/ DFTK.jl Public
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 # # Custom solvers # In this example, we show how to define custom solvers. Our system # will again be silicon, because we are not very imaginative using DFTK, LinearAlgebra a = 10.26 lattice = a / 2 * [[0 1 1.]; [1 0 1.]; [1 1 0.]] Si = ElementPsp(:Si, psp=load_psp("hgh/lda/Si-q4")) atoms = [Si, Si] positions = [ones(3)/8, -ones(3)/8] ## We take very (very) crude parameters model = model_LDA(lattice, atoms, positions) basis = PlaneWaveBasis(model; Ecut=5, kgrid=[1, 1, 1]); # We define our custom fix-point solver: simply a damped fixed-point function my_fp_solver(f, x0, max_iter; tol) mixing_factor = .7 x = x0 fx = f(x) for n = 1:max_iter inc = fx - x if norm(inc) < tol break end x = x + mixing_factor * inc fx = f(x) end (fixpoint=x, converged=norm(fx-x) < tol) end; # Our eigenvalue solver just forms the dense matrix and diagonalizes # it explicitly (this only works for very small systems) function my_eig_solver(A, X0; maxiter, tol, kwargs...) n = size(X0, 2) A = Array(A) E = eigen(A) λ = E.values[1:n] X = E.vectors[:, 1:n] (; λ, X, residual_norms=[], iterations=0, converged=true, n_matvec=0) end; # Finally we also define our custom mixing scheme. It will be a mixture # of simple mixing (for the first 2 steps) and than default to Kerker mixing. # In the mixing interface δF is (ρ_\text{out} - ρ_\text{in}), i.e. # the difference in density between two subsequent SCF steps and the mix # function returns δρ, which is added to ρ_\text{in} to yield ρ_\text{next}, # the density for the next SCF step. struct MyMixing n_simple # Number of iterations for simple mixing end MyMixing() = MyMixing(2) function DFTK.mix_density(mixing::MyMixing, basis, δF; n_iter, kwargs...) if n_iter <= mixing.n_simple return δF # Simple mixing -> Do not modify update at all else ## Use the default KerkerMixing from DFTK DFTK.mix_density(KerkerMixing(), basis, δF; kwargs...) end end # That's it! Now we just run the SCF with these solvers scfres = self_consistent_field(basis; tol=1e-8, solver=my_fp_solver, eigensolver=my_eig_solver, mixing=MyMixing()); # Note that the default convergence criterion is the difference in # density. When this gets below tol, the # "driver" self_consistent_field artificially makes the fixed-point # solver think it's converged by forcing f(x) = x. You can customize # this with the is_converged keyword argument to # self_consistent_field.