAdaptiveAlgorithm{CS, AD, FDT, ST, CJ}
+ linsolve::F
+ precs::P
+ smooth_est::Bool
+ extrapolant::Symbol
+ κ::Tol
+ maxiters::Int
+ fast_convergence_cutoff::C1
+ new_W_γdt_cutoff::C2
+ controller::Symbol
+ step_limiter!::StepLimiter
+ num_stages::Int
+end
+
+function AdaptiveRadau(; chunk_size = Val{0}(), autodiff = Val{true}(),
+     standardtag = Val{true}(), concrete_jac = nothing,
+     diff_type = Val{:forward}, num_stages = 3, 
+     linsolve = nothing, precs = DEFAULT_PRECS,
+     extrapolant = :dense, fast_convergence_cutoff = 1 // 5,
+     new_W_γdt_cutoff = 1 // 5,
+     controller = :Predictive, κ = nothing, maxiters = 10, smooth_est = true,
+     step_limiter! = trivial_limiter!)
+ AdaptiveRadau{_unwrap_val(chunk_size), _unwrap_val(autodiff), typeof(linsolve),
+     typeof(precs), diff_type, _unwrap_val(standardtag), _unwrap_val(concrete_jac),
+     typeof(κ), typeof(fast_convergence_cutoff),
+     typeof(new_W_γdt_cutoff), typeof(step_limiter!)}(linsolve,
+     precs,
+     smooth_est,
+     extrapolant,
+     κ,
+     maxiters,
+     fast_convergence_cutoff,
+     new_W_γdt_cutoff,
+     controller,
+     step_limiter!, num_stages)
+end
+

lib/OrdinaryDiffEqFIRK/src/firk_caches.jl

@@ -287,6 +287,7 @@ mutable struct RadauIIA9ConstantCache{F, Tab, Tol, Dt, U, JType} <:
     cont2::U
     cont3::U
     cont4::U
+    cont5::U
     dtprev::Dt
     W_γdt::Dt
     status::NLStatus
@@ -304,7 +305,7 @@ function alg_cache(alg::RadauIIA9, u, rate_prototype, ::Type{uEltypeNoUnits},
     κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100)
     J = false .* _vec(rate_prototype) .* _vec(rate_prototype)'
 
-    RadauIIA9ConstantCache(uf, tab, κ, one(uToltype), 10000, u, u, u, u, dt, dt,
+    RadauIIA9ConstantCache(uf, tab, κ, one(uToltype), 10000, u, u, u, u, u, dt, dt,
         Convergence, J)
 end
 
@@ -333,6 +334,7 @@ mutable struct RadauIIA9Cache{uType, cuType, uNoUnitsType, rateType, JType, W1Ty
     cont2::uType
     cont3::uType
     cont4::uType
+    cont5::uType
     du1::rateType
     fsalfirst::rateType
     k::rateType
@@ -407,6 +409,7 @@ function alg_cache(alg::RadauIIA9, u, rate_prototype, ::Type{uEltypeNoUnits},
     cont2 = zero(u)
     cont3 = zero(u)
     cont4 = zero(u)
+    cont5 = zero(u)
 
     fsalfirst = zero(rate_prototype)
     k = zero(rate_prototype)
@@ -462,11 +465,193 @@ function alg_cache(alg::RadauIIA9, u, rate_prototype, ::Type{uEltypeNoUnits},
 
