Fortran error: Program received signal SIGSEGV: Segmentation fault - invalid memory reference - cygwin

Question

I'm try to run an ocean temperature model for 25 years using the explicit method (parabolic differential equation).
If I run for a year a = 3600 or five years a = 18000 it works fine.
However, when I run it for 25 years a = 90000 it crashes.
a is the amount of time steps used. And a year is considered to be 360 days. The time step is 4320 seconds, delta_t = 4320..
Here is my code:
program task
!declare the variables
implicit none
! initial conditions
real,parameter :: initial_temp = 4.
! vertical resolution (delta_z) [m], vertical diffusion coefficient (av) [m^2/s], time step delta_t [s]
real,parameter :: delta_z = 2., av = 2.0E-04, delta_t = 4320.
! gamma
real,parameter :: y = (av * delta_t) / (delta_z**2)
! horizontal resolution (time) total points
integer,parameter :: a = 18000
!declaring vertical resolution
integer,parameter :: k = 101
! declaring pi
real, parameter :: pi = 4.0*atan(1.0)
! t = time [s], temp_a = temperature at upper boundary [°C]
real,dimension(0:a) :: t
real,dimension(0:a) :: temp_a
real,dimension(0:a,0:k) :: temp
integer :: i
integer :: n
integer :: j
t(0) = 0
do i = 1,a
t(i) = t(i-1) + delta_t
end do
! temperature of upper boundary
temp_a = 12. + 6. * sin((2. * t * pi) / 31104000.)
temp(:,0) = temp_a(:)
temp(0,1:k) = 4.
! Vertical resolution
do j = 1,a
do n = 1,k
temp(j,n) = temp(j-1,n) + (y * (temp(j-1,n+1) - (2. * temp(j-1,n)) + temp(j-1,n-1)))
end do
temp(:,101) = temp(:,100)
end do
print *, temp(:,:)
end program task
The variable a is on line 11 (integer,parameter :: a = 18000)
As said, a = 18000 works, a = 90000 doesn't.
At 90000 get I get:
Program received signal SIGSEGV: Segmentation fault - invalid memory reference.
Backtrace for this error:
RUN FAILED (exit value 1, total time: 15s)
I'm using a fortran on windows 8.1, NetBeans and Cygwin (which has gfortran built in).
I'm not sure if this problem is caused through bad compiler or anything else.
Does anybody have any ideas to this? It would help me a lot!
Regards

Answer 1

Take a look at the following lines from your code:
integer,parameter :: k = 101
real,dimension(0:a,0:k) :: temp
integer :: n
do n = 1,k
temp(j,n) = temp(j-1,n) + (y * (temp(j-1,n+1) - (2. * temp(j-1,n)) + temp(j-1,n-1)))
end do
Your array temp has bounds of 0:101, you loop n from 1 to 101 where in iteration n=101 you access temp(j-1,102), which is out of bounds.
This means you are writing to whatever memory lies beyond temp and while this makes your program always incorrect, it is only causing a crash sometimes which depends on various other things. Increasing a triggers this because column major ordering of your array means k changes contiguously and is strided by a, and as a increases your out of bounds access of the second dimension is further in memory beyond temp changing what is getting overwritten by your invalid access.
After your loop you set temp(:,101) = temp(:,100) meaning there is no need to calculate temp(:,101) in the above loop, so you can change its loop bounds from
do n = 1,k
to
do n = 1, k-1
which will fix the out of bounds access on temp.