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Merge pull request #612 from JuliaDiffEq/myb/radau
WIP: implement fifth order Radau IIA
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,25 @@ | ||
| mutable struct RadauIIA5ConstantCache{F,Tab,Tol,Dt,U} <: OrdinaryDiffEqConstantCache | ||
| uf::F | ||
| tab::Tab | ||
| κ::Tol | ||
| tol::Tol | ||
| ηold::Tol | ||
| nl_iters::Int | ||
| dtprev::Dt | ||
| cont1::U | ||
| cont2::U | ||
| cont3::U | ||
| end | ||
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| function alg_cache(alg::RadauIIA5,u,rate_prototype,uEltypeNoUnits,uBottomEltypeNoUnits, | ||
| tTypeNoUnits,uprev,uprev2,f,t,dt,reltol,p,calck,::Type{Val{false}}) | ||
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| uf = DiffEqDiffTools.UDerivativeWrapper(f, t, p) | ||
| uToltype = real(uBottomEltypeNoUnits) | ||
| tab = RadauIIA5Tableau(uToltype, real(tTypeNoUnits)) | ||
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| κ = alg.κ !== nothing ? uToltype(alg.κ) : uToltype(1//100) | ||
| tol = alg.tol !== nothing ? uToltype(alg.tol) : uToltype(min(0.03,first(reltol)^(0.5))) | ||
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| RadauIIA5ConstantCache(uf, tab, κ, tol, zero(tol), 10000, dt, u, u, u) | ||
| end |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,158 @@ | ||
| function initialize!(integrator, cache::RadauIIA5ConstantCache) | ||
| integrator.kshortsize = 2 | ||
| integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) | ||
| integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal | ||
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| # Avoid undefined entries if k is an array of arrays | ||
| integrator.fsallast = zero(integrator.fsalfirst) | ||
| integrator.k[1] = integrator.fsalfirst | ||
| integrator.k[2] = integrator.fsallast | ||
| end | ||
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| @muladd function perform_step!(integrator, cache::RadauIIA5ConstantCache, repeat_step=false) | ||
| @unpack t,dt,uprev,u,f,p = integrator | ||
| @unpack T11, T12, T13, T21, T22, T23, T31, TI11, TI12, TI13, TI21, TI22, TI23, TI31, TI32, TI33 = cache.tab | ||
| @unpack c1, c2, γ, α, β, e1, e2, e3 = cache.tab | ||
| @unpack tol, κ, cont1, cont2, cont3 = cache | ||
| @unpack internalnorm, abstol, reltol, adaptive = integrator.opts | ||
| alg = unwrap_alg(integrator, true) | ||
| @unpack min_iter, max_iter = alg | ||
| mass_matrix = integrator.f.mass_matrix | ||
| is_compos = integrator.alg isa CompositeAlgorithm | ||
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| # precalculations | ||
| c1m1 = c1-1 | ||
| c2m1 = c2-1 | ||
| c1mc2= c1-c2 | ||
| κtol = κ*tol # used in Newton iteration | ||
| γdt, αdt, βdt = γ/dt, α/dt, β/dt | ||
| J = calc_J(integrator, cache, is_compos) | ||
| if u isa Number | ||
| LU1 = γdt*mass_matrix - J | ||
| LU2 = (αdt + βdt*im)*mass_matrix - J | ||
| else | ||
| LU1 = lu(γdt*mass_matrix - J) | ||
| LU2 = lu((αdt + βdt*im)*mass_matrix - J) | ||
| end | ||
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| # TODO better initial guess | ||
| if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant | ||
| cache.dtprev = one(cache.dtprev) | ||
| z1 = w1 = map(zero, u) | ||
| z2 = w2 = map(zero, u) | ||
| z3 = w3 = map(zero, u) | ||
| cache.cont1 = map(zero, u) | ||
| cache.cont2 = map(zero, u) | ||
| cache.cont3 = map(zero, u) | ||
| else | ||
| c3′ = dt/cache.dtprev | ||
| c1′ = c1*c3′ | ||
| c2′ = c2*c3′ | ||
| z1 = @. c1′ * (cont1 + (c1′-c2m1) * (cont2 + (c1′-c1m1) * cont3)) | ||
| z2 = @. c2′ * (cont1 + (c2′-c2m1) * (cont2 + (c2′-c1m1) * cont3)) | ||
| z3 = @. c3′ * (cont1 + (c3′-c2m1) * (cont2 + (c3′-c1m1) * cont3)) | ||
| w1 = @. TI11 * z1 + TI12 * z2 + TI13 * z3 | ||
| w2 = @. TI21 * z1 + TI22 * z2 + TI23 * z3 | ||
| w3 = @. TI31 * z1 + TI32 * z2 + TI33 * z3 | ||
| end | ||
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| # Newton iteration | ||
