Use BFGS as default in optimization for function space operators (#416)

* use BFGS as default in function space operators

* increase some tolerances again

Author: JoshuaLampert

ext/SummationByPartsOperatorsOptimForwardDiffExt.jl

@@ -1,6 +1,6 @@
 module SummationByPartsOperatorsOptimForwardDiffExt
 
-using Optim: Optim, Options, LBFGS, optimize, minimizer
+using Optim: Optim, Options, BFGS, optimize, minimizer
 using ForwardDiff: ForwardDiff
 
 using SummationByPartsOperators: SummationByPartsOperators, GlaubitzNordströmÖffner2023,
@@ -13,7 +13,7 @@ function SummationByPartsOperators.function_space_operator(basis_functions,
                                                            source::SourceOfCoefficients;
                                                            derivative_order = 1,
                                                            accuracy_order = 0,
-                                                           opt_alg = LBFGS(),
+                                                           opt_alg = BFGS(),
                                                            options = Options(g_tol = 1e-14,
                                                                              iterations = 10000),
                                                            verbose = false) where {T,

test/function_space_operators_test.jl

@@ -31,7 +31,7 @@ import Optim, ForwardDiff # to enable loading the function space operator optimi
         D = function_space_operator(basis_functions, nodes, source)
 
         @test grid(D) ≈ nodes
-        @test all(isapprox.(D * ones(N), zeros(N); atol = 1e-12))
+        @test all(isapprox.(D * ones(N), zeros(N); atol = 1e-13))
         @test D * nodes ≈ ones(N)
         @test D * exp.(nodes) ≈ exp.(nodes)
         M = mass_matrix(D)
@@ -44,12 +44,10 @@ import Optim, ForwardDiff # to enable loading the function space operator optimi
         0.8574665549914025, 1.0]
     N = length(nodes)
     let basis_functions = [one, identity, exp]
-        D = function_space_operator(basis_functions, nodes, source, verbose = true,
-                                    options = Optim.Options(g_tol = 1e-15,
-                                                            iterations = 25000))
+        D = function_space_operator(basis_functions, nodes, source, verbose = true)
 
         @test grid(D) ≈ nodes
-        @test all(isapprox.(D * ones(N), zeros(N); atol = 1e-11))
+        @test all(isapprox.(D * ones(N), zeros(N); atol = 1e-12))
         @test D * nodes ≈ ones(N)
         @test D * exp.(nodes) ≈ exp.(nodes)
         M = mass_matrix(D)