mpi fortran wave equation solver code



!cc MAIN is the main program for WAVE_MPI.

!c

!c Discussion:

!c

!c WAVE_MPI solves the wave equation in parallel using MPI.

!c

!c Discretize the equation for u(x,t):

!c d^2 u/dt^2 - c^2 * d^2 u/dx^2 = 0 for 0 < x < 1, 0 < t

!c with boundary conditions:

!c u(0,t) = u0(t) = sin ( 2 * pi * ( 0 - c * t ) )

!c u(1,t) = u1(t) = sin ( 2 * pi * ( 1 - c * t ) )

!c and initial conditions:

!c u(x,0) = g(x,t=0) = sin ( 2 * pi * ( x - c * t ) )

!c dudt(x,0) = h(x,t=0) = - 2 * pi * c * cos ( 2 * pi * ( x - c * t ) )

!c

!c by:

!c

!c alpha = c * dt / dx.

!c

!c U(x,t+dt) = 2 U(x,t) - U(x,t-dt)

!c + alpha^2 ( U(x-dx,t) - 2 U(x,t) + U(x+dx,t) ).

!c

!c Licensing:

!c

!c This code is distributed under the GNU LGPL license.

!c

!c Modified:

!c

!c 17 November 2013

!c

!c Author:

!c

reza-mpi fortran wave equation solver code



!cc MAIN is the main program for WAVE_MPI.

!c

!c　Discussion:

!c

!c　　WAVE_MPI solves the wave equation in parallel using MPI.

!c

!c　　Discretize the equation for u(x,t):

!c　　　d^2 u/dt^2 - c^2 * d^2 u/dx^2 = 0　for 0 < x < 1, 0 < t

!c　　with boundary conditions:

!c　　　u(0,t) = u0(t) = sin ( 2 * pi * ( 0 - c * t ) )

!c　　　u(1,t) = u1(t) = sin ( 2 * pi * ( 1 - c * t ) )

!c　　and initial conditions:

!c　　　　 u(x,0) = g(x,t=0) =　　　　　　　　sin ( 2 * pi * ( x - c * t ) )

!c　　　dudt(x,0) = h(x,t=0) = - 2 * pi * c * cos ( 2 * pi * ( x - c * t ) )

!c

!c　　by:

!c

!c　　　alpha = c * dt / dx.

!c

!c　　　U(x,t+dt) = 2 U(x,t) - U(x,t-dt)

!c　　　　+ alpha^2 ( U(x-dx,t) - 2 U(x,t) + U(x+dx,t) ).

!c

!c　Licensing:

!c

!c　　This code is distributed under the GNU LGPL license.

!c

!c　Modified:

!c

!c　　17 November 2013

!c

!c　Author:

!c

reza