Added Low Storage RK methods

Project.toml

@@ -40,6 +40,7 @@ SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SimpleUnPack = "ce78b400-467f-4804-87d8-8f486da07d0a"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
+Static = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
 StaticArrayInterface = "0d7ed370-da01-4f52-bd93-41d350b8b718"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 TruncatedStacktraces = "781d530d-4396-4725-bb49-402e4bee1e77"

lib/OrdinaryDiffEqLowStorageRK/Project.toml

@@ -0,0 +1,24 @@
+name = "OrdinaryDiffEqLowStorageRK"
+uuid = "b0944070-b475-4768-8dec-fb6eb410534d"
+authors = ["ParamThakkar123 <[email protected]>"]
+version = "1.0.0"
+
+[deps]
+FastBroadcast = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
+MuladdMacro = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221"
+OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+Polyester = "f517fe37-dbe3-4b94-8317-1923a5111588"
+RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
+Static = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
+
+[compat]
+julia = "1.10"
+
+[extras]
+DiffEqDevTools = "f3b72e0c-5b89-59e1-b016-84e28bfd966d"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["DiffEqDevTools", "Random", "SafeTestsets", "Test"]

lib/OrdinaryDiffEqLowStorageRK/src/OrdinaryDiffEqLowStorageRK.jl

@@ -0,0 +1,33 @@
+module OrdinaryDiffEqLowStorageRK
+
+import OrdinaryDiffEq: alg_order, alg_adaptive_order, calculate_residuals!,
+                       beta2_default, beta1_default, gamma_default,
+                       initialize!, perform_step!, @unpack, unwrap_alg,
+                       calculate_residuals, ssp_coefficient,
+                       OrdinaryDiffEqAlgorithm, ispredictive,
+                       OrdinaryDiffEqMutableCache, OrdinaryDiffEqConstantCache,
+                       OrdinaryDiffEqAdaptiveAlgorithm, uses_uprev,
+                       default_controller, PIDController,
+                       alg_cache, _vec, _reshape, @cache, isfsal, full_cache,
+                       constvalue, _unwrap_val, du_alias_or_new, ArrayFuse
+using DiffEqBase, FastBroadcast, Polyester, MuladdMacro, RecursiveArrayTools
+import StaticArrays: SArray, MVector, SVector, @SVector, StaticArray, MMatrix, SA
+
+include("algorithms.jl")
+include("alg_utils.jl")
+include("low_storage_rk_caches.jl")
+include("low_storage_rk_perform_step.jl")
+
+export ORK256, CarpenterKennedy2N54, SHLDDRK64, HSLDDRK64, DGLDDRK73_C, DGLDDRK84_C,
+       DGLDDRK84_F, NDBLSRK124, NDBLSRK134, NDBLSRK144, 
+       CFRLDDRK64, TSLDDRK74, CKLLSRK43_2, CKLLSRK54_3C, 
+       CKLLSRK95_4S, CKLLSRK95_4C, CKLLSRK95_4M,
+       CKLLSRK54_3C_3R, CKLLSRK54_3M_3R, CKLLSRK54_3N_3R, CKLLSRK85_4C_3R, CKLLSRK85_4M_3R, CKLLSRK85_4P_3R,
+       CKLLSRK54_3N_4R, CKLLSRK54_3M_4R, CKLLSRK65_4M_4R, CKLLSRK85_4FM_4R, CKLLSRK75_4M_5R, 
+       ParsaniKetchesonDeconinck3S32, ParsaniKetchesonDeconinck3S82,
+       ParsaniKetchesonDeconinck3S53, ParsaniKetchesonDeconinck3S173,
+       ParsaniKetchesonDeconinck3S94, ParsaniKetchesonDeconinck3S184,
+       ParsaniKetchesonDeconinck3S105, ParsaniKetchesonDeconinck3S205,
+       RDPK3Sp35, RDPK3SpFSAL35, RDPK3Sp49, RDPK3SpFSAL49, RDPK3Sp510, RDPK3SpFSAL510,
+       KYK2014DGSSPRK_3S2, RK46NL
+end

