Program received signal SIGSEGV: Segmentation fault – invalid memory reference in arrays with big sizes

Your particle_ad arrays only have space for 10*L particles, but you appear to be trying to store up to N=2*L**2 particles in them (depending on how the random numbers fall). On average, each will have enough space, but your code will fail if too many particles fall into a single block, and (if I’m remembering the probabilities right) the chances of this happening increase as L increases.

You could solve this problem by replacing Integer :: particle_ad(10*L) with Integer :: particle_ad(N), but this will waste an awful lot of space.

A better solution would be to re-size the particle_ad arrays on the fly, making them bigger every time they get full. For convenience, you could wrap this behaviour in a method of the block_p class.

For example,

type block_p
  Integer :: partical_N
  Integer, allocatable :: particle_ad(:)
contains
  subroutine add_particle(this, index)
    class(block_p), intent(inout) :: this
    integer, intent(in) :: index
    
    integer, allocatable :: temp
    
    ! Update partical_N.
    this%partical_N = this%partical_N + 1
    
    ! Resize particle_ad if it is full.
    if (size(this%particle_ad)<this%partical_N) then
      temp = this%particle_ad
      deallocate(this%particle_ad)
      allocate(this%particle_ad(2*this%partical_N))
      this%particle_ad(:size(temp)) = temp
    endif
    
    ! Add the new index to particle_ad.
    this%particle_ad(this%partical_N) = index
  end subroutine
end type

You could then replace the lines

C(I_b,J_b)%partical_N = C(I_b,J_b)%partical_N + 1
C(I_b,J_b)%particle_ad( C(I_b,J_b)%partical_N ) = i

with

call C(I_b,J_b)%add_particle(i)

Note that as each particle_ad array is now allocatable, you will need to initialise each array before you can call add_particle.