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Hyperbolic-Parabolic elixir using SparseConnectivityTracer #2604
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| Review checklistThis checklist is meant to assist creators of PRs (to let them know what reviewers will typically look for) and reviewers (to guide them in a structured review process). Items do not need to be checked explicitly for a PR to be eligible for merging. Purpose and scope
 Code quality
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 Created with ❤️ by the Trixi.jl community. | 
| Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@           Coverage Diff           @@
##             main    #2604   +/-   ##
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  Coverage   96.83%   96.83%           
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  Files         535      536    +1     
  Lines       42785    42804   +19     
=======================================
+ Hits        41429    41448   +19     
  Misses       1356     1356           
 Flags with carried forward coverage won't be shown. Click here to find out more. ☔ View full report in Codecov by Sentry. 🚀 New features to boost your workflow:
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| @DanielDoehring Could you please review this initially and ping me for a final review? | 
        
          
                examples/tree_1d_dgsem/elixir_advection_diffusion_implicit_sparse_jacobian.jl
              
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      …rse_jacobian_restart.jl
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Thanks you!
        
          
                src/semidiscretization/semidiscretization_hyperbolic_parabolic.jl
              
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                src/semidiscretization/semidiscretization_hyperbolic_parabolic.jl
              
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                src/semidiscretization/semidiscretization_hyperbolic_parabolic.jl
              
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                src/semidiscretization/semidiscretization_hyperbolic_parabolic.jl
              
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                examples/tree_1d_dgsem/elixir_advection_diffusion_implicit_sparse_jacobian.jl
              
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                examples/tree_1d_dgsem/elixir_advection_diffusion_implicit_sparse_jacobian.jl
              
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                examples/tree_1d_dgsem/elixir_advection_diffusion_implicit_sparse_jacobian_restart.jl
              
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                examples/tree_1d_dgsem/elixir_advection_diffusion_implicit_sparse_jacobian_restart.jl
              
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                examples/tree_1d_dgsem/elixir_advection_diffusion_implicit_sparse_jacobian.jl
              
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      Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>
        
          
                src/semidiscretization/semidiscretization_hyperbolic_parabolic.jl
              
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                examples/tree_1d_dgsem/elixir_advection_diffusion_implicit_sparse_jacobian_restart.jl
          
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Thanks
In the footsteps of #2532, here's a hyperbolic-parabolic elixir that is sped up using SparseConnectivityTracer