| local ndw, η | ||
| do_newton = true | ||
| iter = 0 | ||
| while do_newton && iter < max_iter | ||
| iter += 1 | ||
| ff1 = f(uprev+z1, p, t+c1*dt) | ||
| ff2 = f(uprev+z2, p, t+c2*dt) | ||
| ff3 = f(uprev+z3, p, t+ dt) # c3 = 1 | ||
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| fw1 = @. TI11 * ff1 + TI12 * ff2 + TI13 * ff3 | ||
| fw2 = @. TI21 * ff1 + TI22 * ff2 + TI23 * ff3 | ||
| fw3 = @. TI31 * ff1 + TI32 * ff2 + TI33 * ff3 | ||
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| if mass_matrix isa UniformScaling # `UniformScaling` doesn't play nicely with broadcast | ||
| Mw1 = @. mass_matrix.λ * w1 | ||
| Mw2 = @. mass_matrix.λ * w2 | ||
| Mw3 = @. mass_matrix.λ * w3 | ||
| else | ||
| Mw1 = mass_matrix*w1 | ||
| Mw2 = mass_matrix*w2 | ||
| Mw3 = mass_matrix*w3 | ||
| end | ||
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| rhs1 = @. fw1 - γdt*Mw1 | ||
| rhs2 = @. fw2 - αdt*Mw2 + βdt*Mw3 | ||
| rhs3 = @. fw3 - βdt*Mw2 - αdt*Mw3 | ||
| dw1 = LU1 \ rhs1 | ||
| dw23 = LU2 \ (@. rhs2 + rhs3*im) | ||
| dw2 = real(dw23) | ||
| dw3 = imag(dw23) | ||
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| iter != 1 && (ndwprev = ndw) | ||
| ndw = internalnorm(dw1) + internalnorm(dw2) + internalnorm(dw3) | ||
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| # check early stopping criterion | ||
| if iter != 1 | ||
| θ = ndw/ndwprev | ||
| θ ≥ 1 || ndw * θ^(max_iter - iter) > κtol * (1 - θ) && break | ||
| end | ||
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| w1 = @. w1 + dw1 | ||
| w2 = @. w2 + dw2 | ||
| w3 = @. w3 + dw3 | ||
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| # transform `w` to `z` | ||
| z1 = @. T11 * w1 + T12 * w2 + T13 * w3 | ||
| z2 = @. T21 * w1 + T22 * w2 + T23 * w3 | ||
| z3 = @. T31 * w1 + w2 # T32 = 1, T33 = 0 | ||
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| # check stopping criterion | ||
| if iter == 1 | ||
| η = max(cache.ηold, eps(eltype(reltol)))^(0.8) | ||
| do_newton = iszero(integrator.success_iter) || iter < min_iter || η * ndw > κtol | ||
| else | ||
| η = θ / (1 - θ) # calculated for possible early stopping | ||
| do_newton = iter < min_iter || η * ndw > κtol | ||
| end | ||
| end | ||
| cache.ηold = η | ||
| integrator.force_stepfail = do_newton | ||
| cache.nl_iters = iter | ||
| do_newton && return | ||
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| u = @. uprev + z3 | ||
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| if adaptive | ||
| e1dt, e2dt, e3dt = e1/dt, e2/dt, e3/dt | ||
| tmp = @. e1dt*z1 + e2dt*z2 + e3dt*z3 | ||
| mass_matrix != I && (tmp = mass_matrix*tmp) | ||
| utilde = @. integrator.fsalfirst + tmp | ||
| alg.smooth_est && (utilde = LU1 \ utilde) | ||
| atmp = calculate_residuals(utilde, uprev, u, abstol, reltol, internalnorm) | ||
| integrator.EEst = internalnorm(atmp) | ||
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| if integrator.iter == 1 || integrator.u_modified || integrator.EEst > oneunit(integrator.EEst) | ||
| f0 = f(uprev .+ utilde, p, t) | ||
| utilde = @. f0 + tmp | ||
| alg.smooth_est && (utilde = LU1 \ utilde) | ||
| atmp = calculate_residuals(utilde, uprev, u, abstol, reltol, internalnorm) | ||
| integrator.EEst = internalnorm(atmp) | ||
| end | ||
| end | ||
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| if integrator.EEst <= oneunit(integrator.EEst) | ||
| cache.dtprev = dt | ||
| if alg.extrapolant != :constant | ||
| cache.cont1 = @. (z2 - z3)/c2m1 | ||
| tmp = @. (z1 - z2)/c1mc2 | ||
| cache.cont2 = @. (tmp - cache.cont1) / c1m1 | ||
| cache.cont3 = @. cache.cont2 - (tmp - z1/c1)/c2 | ||
| end | ||
| end | ||
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| integrator.fsallast = f(u, p, t+dt) | ||
| integrator.k[1] = integrator.fsalfirst | ||
| integrator.k[2] = integrator.fsallast | ||
| integrator.u = u | ||
| return | ||
| end |
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