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Important 1: ###

For this assignment, you must have the packages Gridap.jl and Gmsh.jl installed, as well as one of the compatible visualizers: VisIt https://wci.llnl.gov/simulation/computer-codes/visit/ or Paraview https://www.paraview.org/

Important 2: ###

Rename the file as: group_name_lab_7.ipynb

All the generated code and the presentation must be included in this notebook.

The objectives of the assignment are varied:

1. Get familiar with the Gridap package and solving problems using Finite Elements.

2. Solve Dirichlet problems for the Laplace or Poisson equation.

3. Get acquainted with modern visualizers.

4. Process the obtained data.

1) Run the notebook Poisson_example.ipynb in its test mode and verify that it works correctly. Experiment with different "solution" functions and their "sources". Visualize the results using the selected visualizer (VisIt or Paraview).

2) Experiment with different solver configurations (different methods, number of iterations, tolerances). Try different types of Finite Elements and different orders.

3) Run the notebook Poisson_example_b2.ipynb with options for computing the capacities of different conductor configurations. Experiment with different conductor setups, or by changing their relative distances, sizes, shapes, etc.

4) Use different resolutions and observe how it affects the computed capacities.

5) For the adventurous: Change the boundary conditions to Neumann or Mixed, think of a specific (physical or engineering) problem and apply them. Asymptotic conditions: For isolated systems, boundary conditions of the "Robin" type are used. These impose a decay like (in 3D) $u = \frac{C}{r}$ without specifying $C$, for example by imposing (in 3D) $\partial_r u + \frac{u}{r} = 0$ on a sphere of radius $R$ large enough. Implement this condition for this system (in 2D). .