use banded matrix decomposition instead of dense LU for BBM-BBM

[ranocha]

sparse matrix times banded matrix constructed a dense matrix

[JoshuaLampert]

Thanks!

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.02%. Comparing base (3a32a5c) to head (c2b6365).
Report is 2 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #170   +/-   ##
=======================================
  Coverage   98.02%   98.02%           
=======================================
  Files          19       19           
  Lines        1877     1877           
=======================================
  Hits         1840     1840           
  Misses         37       37           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[github-actions]

Benchmark Results

	main	c2b6365...	main/c2b6365061fac7...
bbm_1d/bbm_1d_basic.jl	14.2 ± 0.49 μs	13.9 ± 0.37 μs	1.02
bbm_1d/bbm_1d_fourier.jl	0.298 ± 0.31 ms	0.215 ± 0.089 ms	1.39
bbm_bbm_1d/bbm_bbm_1d_basic_reflecting.jl	0.113 ± 0.0028 ms	0.0812 ± 0.00027 ms	1.39
bbm_bbm_1d/bbm_bbm_1d_dg.jl	0.0341 ± 0.00046 ms	0.0347 ± 0.00051 ms	0.982
bbm_bbm_1d/bbm_bbm_1d_relaxation.jl	27.1 ± 0.45 μs	27.4 ± 0.49 μs	0.988
bbm_bbm_1d/bbm_bbm_1d_upwind_relaxation.jl	0.0486 ± 0.00044 ms	0.0486 ± 0.00055 ms	0.999
hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_dingemans.jl	4.18 ± 0.016 μs	4.1 ± 0.013 μs	1.02
serre_green_naghdi_1d/serre_green_naghdi_well_balanced.jl	0.197 ± 0.006 ms	0.195 ± 0.0066 ms	1.01
svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_relaxation.jl	0.148 ± 0.0038 ms	0.143 ± 0.0031 ms	1.03
time_to_load	1.92 ± 0.009 s	1.93 ± 0.014 s	0.998

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.