Appendix: Memory Usage

The majority of memory in a typical SCF calculation is consumed by the storage of mono-constrained partition functions (forward and backward) and, if solved using the quasi Newton-Raphson, by the storage of the inverse Jacobian matrix needed in Broyden’s method.

Chain Partition Functions

The memory (in bytes) needed to store the two mono-constrained partition function is determined by the following factors:

Factor	Value
number of grid points	ngrid(1)*ngrid(2)*ngrid(3)
number of contour segments	2*chain_length/chain_step
bytes per real (double) number	8

The product of these numbers yield:

mem(Q) = (ngrid(1)*ngrid(2)*ngrid(3)) * (chain_length/chain_step) * 16

Jacobian Matrix

The dimension of Jacobian is “N_monomer * N_basis” as long as the N_cell_param (<= 6) is ignored, thus the memory requirement, in bytes, is:

mem(J) = (N_monomer*N_basis)^2 * 8

The number of basis function (N_basis) may be roughfully estimated, if needed, to be the number of the grid points divided by the number of space group symmetry elements.

Numerical Example

Imagine simulating a gyroid phase for an ABC triblock copolymer (N_monomer=3) using normalized chain_length=1, chain_step=0.01, a grid with dimensions ngrid(1)=ngrid(2)=ngrid(3)=56 The I a -3 d space group of the gyroid phase has 96 symmetry elements, so our simple estimate suggests N_basis = 56*56*56/96=1829.3. In fact, we obtain a slightly higher value of N_basis=1856. mem(Q) and mem(J) are found to be 0.28GB and 0.25GB, respectively.