Add BVDAE solvers

.github/workflows/Tests.yml

@@ -33,6 +33,7 @@ jobs:
           - "SHOOTING"
           - "FIRK(EXPANDED)"
           - "FIRK(NESTED)"
+          - "ASCHER"
           - "WRAPPERS"
         version: ['1.10']
     uses: "SciML/.github/.github/workflows/tests.yml@v1"

lib/BoundaryValueDiffEqAscher/LICENSE.md

@@ -0,0 +1,21 @@
+The BoundaryValueDiffEq.jl package is licensed under the MIT "Expat" License:
+
+> Copyright (c) 2017: ChrisRackauckas.
+> 
+> Permission is hereby granted, free of charge, to any person obtaining a copy
+> of this software and associated documentation files (the "Software"), to deal
+> in the Software without restriction, including without limitation the rights
+> to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+> copies of the Software, and to permit persons to whom the Software is
+> furnished to do so, subject to the following conditions:
+> 
+> The above copyright notice and this permission notice shall be included in all
+> copies or substantial portions of the Software.
+> 
+> THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+> IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+> FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+> AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+> LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+> OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+> SOFTWARE.

lib/BoundaryValueDiffEqAscher/Project.toml

@@ -0,0 +1,75 @@
+name = "BoundaryValueDiffEqAscher"
+uuid = "7227322d-7511-4e07-9247-ad6ff830280e"
+authors = ["Qingyu Qu <erikqqy123@gmail.com>"]
+version = "1.0.0"
+
+[deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+AlmostBlockDiagonals = "a95523ee-d6da-40b5-98cc-27bc505739d5"
+ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+BoundaryValueDiffEqCore = "56b672f2-a5fe-4263-ab2d-da677488eb3a"
+ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
+Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
+NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
+PreallocationTools = "d236fae5-4411-538c-8e31-a6e3d9e00b46"
+PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
+Preferences = "21216c6a-2e73-6563-6e65-726566657250"
+RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
+Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
+
+[compat]
+ADTypes = "1.2"
+Adapt = "4"
+AlmostBlockDiagonals = "0.1.10"
+ArrayInterface = "7.7"
+BandedMatrices = "1.4"
+BoundaryValueDiffEqCore = "1.0.0"
+ConcreteStructs = "0.2.3"
+DiffEqBase = "6.146"
+DiffEqDevTools = "2.44"
+FastClosures = "0.3"
+ForwardDiff = "0.10.36"
+JET = "0.8"
+LinearAlgebra = "1.10"
+LinearSolve = "2.21"
+Logging = "1.10"
+NonlinearSolve = "3.8.1"
+PreallocationTools = "0.4.24"
+PrecompileTools = "1.2"
+Preferences = "1.4"
+Random = "1.10"
+ReTestItems = "1.23.1"
+RecursiveArrayTools = "3.27.0"
+Reexport = "1.2"
+SciMLBase = "2.40"
+Setfield = "1"
+SparseArrays = "1.10"
+SparseDiffTools = "2.14"
+StaticArrays = "1.8.1"
+Test = "1.10"
+julia = "1.10"
+
+[extras]
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+DiffEqDevTools = "f3b72e0c-5b89-59e1-b016-84e28bfd966d"
+JET = "c3a54625-cd67-489e-a8e7-0a5a0ff4e31b"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
+RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["Aqua", "DiffEqDevTools", "JET", "LinearSolve", "Random", "ReTestItems", "RecursiveArrayTools", "StaticArrays", "Test"]

