1. Mandatory programming project TMA4220

3. Cooking beef and other applications of FEM in the kitchen

4. The laws of physics

6. Task: to cook a beef ● How would one optimally go about cooking this thing? ● Too high temperature: dry tasteless ● Too low temperature: raw uneatable ● Too varying temperature: all of the above

7. Task: To cook a beef ● Want the optimal temperature distribution ● What would one do to acquire this?

8. Task: To cook a beef ● Want the optimal temperature distribution ● What would one do to acquire this? ● ← Actual problem geometry

9. The beef ● Given as a parametric volume (3d)

10. Cooking and Boundary conditions

11. ● Room temperature Dirichlet boundary conditions

12. Cooking and Boundary conditions ● Room temperature Dirichlet boundary conditions ● Cooking temperature Dirichlet boundary conditions

13. FEM program structure Preprocess Computation Postprocess

14. FEM program structure Preprocess Computation Postprocess ● Mesh generation ● Boundary conditions ● Material properties

15. FEM program structure Preprocess Computation Postprocess ● Finite element loop ● Integration (by quadrature) ● Linear system solver

16. FEM program structure Preprocess Computation Postprocess ● Solution plotting ● Error evaluation or estimation ● Set up for another run (adaptive solvers)

17. The actual problem set ● Series of problems 1a) - 3e)

18. The actual problem set ● Series of problems 1a) - 3e) ● Gauss quadrature

19. The actual problem set ● Series of problems 1a) - 3e) ● Gauss quadrature ● FEM theory

20. The actual problem set ● Series of problems 1a) - 3e) ● Gauss quadrature ● FEM theory ● Sample 2d problem

21. The actual problem set ● Series of problems 1a) - 3e) ● Gauss quadrature ● FEM theory ● Sample 2d problem ● Sample 3d problem

22. The actual problem set ● Series of problems 1a) - 3e) ● Gauss quadrature ● FEM theory ● Sample 2d problem ● Sample 3d problem ● Time dependent 3d problem

23. The required report ● On the introductory questions, answer short and answer right.

24. The required report ● On the introductory questions, answer short and answer right. ● Core question: “How to cook a beef”, elaborate on this as much as possible

25. The required report ● On the introductory questions, answer short and answer right. ● Core question: “How to cook a beef”, elaborate on this as much as possible ● Source code is not required, but comment briefly on how you've done things (especially if you've done something clever)

26. The required report ● On the introductory questions, answer short and answer right. ● Core question: “How to cook a beef”, elaborate on this as much as possible ● Source code is not required, but comment briefly on how you've done things (especially if you've done something clever) ● 2 people on each group

27. Extensions how to make a princess

28. The princess cake ● How is this cake made?

29. The princess cake ● Make a bowl ● Decorate with marzipan or cream ● Put in a Barbie doll

30. The problem ● Skirt (bowl) is almost spherical ● The worst shape to get equal baked ● Either the core will be raw, or the outer edge will be burned

31. The solution ● A metal shaped pole through the center axis