Update example with larger matrix size and iterative solver implementation

[TLCFEM]

Enhance the example to utilize a larger matrix size and adjust solver options. Introduce the LIS header and implementation for the iterative solver.

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.4480%. Comparing base (44bdd7e) to head (cf6c842).
Report is 1 commits behind head on master.

Additional details and impacted files

@@               Coverage Diff                @@
##             master         #9        +/-   ##
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+ Coverage   99.4220%   99.4480%   +0.0260%     
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  Files            30         31         +1     
  Lines          1211       1268        +57     
  Branches         98        100         +2     
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+ Hits           1204       1261        +57     
  Misses            7          7                

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