lib/BoundaryValueDiffEqAscher/src/BoundaryValueDiffEqAscher.jl

@@ -0,0 +1,39 @@
+module BoundaryValueDiffEqAscher
+
+using ADTypes
+using AlmostBlockDiagonals
+using BoundaryValueDiffEqCore
+using ConcreteStructs
+using FastClosures
+using ForwardDiff
+using LinearAlgebra
+using NonlinearSolve
+using PreallocationTools
+using RecursiveArrayTools
+using Reexport
+using SciMLBase
+using Setfield
+
+import BoundaryValueDiffEqCore: BVPJacobianAlgorithm, __extract_problem_details,
+                                concrete_jacobian_algorithm, __Fix3,
+                                __concrete_nonlinearsolve_algorithm,
+                                __unsafe_nonlinearfunction, BoundaryValueDiffEqAlgorithm,
+                                __sparse_jacobian_cache, __vec, __vec_f, __vec_f!, __vec_bc,
+                                __vec_bc!
+
+import SciMLBase: AbstractDiffEqInterpolation, StandardBVProblem, __solve, _unwrap_val
+
+@reexport using ADTypes, DiffEqBase, NonlinearSolve, SparseDiffTools, SciMLBase
+
+include("types.jl")
+include("utils.jl")
+include("algorithms.jl")
+include("alg_utils.jl")
+include("ascher_tableaus.jl")
+include("ascher.jl")
+include("adaptivity.jl")
+include("collocation.jl")
+
+export Ascher1, Ascher2, Ascher3, Ascher4, Ascher5, Ascher6, Ascher7
+
+end # module BoundaryValueDiffEqAscher

