Lab 09 - Vector valued problems

Theory and Practice of Finite Elements

Luca Heltai [email protected]

Starter code documentation can be accessed here:

https://dealii-courses.github.io/sissa-mhpc-lab-08/

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General Instructions

For each of the point below, extend the Poisson class with functions that perform the indicated tasks, trying to minimize the amount of code you copy and paste, possibly restructuring existing code by adding arguments to existing functions, and generating wrappers similar to the run method (e.g., run_exercise_3).

Once you created a function that performs the given task, add it to the poisson-tester.cc file, and make sure all the exercises are run through the gtest executable, e.g., adding a test for each exercise, as in the following snippet:

TEST_F(PoissonTester, Exercise3) {
   run_exercise_3();
}

By the end of this laboratory, you will have modified your Poisson code to run in parallel using shared memory parallelization on multiple threads, and you will have some knowledge of Task based parallelization

Lab-09

1. Transform your PoissonProblem code to a LinearElasticityProblem class (create a copy of the PoissonProblem class, and modify your copy)

2. Add a n_components=dim argument to the LinearElasticityProblem class, and make sure that all members that need to know the number of components of the problem (e.g., all classes derived from the dealii::Function class) throw an assertion in Debug mode if the number of components is wrong.

3. Create the finite element space from the parameter file using FETools::get_fe_by_name, and check with an assertion that the number of components is correct (removing fe_degree from the parameters).

4. Add the parameters mu and lambda to the parameter file, and assemble the problem (mu eps u, eps v) + (lambda div u, div v) = (f,v) where u and v are in $H^1_0(\Omega)^{dim}$, and eps u = 0.5((grad u) + (grad u)^T). Make sure you add mu and lambda to the problem constants map, so you can use them in the functions and in the exact soluion.

5. Make sure the output of your code is vector based, by instructing DataOut to output a vector based solution.

6. Create a common class BaseProblem, that contains everything that is shared between PoissonProblem and LinearElasticity, and make sure both PoissonProblem and LinearElasticityProblem are derived from the base class. Make sure you initialize the ParameterAcceptor class explicitly in the BaseProblem, and then in the derived classes.

7. Make sure you create a LinearElasticityProblemTester class to test your problem using gtest, and create pure shear and pure compression/dilation test cases.