     RadauIIA9Cache(u, uprev,
         z1, z2, z3, z4, z5, w1, w2, w3, w4, w5,
-        dw1, ubuff, dw23, dw45, cubuff1, cubuff2, cont1, cont2, cont3, cont4,
+        dw1, ubuff, dw23, dw45, cubuff1, cubuff2, cont1, cont2, cont3, cont4, cont5,
         du1, fsalfirst, k, k2, k3, k4, k5, fw1, fw2, fw3, fw4, fw5,
         J, W1, W2, W3,
         uf, tab, κ, one(uToltype), 10000,
         tmp, tmp2, tmp3, tmp4, tmp5, tmp6, atmp, jac_config,
         linsolve1, linsolve2, linsolve3, rtol, atol, dt, dt,
         Convergence, alg.step_limiter!)
 end
+
+mutable struct AdaptiveRadauConstantCache{F, Tab, Tol, Dt, U, JType} <:
+    OrdinaryDiffEqConstantCache
+    uf::F
+    tab::Tab
+    κ::Tol
+    ηold::Tol
+    iter::Int
+    cont::Vector{U}
+    dtprev::Dt
+    W_γdt::Dt
+    status::NLStatus
+    J::JType
+end
+
+function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits},
+        ::Type{uBottomEltypeNoUnits},
+        ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck,
+        ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits}
+    uf = UDerivativeWrapper(f, t, p)
+    uToltype = constvalue(uBottomEltypeNoUnits)
+    num_stages = alg.num_stages
+
+    if (num_stages == 3)
+        tab = BigRadauIIA5Tableau(uToltype, constvalue(tTypeNoUnits))
+    elseif (num_stages == 5)
+        tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits))
+    elseif (num_stages == 7)
+        tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits))
+    elseif iseven(num_stages) || num_stages <3
+        error("num_stages must be odd and 3 or greater")
+    else
+        tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages)
+    end
+
+    cont = Vector{typeof(u)}(undef, num_stages)
+    for i in 1: num_stages
+        cont[i] = zero(u)
+    end
+
+    κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100)
+    J = false .* _vec(rate_prototype) .* _vec(rate_prototype)'
+
+    AdaptiveRadauConstantCache(uf, tab, κ, one(uToltype), 10000, cont, dt, dt,
+        Convergence, J)
+end
+
+mutable struct AdaptiveRadauCache{uType, cuType, tType, uNoUnitsType, rateType, JType, W1Type, W2Type,
+    UF, JC, F1, F2, Tab, Tol, Dt, rTol, aTol, StepLimiter} <:
+               FIRKMutableCache
+    u::uType
+    uprev::uType
+    z::Vector{uType}
+    w::Vector{uType}
+    c_prime::Vector{tType}
+    dw1::uType
+    ubuff::uType
+    dw2::Vector{cuType}
+    cubuff::Vector{cuType}
+    dw::Vector{uType}
+    cont::Vector{uType}
+    derivatives:: Matrix{uType}
+    du1::rateType
+    fsalfirst::rateType
+    ks::Vector{rateType}
+    k::rateType
+    fw::Vector{rateType}
+    J::JType
+    W1::W1Type #real
+    W2::Vector{W2Type} #complex
+    uf::UF
+    tab::Tab
+    κ::Tol
+    ηold::Tol
+    iter::Int
+    tmp::uType
+    atmp::uNoUnitsType
+    jac_config::JC
+    linsolve1::F1 #real
+    linsolve2::Vector{F2} #complex
+    rtol::rTol
+    atol::aTol
+    dtprev::Dt
+    W_γdt::Dt
+    status::NLStatus
+    step_limiter!::StepLimiter
+end
+
+function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits},
+        ::Type{uBottomEltypeNoUnits},
+        ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck,
+        ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits}
+    uf = UJacobianWrapper(f, t, p)
+    uToltype = constvalue(uBottomEltypeNoUnits)
+    num_stages = alg.num_stages
+
+    if (num_stages == 3)
+        tab = BigRadauIIA5Tableau(uToltype, constvalue(tTypeNoUnits))
+    elseif (num_stages == 5)
+        tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits))
+    elseif (num_stages == 7)
+        tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits))
+    elseif iseven(num_stages) || num_stages < 3
+        error("num_stages must be odd and 3 or greater")
+    else
+        tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages)
+    end
+
+    κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100)
+
+    z = Vector{typeof(u)}(undef, num_stages)
+    w = Vector{typeof(u)}(undef, num_stages)
+    for i in 1 : num_stages
+        z[i] = w[i] = zero(u)
+    end
+
+    c_prime = Vector{typeof(t)}(undef, num_stages) #time stepping
+
+    dw1 = zero(u)
+    ubuff = zero(u)
+    dw2 = [similar(u, Complex{eltype(u)}) for _ in 1 : (num_stages - 1) ÷ 2]
+    recursivefill!.(dw2, false)
+    cubuff = [similar(u, Complex{eltype(u)}) for _ in 1 : (num_stages - 1) ÷ 2]
+    recursivefill!.(cubuff, false)
+    dw = Vector{typeof(u)}(undef, num_stages - 1)
+
+    cont = Vector{typeof(u)}(undef, num_stages)
+    for i in 1 : num_stages
+        cont[i] = zero(u)
+    end
+
+    derivatives = Matrix{typeof(u)}(undef, num_stages, num_stages)
+    for i in 1 : num_stages, j in 1 : num_stages
+        derivatives[i, j] = zero(u)
+    end
+
+    fsalfirst = zero(rate_prototype)
+    fw = Vector{typeof(rate_prototype)}(undef, num_stages)
+    ks = Vector{typeof(rate_prototype)}(undef, num_stages)
+    for i in 1: num_stages
+        ks[i] = fw[i] = zero(rate_prototype)
+    end
+    k = ks[1]
+
+    J, W1 = build_J_W(alg, u, uprev, p, t, dt, f, uEltypeNoUnits, Val(true))
+    if J isa AbstractSciMLOperator
+        error("Non-concrete Jacobian not yet supported by AdaptiveRadau.")
+    end
+
+    W2 = [similar(J, Complex{eltype(W1)}) for _ in 1 : (num_stages - 1) ÷ 2]
+    recursivefill!.(W2, false)
+
+    du1 = zero(rate_prototype)
+
+    tmp = zero(u)
+
+    atmp = similar(u, uEltypeNoUnits)
+    recursivefill!(atmp, false)
+
+    jac_config = build_jac_config(alg, f, uf, du1, uprev, u, zero(u), dw1)
+
+    linprob = LinearProblem(W1, _vec(ubuff); u0 = _vec(dw1))
+    linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true,
+        assumptions = LinearSolve.OperatorAssumptions(true))
+
+    linsolve2 = [
+        init(LinearProblem(W2[i], _vec(cubuff[i]); u0 = _vec(dw2[i])), alg.linsolve, alias_A = true, alias_b = true,
+            assumptions = LinearSolve.OperatorAssumptions(true)) for i in 1 : (num_stages - 1) ÷ 2]
+
+    rtol = reltol isa Number ? reltol : zero(reltol)
+    atol = reltol isa Number ? reltol : zero(reltol)
+
+    AdaptiveRadauCache(u, uprev,
+        z, w, c_prime, dw1, ubuff, dw2, cubuff, dw, cont, derivatives, 
+        du1, fsalfirst, ks, k, fw,
+        J, W1, W2,
+        uf, tab, κ, one(uToltype), 10000, tmp,
+        atmp, jac_config,
+        linsolve1, linsolve2, rtol, atol, dt, dt,
+        Convergence, alg.step_limiter!)
+end
+