Efficient Alternative for Construction of the Linear System Stemming from Numerical Solution of Heat Transfer Problems via FEM

Code 2

Gauss-Seidel method used for calculating the global linear system.

! GAUSS SEIDEL METHOD

T = 1.d0; Ti = T; rAux = 0.d0; Emax = 0.0000000001d0  !T: Temperature; Ti: initial shot

do i = 1, 200000

ii = 1; rAuxE = 0.d0

  do j = 1,nnost

    soma = 0.d0

    do jj = ii,k

     if(Mirow(jj).eq.j.and.Mjcol(jj).eq.j) then

     rAux = GG(jj)

     end if

     if(Mirow(jj).eq.j) then

      if(Mjcol(jj).eq.j) then

      continue

      else

      soma = soma + GG(jj)T(Mjcol(jj))

      end if

     else

      ii = jj

      go to (2)

     end if

     end do

(2) T(j) = (1.d0/rAux)(FG(j) - soma)

   end do

   do j = 1,nnost

    Erro = dabs(Ti(j) - T(j))

    if(Erro>rAuxE) then

    rAuxE = Erro

    end if

  end do

  if(rAuxE>Emax) then  !Emax: stop criterion

  Ti = T

  else

  go to (1)

  end if

end do

(1) continue