Add `factorise` to lock_exchange.cpp example

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Assessment

Difficulty
2/5
Estimated time
1-3 hours
Newbie friendliness
84/100
Issue type
Feature
Clarity
Clearly specified
Activity status
Active
Tech stack
cpp
Domain
hpc

Research direction

Open lock_exchange.cpp and inspect how the sparse system is currently solved across repeated steps. Use the requested Armadillo factoriser setup and solve flow as the starting point, then run the example with the higher-resolution parameters given in the issue; done means the example completes and renders the billows.

Written by the indexing model from the issue text.

Description

C++ Enhancement Examples

Is your feature request related to a problem? Please describe.
When solving a system, if the LHS does not change, there are mechanisms to reuse the factorization. In Armadillo, this is achieved with factorise.

Describe the solution you'd like
Implement factorise in the lock_exchange.cpp example. This will let users run a higher resolution in the example, which will render the billows.

  // Factorizer for the sparse solve, Armadillo
  spsolve_factoriser SF;
  
  // L is a pure-Neumann Laplacian, singular to working precision (constants are
  // in its null space); factorise() rejects it unless allow_ugly is set.
  superlu_opts opts;
  opts.allow_ugly = true;
  bool status = SF.factorise(L, opts);

  ...
  bool solution1_ok = SF.solve(p_vec, b);
    
  if(solution1_ok == false) { cout << "couldn't find pvec" << endl; }

Here is an example with b=50, d=5, m=800, n=160, dt=0.1.

Image

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Merged PRs (30d)
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