Merge #164

164: Add background info for ODE solvers r=dennisYatunin a=dennisYatunin



Co-authored-by: Dennis Yatunin <[email protected]>

Author: bors[bot]

docs/make.jl

@@ -9,16 +9,16 @@ bib = CitationBibliography(joinpath(@__DIR__, "refs.bib"))
 #! format: off
 pages = [
     "index.md",
+    "Background Information" => [
+        "ODE Solvers" => "background/ode_solvers.md",
+        "Newtons Method" => "background/newtons_method.md",
+    ],
     "Algorithm formulations" => [
         "algo_formulations/lsrk.md",
         "algo_formulations/ssprk.md",
         "algo_formulations/ark.md",
         "algo_formulations/mrrk.md",
     ],
-    "Non-linear solvers" => [
-        "Formulation" => "nl_solvers/formulation.md",
-        "Newtons method" => "nl_solvers/newtons_method.md",
-    ],
     "Test problems" => [
         "test_problems/index.md",
     ],

docs/refs.bib

@@ -215,3 +215,20 @@ @article{RobertsSarsharSandu2018arxiv
     journal={arXiv preprint arXiv:1812.00808},
     year={2019}
 }
+
+@article{GTS2014,
+  title={Optimization-based limiters for the spectral element method},
+  author={Guba, Oksana and Taylor, Mark and St-Cyr, Amik},
+  journal={Journal of computational physics},
+  volume={267},
+  pages={176--195},
+  year={2014},
+  doi={10.1016/j.jcp.2014.02.029},
+}
+
+@article{HR2018arxiv,
+  title={New third order low-storage SSP explicit Runge-Kutta methods},
+  author={Higueras, Inmaculada and Roldán, Teo},
+  journal={arXiv preprint arXiv:1809.04807},
+  year={2018},
+}

docs/src/background/newtons_method.md

@@ -0,0 +1,3 @@
+# Newton's Method
+
+TODO: fill out

docs/src/background/ode_solvers.md

@@ -1,13 +1,12 @@
 import DiffEqBase
 export ClimaODEFunction, ForwardEulerODEFunction
 
-Base.@kwdef struct ClimaODEFunction{TL, TE, TI, L, D, S} <: DiffEqBase.AbstractODEFunction{true}
+Base.@kwdef struct ClimaODEFunction{TL, TE, TI, L, D} <: DiffEqBase.AbstractODEFunction{true}
     T_lim!::TL = nothing # nothing or (uₜ, u, p, t) -> ...
     T_exp!::TE = nothing # nothing or (uₜ, u, p, t) -> ...
     T_imp!::TI = nothing # nothing or (uₜ, u, p, t) -> ...
     lim!::L = (u, p, t, u_ref) -> nothing
     dss!::D = (u, p, t) -> nothing
-    stage_callback!::S = (u, p, t) -> nothing
 end
 
 # Don't wrap a ClimaODEFunction in an ODEFunction (makes ODEProblem work).

docs/src/nl_solvers/formulation.md

@@ -45,7 +45,7 @@ end
 function step_u!(integrator, cache::IMEXARKCache)
     (; u, p, t, dt, sol, alg) = integrator
     (; f) = sol.prob
-    (; T_lim!, T_exp!, T_imp!, lim!, dss!, stage_callback!) = f
+    (; T_lim!, T_exp!, T_imp!, lim!, dss!) = f
     (; name, tableau, newtons_method) = alg
     (; a_exp, b_exp, a_imp, b_imp, c_exp, c_imp) = tableau
     (; U, T_lim, T_exp, T_imp, temp, γ, newtons_method_cache) = cache
@@ -125,8 +125,6 @@ function step_u!(integrator, cache::IMEXARKCache)
             end
         end
 
-        stage_callback!(U[i], p, t_exp)
-
         if !all(iszero, a_exp[:, i]) || !iszero(b_exp[i])
             if !isnothing(T_lim!)
                 T_lim!(T_lim[i], U[i], p, t_exp)

docs/src/nl_solvers/newtons_method.md

@@ -54,7 +54,7 @@ end
 function step_u!(integrator, cache::IMEXSSPRKCache)
     (; u, p, t, dt, sol, alg) = integrator
     (; f) = sol.prob
-    (; T_lim!, T_exp!, T_imp!, lim!, dss!, stage_callback!) = f
+    (; T_lim!, T_exp!, T_imp!, lim!, dss!) = f
     (; name, tableau, newtons_method) = alg
     (; a_imp, b_imp, c_exp, c_imp) = tableau
     (; U, U_lim, U_exp, T_lim, T_exp, T_imp, temp, β, γ, newtons_method_cache) = cache
@@ -134,8 +134,6 @@ function step_u!(integrator, cache::IMEXSSPRKCache)
             end
         end
 
-        stage_callback!(U, p, t_exp)
-
         if !iszero(β[i])
             if !isnothing(T_lim!)
                 T_lim!(T_lim, U, p, t_exp)