Selection of ProjectsProject 1 (Finite Volume – See Lecture 8 and waveqn2da.m)Project 2 (Using parmetis to redistribute a problem)Project 3 (Multigrid Solver in Parallel)Project 4 (Fourier Methods in Parallel)Project 5Deadline and FormatSelection of ProjectsMA471 Fall 2003Project 1 (Finite Volume – See Lecture 8 and waveqn2da.m)1. Create a parallel finite volume code for the equation2. Test for a constant (a,b) vector, plot convergence with decreasing element size.3. Do a parallel scaling test on 1,2,4,8,16 processes(i.e. run for 20 time steps)4. upshot the code to identify any parallel bottlenecks5. Hint: you can use the parallel sparse matrix vector product routines to figure out element neighbors.6. Extra credit: try a non-constant (a,b) see today’s notes.0a bt x yr r r� � �+ + =� � �Project 2(Using parmetis to redistribute a problem)1) Download the parmetis code from:http://www-users.cs.umn.edu/~karypis/metis/parmetis/download.html2) Create a distributed symmetric, random, matrix.3) Use ParMETIS_V3_PartKway to determine a renumbering of the rows and columns.4) Re-distribute the matrix according to the partition and use the Jacobi solve routine to solve with a random right hand side vector.5) See if this repartitioning makes any difference to the parallel scaling performance.6) Compare upshot profiles of the Jacobi solve with the original distribution and with the new partitioning.Project 3(Multigrid Solver in Parallel)1) Create a 1-D heat equation system, using the second order finite difference formula, in parallel. 2) Create a sequence of nested coarse grid problems.3) Build a distributed multigrid solver for this problem.4) upshot the code for parallel performance5) Perform a scaling test.6) Analyze any parallel bottlenecks.7) (This might appear to be an easy option, but beware).8) An example two-grid solver in heatMG1d.m and heatmatrix1d.m1) Same as Project 1 – BUT you are to use a spectral method (described today).2) Use MPI_alltoall to exchange data before the fft3) Use fftw to perform the Fast Fourier Transform (efficient discrete Fourier transform):1) http://www.fftw.org/2) http://www.fftw.org/fftw3.pdf3) http://www.fftw.org/fftw3.pdf4) Note that version fftw 2.1.5 has an MPI based parallel fft included.5) upshot profile the code.6) Perform scaling tests (use N=2^M )Project 4(Fourier Methods in Parallel)Project 5•A student may propose a project.•This requires instructor approval.Deadline and Format1) Due 12/08/032) Powerpoint presentation, including scaling graph, upshot, convergence plots, field output.3) Report – must conform to usual standard.4) Non-extraordinary extensions granted at a cost of 10% of grade per