I have a large PDE system that I originally was solving with an explicit ODE solver via ODEProblem with DiffEq.jl. I have added a component to that system that requires the time derivative info so I changed it to a DDE and swapped over to the DDEProblem solver. The issue I am having now is that when using the DDE solver I am running out of memory, whereas my original ODE problem stayed at a fixed memory usage.

I have the following MWE below. When running on my machine the ODE solve takes about 1 GB of RAM whereas the DDE solve quickly jumps to 10GB+ of RAM. Is there some kind of issue with the DDE suite or is there a simple optimization that I need to be aware of?

*Note that my actual code follows all of the performance tips and guidelines as far as not allocating variables and performing calculations in-place as much as possible.

```
using DifferentialEquations, LinearAlgebra, SparseArrays
using Logging: global_logger
using TerminalLoggers: TerminalLogger
global_logger(TerminalLogger())
const N = 32
const xyd_brusselator = range(0, stop=1, length=N)
brusselator_f(x, y, t) = (((x - 0.3)^2 + (y - 0.6)^2) <= 0.1^2) * (t >= 1.1) * 5.0
limit(a, N) = a == N + 1 ? 1 : a == 0 ? N : a
function brusselator_2d_loop(du, u, p, t)
A, B, alpha, dx = p
alpha = alpha / dx^2
@inbounds for I in CartesianIndices((N, N))
i, j = Tuple(I)
x, y = xyd_brusselator[I[1]], xyd_brusselator[I[2]]
ip1, im1, jp1, jm1 = limit(i + 1, N), limit(i - 1, N), limit(j + 1, N),
limit(j - 1, N)
du[i, j, 1] = alpha * (u[im1, j, 1] + u[ip1, j, 1] + u[i, jp1, 1] + u[i, jm1, 1] -
4u[i, j, 1]) +
B + u[i, j, 1]^2 * u[i, j, 2] - (A + 1) * u[i, j, 1] +
brusselator_f(x, y, t)
du[i, j, 2] = alpha * (u[im1, j, 2] + u[ip1, j, 2] + u[i, jp1, 2] + u[i, jm1, 2] -
4u[i, j, 2]) +
A * u[i, j, 1] - u[i, j, 1]^2 * u[i, j, 2]
end
end
p = (3.4, 1.0, 10.0, step(xyd_brusselator))
function init_brusselator_2d(xyd)
N = length(xyd)
u = zeros(N, N, 2)
for I in CartesianIndices((N, N))
x = xyd[I[1]]
y = xyd[I[2]]
u[I, 1] = 22 * (y * (1 - y))^(3 / 2)
u[I, 2] = 27 * (x * (1 - x))^(3 / 2)
end
u
end
u0 = init_brusselator_2d(xyd_brusselator)
prob_ode_brusselator_2d = ODEProblem(brusselator_2d_loop, u0, (0.0, 20.0), p)
@time solve(prob_ode_brusselator_2d, SSPRK43(), saveat=0.5, progress=true, progress_steps=1);
function brusselator_2d_loop_h(du, u, h, p, t)
A, B, alpha, dx = p
alpha = alpha / dx^2
@inbounds for I in CartesianIndices((N, N))
i, j = Tuple(I)
x, y = xyd_brusselator[I[1]], xyd_brusselator[I[2]]
ip1, im1, jp1, jm1 = limit(i + 1, N), limit(i - 1, N), limit(j + 1, N),
limit(j - 1, N)
du[i, j, 1] = alpha * (u[im1, j, 1] + u[ip1, j, 1] + u[i, jp1, 1] + u[i, jm1, 1] -
4u[i, j, 1]) +
B + u[i, j, 1]^2 * u[i, j, 2] - (A + 1) * u[i, j, 1] +
brusselator_f(x, y, t)
du[i, j, 2] = alpha * (u[im1, j, 2] + u[ip1, j, 2] + u[i, jp1, 2] + u[i, jm1, 2] -
4u[i, j, 2]) +
A * u[i, j, 1] - u[i, j, 1]^2 * u[i, j, 2]
end
end
D_dt = similar(u0)
h(D_dt, p, t, ::Type{Val{1}}) = (D_dt .= 0.0)
prod_dde = DDEProblem(brusselator_2d_loop_h, u0, h, (0.0, 20.0), p)
alg = MethodOfSteps(SSPRK43())
@time sol = solve(prod_dde, alg, saveat=0.5, progress=true, progress_steps=1);
```