lib/BoundaryValueDiffEqAscher/src/adaptivity.jl

@@ -0,0 +1,222 @@
+# mesh_selector refine nd redistribute according to the initial mesh
+function mesh_selector!(
+        cache::AscherCache{iip, T}, z, dmz, mesh, mesh_dt, abstol) where {iip, T}
+    (; k, ncomp) = cache
+    # weights for mesh selection
+    cnsts2 = [1.25e-1, 2.604e-3, 8.019e-3, 2.170e-5, 7.453e-5, 5.208e-4, 9.689e-8,
+        3.689e-7, 3.100e-6, 2.451e-5, 2.691e-10, 1.120e-9, 1.076e-8, 9.405e-8,
+        1.033e-6, 5.097e-13, 2.290e-12, 2.446e-11, 2.331e-10, 2.936e-9, 3.593e-8,
+        7.001e-16, 3.363e-15, 3.921e-14, 4.028e-13, 5.646e-12, 7.531e-11, 1.129e-9]
+
+    koff = Int(k * (k + 1) / 2)
+    wgtmsh = 10 * cnsts2[koff]
+    root = 1 / (k + 1)
+    n = length(mesh) - 1
+    slope = Vector{T}(undef, n)
+    accum = Vector{T}(undef, n + 1)
+    d = Vector{T}(undef, ncomp)
+    d1 = similar(d)
+    d2 = similar(d)
+    # the first interval has to be treated separately from the
+    # other intervals (generally the solution on the (i-1)st and ith
+    # intervals will be used to approximate the needed derivative, but
+    # here the 1st and second intervals are used.)
+    hiold = mesh_dt[1]
+    @views horder(cache, d1, hiold, dmz[1])
+    hiold = mesh_dt[2]
+    @views horder(cache, d2, hiold, dmz[2])
+    oneovh = 2.0 / (mesh[3] - mesh[1])
+    slp = @. (abs(d2 - d1) * wgtmsh * oneovh / (abstol * (T(1) + abs(z[1]))))^root
+    slope[1] = maximum(slp)
+    slphmx = slope[1] * mesh_dt[1]
+    accum[2] = slphmx
+    iflip = 1
+
+    # go through the remaining intervals generating slope
+    # and  accum
+    for i in 2:n
+        hiold = mesh_dt[i]
+        iflip == -1 && @views horder(cache, d1, hiold, dmz[i])
+        iflip == 1 && @views horder(cache, d2, hiold, dmz[i])
+        oneovh = 2.0 / (mesh[i + 1] - mesh[i - 1])
+
+        # evaluate function to be equidistributed
+        slp = @. (abs(d2 - d1) * wgtmsh * oneovh / (abstol * (T(1) + abs(z[i]))))^root
+        slope[i] = maximum(slp)
+
+        # accumulate approximate integral of function to be equidistributed
+        temp = slope[i] * hiold
+        slphmx = max(slphmx, temp)
+        accum[i + 1] = accum[i] + temp
+        iflip = -iflip
+    end
+
+    avrg = accum[n + 1] / n
+    # `degequ` is the degree of equidistribution which then is used to
+    # determine whether the mesh redistribution is worthwhile or just
+    # halving the mesh is enough.
+    degequ = avrg / max(slphmx, eps(T))
+
+    # expected n to achieve 0.1x user requested tolerances
+    naccum = floor(Int, accum[n + 1] + 1)
+
+    # decide if mesh selection is worthwhile (otherwise, directly halving mesh is enough)
+    if (avrg < eps(T)) || (degequ >= 0.5)
+        # Just continue with utilizing the halved mesh which was used for error estimation
+        return
+    else
+        redistribute!(cache, length(cache.original_mesh), naccum, slope, accum)
+    end
+end
+
+function redistribute!(cache::AscherCache{iip, T}, nold::I, naccum::I,
+        slope::Vector{T}, accum::Vector{T}) where {iip, T, I <: Integer}
+    (; prob, fixpnt, mesh, mesh_dt) = cache
+    n::Int = length(slope)
+    nmax = copy(n)
+    mesh_old = copy(cache.original_mesh)
+    # nmx assures mesh has at least half as many subintervals as the
+    # previous mesh
+    nmx = max(nold + 1, naccum) / 2
+
+    # assures that halving will be possible later
+    nmax2 = nmax / 2
+
+    # the mesh is at most halved
+    n = min(nmax2, nold, nmx)
+
+    noldp1 = nold + 1
+    nfxp1 = length(fixpnt) + 1
+    # ensure that fixpnt is included in the new mesh
+    (n < nfxp1) && (n = nfxp1)
+
+    # having decided to generate a new mesh with n subintervals we now
+    # do so, taking into account that the nfxpnt points in the array
+    # fixpnt must be included in the new mesh.
+    inn = 1
+    accl = T(0)
+    lold = 2
+    lcarry = 0
+    lnew = 0
+    resize!(mesh, n + 1)
+    mesh[1] = first(prob.tspan)
+    mesh[n + 1] = last(prob.tspan)
+
+    for i in 1:nfxp1
+        if i !== nfxp1
+            for j in lold:noldp1
+                lnew = j
+                (fixpnt[i] <= mesh_old[j]) && break
+            end
