Explore BrainMass
Share

# One Dimensional Dirichlet

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Consider the one-dimensional Dirichlet problem

v_xx = f(x) on (0,1)
v(0) = v(1) = 0

with f(x) = cos(x) and true solution v(x) = -f(x) + x*(f(1.0)-1.0)+1.0. Implement V-cycle multigrid algorithm to solve the above problem. On each level of multigrid use Gauss-Seidel algorithm to solve the system of equations.

Use the following parameters:

- m = 7 - the number of grids to be employed;
- n - number of interior grid points (n = 2^m - 1), ie. finest grid has n = 127;
- k = 2.10 - the number of iterations to be performed in each Gauss-Seidel method;

Use linear interpolation for prolongation operation (I_2h)^h and injection for restriction operation (I_h)^2h.

Perform multigrid V-cycle for each value of k and print out maximum error (mx v_i) for each case.

© BrainMass Inc. brainmass.com March 22, 2019, 12:54 am ad1c9bdddf
https://brainmass.com/math/discrete-math/one-dimensional-dirichlet-516954

#### Solution Preview

I have posted the solution in a zip file containing all .m files used. You need to simply ...

#### Solution Summary

One dimensional dirichlet is examined.

\$2.19