Tested higher-order methods; need to further diagnose KenCarp and ARKODE

Author: GodotMisogi

benchmarks/SimpleHandwrittenPDE/allen_cahn_fdm_wpd.jmd

@@ -87,14 +87,14 @@ plt = heatmap(xs, tslices, ys', xlabel="x", ylabel="t")
 #### Implicit-Explicit Methods
 
 ```julia
-abstols = 0.1 .^ (5:9) # all fixed dt methods so these don't matter much
-reltols = 0.1 .^ (1:5)
-multipliers = 0.5 .^ (0:4)
+abstols = 0.1 .^ (5:8) # all fixed dt methods so these don't matter much
+reltols = 0.1 .^ (1:4)
+multipliers = 0.5 .^ (0:3)
 setups = [
     Dict(:alg => IMEXEuler(), :dts => 1e-4 * multipliers),
     Dict(:alg => CNAB2(), :dts => 1e-4 * multipliers),
     Dict(:alg => CNLF2(), :dts => 1e-4 * multipliers),
-    Dict(:alg => SBDF2(), :dts => 1e-4 * multipliers)
+    Dict(:alg => SBDF2(), :dts => 1e-4 * multipliers),
 ]
 labels = hcat(
     "IMEXEuler",
@@ -112,9 +112,9 @@ plot(wp, label=labels, markershape=:auto, title="Work-Precision Diagram, High To
 #### Exponential Integrators
 
 ```julia
-abstols = 0.1 .^ (5:9) # all fixed dt methods so these don't matter much
-reltols = 0.1 .^ (1:5)
-multipliers = 0.5 .^ (0:4)
+abstols = 0.1 .^ (5:8) # all fixed dt methods so these don't matter much
+reltols = 0.1 .^ (1:4)
+multipliers = 0.5 .^ (0:3)
 setups = [
     Dict(:alg => NorsettEuler(), :dts => 1e-4 * multipliers),
     Dict(:alg => NorsettEuler(krylov=true, m=5), :dts => 1e-4 * multipliers),
@@ -135,39 +135,15 @@ labels = hcat(
     print_names=true, names=labels, numruns=5, error_estimate=:l2,
     save_everystep=false, appxsol=test_sol, maxiters=Int(1e5));
 
-plot(wp, label=labels, markershape=:auto, title="ExpRK methods, High Tolerance")
-```
-
-#### Explicit Methods
-
-```julia
-abstols = 0.1 .^ (5:7) # all fixed dt methods so these don't matter much
-reltols = 0.1 .^ (1:3)
-multipliers = 0.5 .^ (0:4)
-setups = [
-    Dict(:alg => RK4(), :dts => 1e-4 * multipliers),
-    Dict(:alg => Tsit5(), :dts => 1e-4 * multipliers),
-    Dict(:alg => Vern7(), :dts => 1e-4 * multipliers)
-]
-labels = hcat(
-    "RK4",
-    "Tsit5",
-    "Vern7",
-)
-@time wp = WorkPrecisionSet(prob, abstols, reltols, setups;
-    print_names=true, names=labels, numruns=5, error_estimate=:l2,
-    save_everystep=false, appxsol=test_sol, maxiters=Int(1e5));
-
-plot(wp, label=labels, markershape=:auto, title="Work-Precision Diagram, High Tolerance")
+plot(wp, label=labels, markershape=:auto, title="ExpRK Methods, High Tolerance")
 ```
 
-
 #### Comparisons Between Families
 
 ```julia
-abstols = 0.1 .^ (5:9) # all fixed dt methods so these don't matter much
-reltols = 0.1 .^ (1:5)
-multipliers = 0.5 .^ (0:4)
+abstols = 0.1 .^ (5:8) # all fixed dt methods so these don't matter much
+reltols = 0.1 .^ (1:4)
+multipliers = 0.5 .^ (0:3)
 setups = [
     Dict(:alg => CNAB2(), :dts => 1e-4 * multipliers),
     Dict(:alg => CNAB2(linsolve=KrylovJL_GMRES()), :dts => 1e-4 * multipliers),
@@ -184,7 +160,7 @@ labels = hcat(
     print_names=true, names=labels, numruns=5, error_estimate=:l2,
     save_everystep=false, appxsol=test_sol, maxiters=Int(1e5));
 
