1. Finite Element Modeling with COMSOL Ernesto Gutierrez-Miravete Rensselaer at Hartford Presented at CINVESTAV-Queretaro December 2010

2. OUTLINE DAY 1: Introduction to Modeling with COMSOL DAY 2: Some more Advanced Applications

3. OUTLINE – DAY 1 1.-Mathematical Modeling in Science and Engineering 2.- Systems of Partial Differentials Equations as representations of Physical Systems 3.- Solution of PDEs using the Methods of Advanced Calculus 4.- Solution of PDEs using the methods of Numerical Mathematics 5.- The COMSOL User Interface 6.- Selected Basic Examples

4. Summary of Day 1 • The finite element method is a numerical approximation process used for the solution of boundary and initial value problems for differential equations • The FEM produces approximate solutions by writing them as linear combinations of simple basis functions and test functions equal to the basis functions and introducing these into the variational formulation of the problem • The final FEM equations that must be solved are systems of linear algebraic equations • COMSOL is modern software embedding the FEM with a cleverly designed user interface designed to increase the applicability and ease of use of mathematical modeling methods

5. Summary of Day 1 (contd) The COMSOL user interface allows for easy and convenient: • Definition of coordinate system and physical phenomena involved • Creation/Importing of Geometries • Entering of input data (physical properties, boundary and initial conditions) • Meshing of the geometric domain with finite elements • Solving the resulting system of algebraic equations • Visualization of the computed results

6. OUTLINE – DAY 2 • Brief review of main points covered in day 1 • Development and demonstration of selected models • Modes of Vibration of a Turbine Blade • Stresses in an Airframe Bracket • Buckling of Isogrid Plates • Heat Conduction in a Glass Bottle Plunger • Surface Heating with a Moving Intermittent Source • Laminar Flow and Heat Transfer around a Cylinder • Flow and Heat Transfer of Liquid Metal over a Backward facing Step under imposed Magnetic Field • Electro-Thermal Phenomena in Contactors