lib/OrdinaryDiffEqLowStorageRK/src/alg_utils.jl

@@ -0,0 +1,130 @@
+alg_order(alg::KYK2014DGSSPRK_3S2) = 2
+alg_order(alg::ORK256) = 2
+alg_order(alg::CarpenterKennedy2N54) = 4
+alg_order(alg::NDBLSRK124) = 4
+alg_order(alg::NDBLSRK134) = 4
+alg_order(alg::NDBLSRK144) = 4
+alg_order(alg::CFRLDDRK64) = 4
+alg_order(alg::DGLDDRK73_C) = 3
+alg_order(alg::TSLDDRK74) = 4
+alg_order(alg::DGLDDRK84_C) = 4
+alg_order(alg::DGLDDRK84_F) = 4
+alg_order(alg::SHLDDRK64) = 4
+alg_order(alg::RK46NL) = 4
+alg_order(alg::ParsaniKetchesonDeconinck3S32) = 2
+alg_order(alg::ParsaniKetchesonDeconinck3S82) = 2
+alg_order(alg::ParsaniKetchesonDeconinck3S53) = 3
+alg_order(alg::ParsaniKetchesonDeconinck3S173) = 3
+alg_order(alg::ParsaniKetchesonDeconinck3S94) = 4
+alg_order(alg::ParsaniKetchesonDeconinck3S184) = 4
+alg_order(alg::ParsaniKetchesonDeconinck3S105) = 5
+alg_order(alg::ParsaniKetchesonDeconinck3S205) = 5
+alg_order(alg::CKLLSRK43_2) = 3
+alg_order(alg::CKLLSRK54_3C) = 4
+alg_order(alg::CKLLSRK95_4S) = 5
+alg_order(alg::CKLLSRK95_4C) = 5
+alg_order(alg::CKLLSRK95_4M) = 5
+alg_order(alg::CKLLSRK54_3C_3R) = 4
+alg_order(alg::CKLLSRK54_3M_3R) = 4
+alg_order(alg::CKLLSRK54_3N_3R) = 4
+alg_order(alg::CKLLSRK85_4C_3R) = 5
+alg_order(alg::CKLLSRK85_4M_3R) = 5
+alg_order(alg::RDPK3Sp35) = 3
+alg_order(alg::RDPK3SpFSAL35) = 3
+alg_order(alg::RDPK3Sp49) = 4
+alg_order(alg::RDPK3SpFSAL49) = 4
+alg_order(alg::RDPK3Sp510) = 5
+alg_order(alg::RDPK3SpFSAL510) = 5
+alg_order(alg::CKLLSRK85_4P_3R) = 5
+alg_order(alg::CKLLSRK85_4FM_4R) = 5
+alg_order(alg::CKLLSRK54_3N_4R) = 4
+alg_order(alg::CKLLSRK75_4M_5R) = 5
+alg_order(alg::CKLLSRK54_3M_4R) = 4
+alg_order(alg::CKLLSRK65_4M_4R) = 5
+
+isfsal(alg::ORK256) = false
+isfsal(alg::CarpenterKennedy2N54) = false
+isfsal(alg::DGLDDRK84_F) = false
+isfsal(alg::DGLDDRK73_C) = false
+isfsal(alg::DGLDDRK84_C) = false
+isfsal(alg::RDPK3Sp35) = false
+isfsal(alg::RDPK3Sp49) = false
+isfsal(alg::RDPK3Sp510) = false
+isfsal(alg::SHLDDRK64) = false
+isfsal(alg::NDBLSRK134) = false
+isfsal(alg::NDBLSRK124) = false
+isfsal(alg::NDBLSRK144) = false
+
+uses_uprev(alg::ORK256, adaptive::Bool) = false
+uses_uprev(alg::SHLDDRK64, adaptive::Bool) = false
+uses_uprev(alg::CarpenterKennedy2N54, adaptive::Bool) = false
+uses_uprev(alg::NDBLSRK124, adaptive::Bool) = false
+uses_uprev(alg::NDBLSRK134, adaptive::Bool) = false
+uses_uprev(alg::DGLDDRK84_F, adaptive::Bool) = false
+uses_uprev(alg::NDBLSRK144, adaptive::Bool) = false
+uses_uprev(alg::DGLDDRK84_C, adaptive::Bool) = false
+uses_uprev(alg::TSLDDRK74, adaptive::Bool) = false
+uses_uprev(alg::CFRLDDRK64, adaptive::Bool) = false
+uses_uprev(alg::DGLDDRK73_C, adaptive::Bool) = false
+uses_uprev(alg::CKLLSRK43_2, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK54_3C, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK95_4S, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK95_4C, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK95_4M, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK54_3C_3R, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK54_3M_3R, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK54_3N_3R, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK85_4C_3R, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK85_4M_3R, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK85_4P_3R, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK54_3N_4R, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK54_3M_4R, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK65_4M_4R, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK85_4FM_4R, adaptive::Bool) = adaptive
+uses_uprev(alg::CKLLSRK75_4M_5R, adaptive::Bool) = adaptive
+
+"""
+    ssp_coefficient(alg)
+
+Return the SSP coefficient of the ODE algorithm `alg`. If one time step of size
+`dt` with `alg` can be written as a convex combination of explicit Euler steps
+with step sizes `cᵢ * dt`, the SSP coefficient is the minimal value of `1/cᵢ`.
+
+# Examples
+
+```julia-repl
+julia> ssp_coefficient(SSPRK104())
+6
+```
+"""
+ssp_coefficient(alg::KYK2014DGSSPRK_3S2) = 0.8417
+
+function default_controller(alg::RDPK3Sp35, cache, qoldinit, args...)
+    QT = typeof(qoldinit)
+    return PIDController(map(Base.Fix1(convert, QT), (0.64, -0.31, 0.04))...)
+end
+
+function default_controller(alg::RDPK3SpFSAL35, cache, qoldinit, args...)
+    QT = typeof(qoldinit)
+    return PIDController(map(Base.Fix1(convert, QT), (0.70, -0.23, 0.00))...)
+end
+
+function default_controller(alg::RDPK3Sp49, cache, qoldinit, args...)
+    QT = typeof(qoldinit)
+    return PIDController(map(Base.Fix1(convert, QT), (0.25, -0.12, 0.00))...)
+end
+
+function default_controller(alg::RDPK3SpFSAL49, cache, qoldinit, args...)
+    QT = typeof(qoldinit)
+    return PIDController(map(Base.Fix1(convert, QT), (0.38, -0.18, 0.01))...)
+end
+
+function default_controller(alg::RDPK3Sp510, cache, qoldinit, args...)
+    QT = typeof(qoldinit)
+    return PIDController(map(Base.Fix1(convert, QT), (0.47, -0.20, 0.06))...)
+end
+
+function default_controller(alg::RDPK3SpFSAL510, cache, qoldinit, args...)
+    QT = typeof(qoldinit)
+    return PIDController(map(Base.Fix1(convert, QT), (0.45, -0.13, 0.00))...)
+end