-plot(wp, label=labels, markershape=:auto, title="Between family, High Tolerances")
+plot(wp, label=labels, markershape=:auto, title="Between Families, High Tolerances")
 ```
 
 
@@ -197,12 +173,14 @@ Dense/banded linear solvers.
 ```julia
 abstols = 0.1 .^ (7:13)
 reltols = 0.1 .^ (4:10)
-setups = [Dict(:alg => KenCarp3()),
-          Dict(:alg => KenCarp4()),
-          Dict(:alg => KenCarp5()),
-          Dict(:alg => ARKODE(Sundials.Implicit(), order=3, linear_solver=:Band, jac_upper=1, jac_lower=1)),
-          Dict(:alg => ARKODE(Sundials.Implicit(), order=4, linear_solver=:Band, jac_upper=1, jac_lower=1)),
-          Dict(:alg => ARKODE(Sundials.Implicit(), order=5, linear_solver=:Band, jac_upper=1, jac_lower=1))]
+setups = [
+    Dict(:alg => KenCarp3()),
+    Dict(:alg => KenCarp4()),
+    Dict(:alg => KenCarp5()),
+    Dict(:alg => ARKODE(Sundials.Implicit(), order=3, linear_solver=:Band, jac_upper=1, jac_lower=1)),
+    Dict(:alg => ARKODE(Sundials.Implicit(), order=4, linear_solver=:Band, jac_upper=1, jac_lower=1)),
+    Dict(:alg => ARKODE(Sundials.Implicit(), order=5, linear_solver=:Band, jac_upper=1, jac_lower=1)),
+]
 labels = hcat(
     "KenCarp3",
     "KenCarp4",
@@ -211,23 +189,25 @@ labels = hcat(
     "ARKODE4",
     "ARKODE5",
 )
-@time wp = WorkPrecisionSet(prob,abstols,reltols,setups;
-        print_names=true, names=labels, numruns=5, error_estimate=:l2,
-        save_everystep=false, appxsol=test_sol, maxiters=Int(1e5));
+@time wp = WorkPrecisionSet(prob, abstols, reltols, setups;
+    print_names=true, names=labels, numruns=5, error_estimate=:l2,
+    save_everystep=false, appxsol=test_sol, maxiters=Int(1e5));
 
-plot(wp, label=labels, markershape=:auto, title="IMEX methods, band linsolve, Low Tolerances")
+plot(wp, label=labels, markershape=:auto, title="IMEX Methods, Band Linsolve, Low Tolerances")
 ```
 
 Krylov linear solvers.
 ```julia
 abstols = 0.1 .^ (7:13)
 reltols = 0.1 .^ (4:10)
-setups = [Dict(:alg => KenCarp3(linsolve=KrylovJL_GMRES())),
-          Dict(:alg => KenCarp4(linsolve=KrylovJL_GMRES())),
-          Dict(:alg => KenCarp5(linsolve=KrylovJL_GMRES())),
-          Dict(:alg => ARKODE(Sundials.Implicit(), order=3, linear_solver=:GMRES)),
-          Dict(:alg => ARKODE(Sundials.Implicit(), order=4, linear_solver=:GMRES)),
-          Dict(:alg => ARKODE(Sundials.Implicit(), order=5, linear_solver=:GMRES))]
+setups = [
+    Dict(:alg => KenCarp3(linsolve=KrylovJL_GMRES())),
+    Dict(:alg => KenCarp4(linsolve=KrylovJL_GMRES())),
+    Dict(:alg => KenCarp5(linsolve=KrylovJL_GMRES())),
+    Dict(:alg => ARKODE(Sundials.Implicit(), order=3, linear_solver=:GMRES)),
+    Dict(:alg => ARKODE(Sundials.Implicit(), order=4, linear_solver=:GMRES)),
+    Dict(:alg => ARKODE(Sundials.Implicit(), order=5, linear_solver=:GMRES)),
+]
 labels = hcat(
     "KenCarp3",
     "KenCarp4",
@@ -236,11 +216,11 @@ labels = hcat(
     "ARKODE4",
     "ARKODE5",
 )
-@time wp = WorkPrecisionSet(prob,abstols,reltols,setups;
-        print_names=true, names=labels, numruns=5, error_estimate=:l2,
-        save_everystep=false, appxsol=test_sol, maxiters=Int(1e5));
+@time wp = WorkPrecisionSet(prob, abstols, reltols, setups;
+    print_names=true, names=labels, numruns=5, error_estimate=:l2,
+    save_everystep=false, appxsol=test_sol, maxiters=Int(1e5));
 
