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How to speed up the heat equation example? #268

@homocomputeris

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@homocomputeris

It takes several minutes to run the heat eq. example with the Dirichlet BC as is, although the mesh is quite coarse and the order is low.

Can it be sped up somehow?

$ julia
  Activating project at `~/Documents/Code/heat`
               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.8.5 (2023-01-08)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

julia> include("./heat.jl"); exit();
julia  165.39s user 2.28s system 98% cpu 2:50.08 total
Status `~/Documents/Code/heat/Project.toml`
  [5b8099bc] DomainSets v0.6.6
  [94925ecb] MethodOfLines v0.9.1
  [961ee093] ModelingToolkit v8.52.0
  [1dea7af3] OrdinaryDiffEq v6.50.0
  [91a5bcdd] Plots v1.38.9

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