+            accr = accum[lnew] + (fixpnt[i] - mesh_old[lnew]) * slope[lnew - 1]
+            nregn = (accr - accl) / accum[noldp1] * n - T(0.5)
+            nregn = min(nregn, n - inn - nfxp1 + i)
+            mesh[inn + nregn + 1] = fixpnt[i]
+        else
+            accr = accum[noldp1]
+            lnew = noldp1
+            nregn = n - inn
+        end
+        if nregn !== 0
+            temp = accl
+            tsum = (accr - accl) / (nregn + 1)
+            for j in 1:nregn
+                inn = inn + 1
+                temp = temp + tsum
+                for l in lold:lnew
+                    lcarry = l
+                    (temp <= accum[l]) && break
+                end
+                lold = lcarry
+                mesh[inn] = mesh_old[lold - 1] + (temp - accum[lold - 1]) / slope[lold - 1]
+            end
+        end
+        inn = inn + 1
+        accl = accr
+        lold = lnew
+    end
+    mesh_dt = diff(mesh)
+end
+
+function halve_mesh!(cache::AscherCache)
+    (; mesh, mesh_dt, valstr) = cache
+    n = length(mesh) - 1
+    old_mesh = copy(mesh)
+    for i in 1:n
+        x = mesh[i]
+        hd6 = mesh_dt[i] / 6.0
+        for j in 1:4
+            x = x + hd6
+            (j == 3) && (x = x + hd6)
+            @views approx(cache, x, valstr[i][j])
+        end
+    end
+
+    # halve the current mesh
+    N = 2 * n
+    resize!(mesh, N + 1)
+    resize!(mesh_dt, N)
+    mesh[1] = old_mesh[1]
+
+    for i in 1:n
+        mesh[2i] = (old_mesh[i] + old_mesh[i + 1]) / 2.0
+        mesh[2i + 1] = old_mesh[i + 1]
+    end
+    mesh_dt[1:end] = diff(mesh)[1:end]
+end
+
+# determine the error estimate and test to see if the
+# error tolerances are satisfied
+function error_estimate!(cache::AscherCache)
+    (; k, valstr, mesh, mesh_dt, error) = cache
+    # weights for extrapolation error estimate
+    cnsts1 = [0.25e0, 0.625e-1, 7.2169e-2, 1.8342e-2, 1.9065e-2, 5.8190e-2, 5.4658e-3,
+        5.3370e-3, 1.8890e-2, 2.7792e-2, 1.6095e-3, 1.4964e-3, 7.5938e-3, 5.7573e-3,
+        1.8342e-2, 4.673e-3, 4.150e-4, 1.919e-3, 1.468e-3, 6.371e-3, 4.610e-3,
+        1.342e-4, 1.138e-4, 4.889e-4, 4.177e-4, 1.374e-3, 1.654e-3, 2.863e-3]
+    # assign weights for error estimate
+    koff = Int(k * (k + 1) / 2)
+    wgterr = cnsts1[koff]
+    n = length(mesh) - 1
+
+    # error estimates are to be generated and tested
+    # to see if the tolerance requirements are satisfied.
+    for i in n:-1:1
+        # the error estimates are obtained by combining values of the numerical solutions for two meshes.
+        # for each value of iback we will consider the two approximation at 2 points in each of
+        # the new subintervals. we work backwards through the subinterval so that new values can be stored
+        # in valstr in case they prove to be needed later for an error estimate.
+        x = mesh[i] + (mesh_dt[i]) * 2.0 / 3.0
+        @views approx(cache, x, valstr[i][3])
+        error[i] .= wgterr .*
+                    abs.(valstr[i][3] .-
+                         (isodd(i) ? valstr[Int((i + 1) / 2)][2] : valstr[Int(i / 2)][4]))
+
+        x = mesh[i] + (mesh_dt[i]) / 3.0
+        @views approx(cache, x, valstr[i][2])
+        error[i] .= error[i] .+
+                    wgterr .*
+                    abs.(valstr[i][2] .-
+                         (isodd(i) ? valstr[Int((i + 1) / 2)][1] : valstr[Int(i / 2)][3]))
+    end
+    return maximum(reduce(hcat, error), dims = 2)
+end
+
+# determine highest order (piecewise constant) derivatives
+# of the current collocation solution
+function horder(cache::AscherCache, uhigh, hi, dmzi)
+    (; ncomp, k, TU) = cache
+    (; coef) = TU
+    dn = 1.0 / hi^(k - 1)
+    uhigh[1:ncomp] .= 0.0
+
+    idmz = 1
+    vdmzi = reduce(vcat, dmzi)
+    for j in 1:k
+        fact = dn * coef[1, j]
+        for id in 1:ncomp
+            uhigh[id] = uhigh[id] + fact * vdmzi[idmz]
+            idmz = idmz + 1
+        end
+    end
+end

lib/BoundaryValueDiffEqAscher/src/alg_utils.jl

@@ -0,0 +1,6 @@
+for stage in (1, 2, 3, 4, 5, 6, 7)
+    alg = Symbol("Ascher$(stage)")
+    @eval alg_stage(::$(alg)) = $stage
+end
+
+SciMLBase.isadaptive(alg::AbstractAscher) = true