Computational Physics Dr. Guy Tel-Zur Home Assignment Number 2

Parallel Solver for the 1D Wave Equation One-Way, 1-D Wave, Equation (Advection): Initial Condition: Courant Number, r=c  t/  x Verify 0<r<1

Explicit finite difference schemes for first order 1-D wave equation

Part 1: Solve using Forward Euler (FWU) Scheme Part 2: Solve using Upwind (UPW) Scheme Use: c = 0.5,  x=0.04,  t=0.02

Continued: Initial Condition: x range: -2 ≤ x ≤ 2 Boundary Conditions: U(-2,t)=0, U(2,t)=1

The Computational Model

Instructions Solve the 1D Wave Equation in Parallel Use a SPMD model in C using MPI Use a Master-Workers model The entire amplitude array is partitioned and distributed as sub-arrays to all tasks. Each task owns a portion of the total array. Decide about the number of Parallel Tasks Use Point-to-Point and Collective MPI commands as needed

Which of the Schemes behave nicer? Comment on the #Tasks vs. Running time (Computation to communication ratio) Submit plots of the solution, u(x,t), at: t=0, t=1 and t=2 Submit EXE#2 to Due: Two weeks from today