19.10. Numerical Methods for the 2D Wave Equation

Try these first

1. 1.

   What is the purpose of numerical methods?

   Hint

   Think about practical applications in engineering.

2. 2.

   Name the two numerical methods discussed.

   Hint

   Consider abbreviations in your answer.

3. 3.

   What is the CFL condition used for?

   • To ensure solution stability
   • To speed up calculations
   • To define boundary conditions

   Hint

   It deals with how numerical solutions behave over time.

4. 4.

   True or False: FEM works better for complex geometries than FDM.

   • True
   • False

   Hint

   Think about the structure of the domains being analyzed.

5. 5.

   Design a numerical approach to simulate the vibrations of a circular membrane, specifying whether you would use FDM or FEM. Justify your choice.

   Hint

   Think about the shape and complexity of the membrane.

6. 6.

   Compare and contrast the advantages of FDM and FEM in a report focused on civil engineering applications. Include specific scenarios.

   Hint

   Consider the types of geometries encountered in civil engineering.