Reorganized high tolerance and low tolerance order in KdV pseudospectral

Author: GodotMisogi

benchmarks/SimpleHandwrittenPDE/kdv_spectral_wpd.jmd

@@ -80,6 +80,86 @@ plt = heatmap(xs, tslices, ys', xlabel = "x", ylabel = "t")
 
 ## Work-Precision Diagrams
 
+### High Tolerances
+
+#### Implicit-Explicit Methods
+
+```julia
+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),
+]
+labels = hcat(
+    "IMEXEuler",
+    "CNAB2",
+    "CNLF2",
+    "SBDF2",
+)
+@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")
+```
+
+#### Exponential Integrators
+
+```julia
+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),
+    Dict(:alg => NorsettEuler(krylov=true, m=20), :dts => 1e-4 * multipliers),
+    Dict(:alg => ETDRK2(), :dts => 1e-4 * multipliers),
+    Dict(:alg => ETDRK2(krylov=true, m=5), :dts => 1e-4 * multipliers),
+    Dict(:alg => ETDRK2(krylov=true, m=20), :dts => 1e-4 * multipliers)
+]
+labels = hcat(
+    "NorsettEuler (caching)", 
+    "NorsettEuler (m=5)",
+    "NorsettEuler (m=20)",
+    "ETDRK2 (caching)", 
+    "ETDRK2 (m=5)", 
+    "ETDRK2 (m=20)"
+)
+@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, High Tolerance")
+```
+
+
+#### Comparisons Between Families
+
+```julia
+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),
+    Dict(:alg => ETDRK2(), :dts => 1e-4 * multipliers),
+]
+labels = hcat(
+    "CNAB2 (dense linsolve)",
+    "CNAB2 (Krylov linsolve)", 
+    "ETDRK2 (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));
+
+plot(wp, label=labels, markershape=:auto, title="Between Families, High Tolerances")
+```
+
 ### Low Tolerances
 
 #### Implicit-Explicit Methods
@@ -163,87 +243,6 @@ labels = hcat(
 plot(wp, label=labels, markershape=:auto, title="Between Families, Low Tolerances")
 ```
 
-
-### High Tolerances
-
-#### Implicit-Explicit Methods
-
-```julia
-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),
-]
-labels = hcat(
-    "IMEXEuler",
-    "CNAB2",
-    "CNLF2",
-    "SBDF2",
-)
-@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")
-```
-
-#### Exponential Integrators
-
-```julia
-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),
-    Dict(:alg => NorsettEuler(krylov=true, m=20), :dts => 1e-4 * multipliers),
-    Dict(:alg => ETDRK2(), :dts => 1e-4 * multipliers),
-    Dict(:alg => ETDRK2(krylov=true, m=5), :dts => 1e-4 * multipliers),
-    Dict(:alg => ETDRK2(krylov=true, m=20), :dts => 1e-4 * multipliers)
-]
-labels = hcat(
-    "NorsettEuler (caching)", 
-    "NorsettEuler (m=5)",
-    "NorsettEuler (m=20)",
-    "ETDRK2 (caching)", 
-    "ETDRK2 (m=5)", 
-    "ETDRK2 (m=20)"
-)
-@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, High Tolerance")
-```
-
-
-#### Comparisons Between Families
-
-```julia
-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),
-    Dict(:alg => ETDRK2(), :dts => 1e-4 * multipliers),
-]
-labels = hcat(
-    "CNAB2 (dense linsolve)",
-    "CNAB2 (Krylov linsolve)", 
-    "ETDRK2 (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));
-
-plot(wp, label=labels, markershape=:auto, title="Between Families, High Tolerances")
-```
-
 ```julia, echo = false
 using SciMLBenchmarks
 SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file])