Example Problem to Demonstrate BiCGStab

So our team has been able to code up a BiCGStab implementation for a class project, and we'd like a potential example problem to try it out on.

So far, we've talked about a 1D Laplacian with Neumann boundaries (so the matrix becomes nonsymmetric), but I am strongly inclined to demonstrate at least a very slightly more exotic problem that can be shown using the BiCGStab.

Given the time and skill constraints, a steady-state problem description would be idea, since no one in the team has a decent idea about time propagation, and our implementation of the BiCGStab is fairly naive (slow).

Any suggestions for a demo problem for our solver would be greatly appreciated.

• Do you need it to be a physics problem? BiCGStab is a general-purpose linear system iterative solver, so solving a random linear system would do the job for you. Trying to get a more "exotic" problem is not really an exercise of your BiCGStab implementation unless you come up with some horribly ill-conditioned system. Apr 13, 2017 at 4:50
• A sparse random matrix is what I've showed the Professor so far, and he seems content with the implementation. He does insist on an application. Being a physics problem is not a requirement, but it would make it easier, since the members of our team are a bit optimization/physics oriented. Apr 13, 2017 at 5:07
• Try the advection-diffusion equation with dirichlet boundary conditions. Careful with your discretization, but this is a fairly canonical non-symmetric PDE. en.wikipedia.org/wiki/Convection%E2%80%93diffusion_equation Apr 13, 2017 at 5:32
• You could try with the Boundary Element Method that leads to non-symmetric, non-diagonal dominant matrices. You could try with the Poisson equation. Apr 13, 2017 at 17:11