-plot(wp, label=labels, markershape=:auto, title="IMEX methods, Krylov linsolve, Low Tolerances")
+plot(wp, label=labels, markershape=:auto, title="IMEX Methods, Krylov Linsolve, Low Tolerances")
 ```
 
 #### Exponential Integrators
@@ -249,19 +229,21 @@ plot(wp, label=labels, markershape=:auto, title="IMEX methods, Krylov linsolve,
 abstols = 0.1 .^ (7:11) # all fixed dt methods so these don't matter much
 reltols = 0.1 .^ (4:8)
 multipliers = 0.5 .^ (0:4)
-setups = [Dict(:alg => ETDRK3(), :dts => 1e-2 * multipliers),
-          Dict(:alg => ETDRK4(), :dts => 1e-2 * multipliers),
-          Dict(:alg => HochOst4(), :dts => 1e-2 * multipliers)]
+setups = [
+    Dict(:alg => ETDRK3(), :dts => 1e-2 * multipliers),
+    Dict(:alg => ETDRK4(), :dts => 1e-2 * multipliers),
+    Dict(:alg => HochOst4(), :dts => 1e-2 * multipliers),
+]
 labels = hcat(
     "ETDRK3 (caching)",
     "ETDRK4 (caching)",
     "HochOst4 (caching)",
 )
-@time wp = WorkPrecisionSet(prob,abstols,reltols,setups;
-        print_names=true, names=labels, numruns=5, error_estimate=:l2,
-        save_everystep=false, appxsol=test_sol, maxiters=Int(1e5));
+@time wp = WorkPrecisionSet(prob, abstols, reltols, setups;
+    print_names=true, names=labels, numruns=5, error_estimate=:l2,
+    save_everystep=false, appxsol=test_sol, maxiters=Int(1e5));
 
-plot(wp, label=labels, markershape=:auto, title="ExpRK methods, Low Tolerances")
+plot(wp, label=labels, markershape=:auto, title="ExpRK Methods, Low Tolerances")
 ```
 
 #### Comparisons Between Families
@@ -270,13 +252,15 @@ plot(wp, label=labels, markershape=:auto, title="ExpRK methods, Low Tolerances")
 abstols = 0.1 .^ (7:11)
 reltols = 0.1 .^ (4:8)
 multipliers = 0.5 .^ (0:4)
-setups = [Dict(:alg => ARKODE(Sundials.Implicit(), order=5, linear_solver=:Band, jac_upper=1, jac_lower=1)),
-          Dict(:alg => ETDRK3(), :dts => 1e-2 * multipliers),
-          Dict(:alg => ETDRK4(), :dts => 1e-2 * multipliers)]
+setups = [
+    Dict(:alg => ARKODE(Sundials.Implicit(), order=5, linear_solver=:GMRES)),
+    Dict(:alg => ETDRK3(), :dts => 1e-2 * multipliers),
+    Dict(:alg => ETDRK4(), :dts => 1e-2 * multipliers),
+]
 labels = hcat("ARKODE (nondiagonal linsolve)", "ETDRK3 ()", "ETDRK4 ()")
-@time wp = WorkPrecisionSet(prob,abstols,reltols,setups;
-        print_names=true, names=labels, numruns=5, error_estimate=:l2,
-        save_everystep=false, appxsol=test_sol, maxiters=Int(1e5));
+@time wp = WorkPrecisionSet(prob, abstols, reltols, setups;
+    print_names=true, names=labels, numruns=5, error_estimate=:l2,
+    save_everystep=false, appxsol=test_sol, maxiters=Int(1e5));
 
 plot(wp, label=labels, markershape=:auto, title="Between Families, Low Tolerances")
 ```