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MOLxPDESystemLibrary.jmd
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---
title: PDESystemLibrary.jl Work-Precision Diagrams with Various MethodOfLines.jl Methods
author: Alex Jones
---
This benchmark is for the MethodOfLines.jl package, which is an automatic PDE discretization package.
It is concerned with comparing the performance of various discretization methods for the Burgers equation.
```julia
using MethodOfLines, DomainSets, OrdinaryDiffEq, ModelingToolkit, DiffEqDevTools, LinearAlgebra,
LinearSolve, Plots, RecursiveFactorization
using PDESystemLibrary
```
Next we define some functions to generate approproiate discretizations for the PDESystemLibrary systems.
```julia
function center_uniform_grid(ex, ivs, N)
map(ivs) do x
xdomain = ex.domain[findfirst(d -> isequal(x, d.variables), ex.domain)]
x => (supremum(xdomain.domain) - infimum(xdomain.domain)) /
(floor(N^(1 / length(ivs))) - 1)
end
end
function edge_uniform_grid(ex, ivs, N)
map(ivs) do x
xdomain = ex.domain[findfirst(d -> isequal(x, d.variables), ex.domain)]
x => (supremum(xdomain.domain) - infimum(xdomain.domain)) /
(floor(N^(1 / length(ivs))))
end
end
function center_chebygrid(ex, ivs, N)
map(ivs) do x
xdomain = ex.domain[findfirst(d -> isequal(x, d.variables), ex.domain)]
x => chebyspace(xdomain, trunc(Int, N^(1 / length(ivs))))
end
end
function edge_chebygrid(ex, ivs, N)
map(ivs) do x
xdomain = ex.domain[findfirst(d -> isequal(x, d.variables), ex.domain)]
x => chebyspace(xdomain, trunc(Int, N^(1 / length(ivs))) - 1)
end
end
function uniformupwind1(ex, ivs, t, N)
dxs = center_uniform_grid(ex, ivs, N)
MOLFiniteDifference(dxs, t, advection_scheme=UpwindScheme())
end
function uniformupwind2(ex, ivs, t, N)
dxs = edge_uniform_grid(ex, ivs, N)
MOLFiniteDifference(dxs, t, advection_scheme=UpwindScheme(), grid_align=edge_align)
end
function chebyupwind1(ex, ivs, t, N)
dxs = center_chebygrid(ex, ivs, N)
MOLFiniteDifference(dxs, t, advection_scheme=UpwindScheme())
end
function chebyupwind2(ex, ivs, t, N)
dxs = edge_chebygrid(ex, ivs, N)
MOLFiniteDifference(dxs, t, advection_scheme=UpwindScheme(), grid_align=edge_align)
end
function discweno1(ex, ivs, t, N)
dxs = center_uniform_grid(ex, ivs, N)
MOLFiniteDifference(dxs, t, advection_scheme=WENOScheme())
end
function discweno2(ex, ivs, t, N)
dxs = edge_uniform_grid(ex, ivs, N)
MOLFiniteDifference(dxs, t, advection_scheme=WENOScheme(), grid_align=edge_align)
end
```
This script tests all systems in PDESystemLibrary against different MethodOfLines.jl discretizations.
It then plots the work precision sets.
