Add modern poisson2d solver & rename optimized.f90

poisson2d/optimized.f90 → poisson2d/archaic.f90

@@ -19,7 +19,7 @@ pure real(dp) function rho(x,y)
 program poisson
 use rhofunc, only: rho
 implicit none
-integer, parameter :: dp=kind(0.d0), M=300
+integer, parameter :: dp=kind(0.d0), M=150
 integer            :: i,j, iter
 real(dp),parameter :: epsilon0=8.85E-12_dp, target=1E-6_dp, a=0.01
 real(dp)           :: delta, b, e, phiprime(M,M), phi(M,M), a2, rhoarr(M,M)

poisson2d/modern.f90

@@ -0,0 +1,83 @@
+module rho_interface
+  !! Define a scalar function over 2-space.
+  implicit none
+
+  private
+  public :: rho, dp
+
+  integer, parameter :: precision = 15, range = 307
+  integer, parameter :: dp = selected_real_kind(precision, range)
+
+  interface 
+    pure real(dp) module function rho(x,y)
+      !! Poisson equation inhomogeneous term.
+      implicit none
+      real(dp), intent(in) :: x,y
+    end function
+  end interface
+
+end module 
+
+submodule(rho_interface) rho_definition
+  implicit none
+contains
+  module procedure rho
+      !! To Do: give meaningful names to the magic numbers.
+      !! See https://en.wikipedia.org/wiki/Magic_number_(programming)#Unnamed_numerical_constants.
+      if (all([x,y]>0.6_dp .and. [x,y]<0.8_dp)) then
+        rho = 1._dp
+      else
+        rho = merge(-1., 0., all([x,y]>0.2_dp .and. [x,y]<0.4_dp))
+      end if
+  end procedure
+end submodule
+
+program poisson
+  !! Solve the 2D Poisson equation using a smoothing operation to iterate.
+  use rho_interface, only: rho, dp
+  implicit none
+
+  integer i,j
+  integer, parameter :: M=150
+  real(dp), parameter :: dx=0.01_dp
+  real(dp) :: t_start, rho_sampled(M,M)
+
+  call cpu_time(t_start)
+
+  associate( dy => (dx) ) ! Associating with an expression provides immutable state so dy cannot be inadvertently redefined.
+
+    do concurrent(i=1:M, j=1:M)
+      rho_sampled(i,j) = rho(i*dx,j*dy)
+    end do
+
+    block ! Tighten the scoping to declutter the code above.
+      real(dp) :: delta_phi, t_end
+      real(dp), parameter :: epsilon0=8.85E-12_dp, tolerance=1E-6_dp
+      real(dp), dimension(M,M) :: phi_prime, phi
+      integer iteration
+
+      phi = 0.
+
+      phi_prime([1,M], 2:M-1) = phi([1,M], 2:M-1) ! Initialize only boundary values except corners. (Internal values will
+      phi_prime(2:M-1, [1,M]) = phi(2:M-1, [1,M]) ! be overwritten in the first iteration. Corners will never be used.)
+
+      delta_phi = tolerance + epsilon(tolerance) ! Ensure at least 1 iteration.
+      iteration = 0
+      do while (delta_phi > tolerance )
+        iteration = iteration + 1
+        do concurrent(i=2:M-1, j=2:M-1) ! Compute updated solution estimate at internal points.
+          phi_prime(i,j) =   (phi(i+1,j) + phi(i-1,j) + phi(i,j+1) + phi(i,j-1))/4._dp &
+                           + (dx/2._dp)*(dy/2._dp)/epsilon0*rho_sampled(i,j)
+        end do
+        delta_phi = maxval(abs(phi_prime - phi))
+        phi(2:M-1, 2:M-1) = phi_prime(2:M-1, 2:M-1) ! Update internal values.
+      end do
+
+      call cpu_time(t_end)
+      print *, t_end-t_start, iteration
+
+    end block
+
+  end associate
+
+end program