In many engineering problems, obtaining exact solutions is impossible due to the complexity of the solution domain and/or the nonlinearity of the problem equations. The use of numerical methods is therefore essential to obtain approximate solutions.
Program:
- Know how to formulate the strong form of a physical problem and understand the classification into elliptic, parabolic, and hyperbolic problems.
- Be familiar with the finite difference method (FDM) for solving stationary partial differential equations (PDEs) and its application to 1D and 2D problems.
- Understand the finite element method (FEM) for solving stationary PDEs and its application to 1D and 2D problems.
- Understand methods for solving linear problems: Gauss methods, LU decomposition, Cholesky, and matrix conditioning.
- Understand iterative methods for solving nonlinear problems: Jacobi method, Gauss-Seidel, Newton-Raphson, and the concept of convergence.
- Be able to apply all these methods to problem solving using FEM and/or FDM.