```julia
N = 100
for ex in PSL.all_systems
try
if ex.analytic_func === nothing
continue
end
ivs = filter(x -> !isequal(Symbol(x), :t), ex.ivs)
if length(ivs) == 0
continue
elseif length(ivs) == length(ex.ivs)
# Skip nonlinear systems until I know the syntax for that
continue
# advection = false
# discuu1 = uniformupwind1(ex, ivs, nothing, N)
# discuu2 = uniformupwind2(ex, ivs, nothing, N)
# discnu1 = chebyupwind1(ex, ivs, nothing, N)
# discnu2 = chebyupwind2(ex, ivs, nothing, N)
# discs = [discuu1, discuu2, discnu1, discnu2]
# if "Advection" in ex.metadata
# advection = true
# discw1 = discweno1(ex, ivs, nothing, N)
# discw2 = discweno2(ex, ivs, nothing, N)
# push!(discs, discw1, discw2)
# end
# probs = map(discs) do disc
# discretize(ex, disc, analytic = ex.analytic_func)
# end
# title = "Work Precision Diagram for $(ex.name), Tags: $(ex.metadata)"
# println("Running $title")
# if advection
# dummy_appxsol = [nothing for i in 1:length(probs1)]
# abstols = 1.0 ./ 10.0 .^ (5:8)
# reltols = 1.0 ./ 10.0 .^ (1:4);
# setups = [Dict(:alg => solver, :prob_choice => 1),
# Dict(:alg => solver, :prob_choice => 2),
# Dict(:alg => solver, :prob_choice => 3),
# Dict(:alg => solver, :prob_choice => 4),
# Dict(:alg => solver, :prob_choice => 5),
# Dict(:alg => solver, :prob_choice => 6),]
# names = ["Uniform Upwind, center_align", "Uniform Upwind, edge_align",
# "Chebyshev Upwind, center_align", "Chebyshev Upwind, edge_align",
# "Uniform WENO, center_align", "Uniform WENO, edge_align"];
# wp = WorkPrecisionSet(probs, abstols, reltols, setups; names=names,
# save_everystep=false, appxsol = dummy_appxsol, maxiters=Int(1e5),
# numruns=10, wrap=Val(false))
# plot(wp, title=title)
# else
# dummy_appxsol = [nothing for i in 1:length(probs)]
# abstols = 1.0 ./ 10.0 .^ (5:8)
# reltols = 1.0 ./ 10.0 .^ (1:4);
# setups = [Dict(:alg => solver, :prob_choice => 1),
# Dict(:alg => solver, :prob_choice => 2),
# Dict(:alg => solver, :prob_choice => 3),
# Dict(:alg => solver, :prob_choice => 4),]
# names = ["Uniform Upwind, center_align", "Uniform Upwind, edge_align",
# "Chebyshev Upwind, center_align", "Chebyshev Upwind, edge_align"];
# wp = WorkPrecisionSet(probs1, abstols, reltols, setups; names=names,
# save_everystep=false, appxsol = dummy_appxsol, maxiters=Int(1e5),
# numruns=10, wrap=Val(false))
# plot(wp, title=title)
# end
else
@parameters t
# Create discretizations
advection = false
discuu1 = uniformupwind1(ex, ivs, t, N)
discuu2 = uniformupwind2(ex, ivs, t, N)
discnu1 = chebyupwind1(ex, ivs, t, N)
discnu2 = chebyupwind2(ex, ivs, t, N)
discs = [discuu1, discuu2, discnu1, discnu2]
if "Advection" in ex.metadata
advection = true
discw1 = discweno1(ex, ivs, t, N)
discw2 = discweno2(ex, ivs, t, N)
push!(discs, discw1, discw2)
end
# Create problems
probs = map(discs) do disc
discretize(ex, disc, analytic = ex.analytic_func)
end
title = "Work Precision Diagram for $(ex.name), Tags: $(ex.metadata)"
println("Running $title")
if advection
dummy_appxsol = [nothing for i in 1:length(probs1)]
abstols = 1.0 ./ 10.0 .^ (5:8)
reltols = 1.0 ./ 10.0 .^ (1:4);
setups = [Dict(:alg => solver, :prob_choice => 1),
Dict(:alg => solver, :prob_choice => 2),
Dict(:alg => solver, :prob_choice => 3),
Dict(:alg => solver, :prob_choice => 4),
Dict(:alg => solver, :prob_choice => 5),
Dict(:alg => solver, :prob_choice => 6),]
names = ["Uniform Upwind, center_align", "Uniform Upwind, edge_align",
"Chebyshev Upwind, center_align", "Chebyshev Upwind, edge_align",
"Uniform WENO, center_align", "Uniform WENO, edge_align"];
wp = WorkPrecisionSet(probs, abstols, reltols, setups; names=names,
save_everystep=false, appxsol = dummy_appxsol, maxiters=Int(1e5),
numruns=10, wrap=Val(false))
plot(wp, title=title)
else
dummy_appxsol = [nothing for i in 1:length(probs)]
abstols = 1.0 ./ 10.0 .^ (5:8)
reltols = 1.0 ./ 10.0 .^ (1:4);
setups = [Dict(:alg => solver, :prob_choice => 1),
Dict(:alg => solver, :prob_choice => 2),
Dict(:alg => solver, :prob_choice => 3),
Dict(:alg => solver, :prob_choice => 4),]
names = ["Uniform, center_align", "Uniform, edge_align",
"Chebyshev, center_align", "Chebyshev, edge_align"];
wp = WorkPrecisionSet(probs1, abstols, reltols, setups; names=names,
save_everystep=false, appxsol = dummy_appxsol, maxiters=Int(1e5),
numruns=10, wrap=Val(false))
plot(wp, title=title)
end
end
catch e
println("Failed on $(ex.name):")
println(e)
end
end
```