Solve partial differential equations using finite element analysis
Finite element analysis is a computational method for analyzing the behavior of physical products under loads and boundary conditions. It is one of the most popular approaches for solving partial differential equations (PDEs) that describe physical phenomena. Typical classes of engineering problems that can be solved using FEA are:
- structural mechanics
- heat transfer
Finite element analysis discretizes a physical domain into smaller elements. The equations in FEA describe physics of these individual elements, which are then assembled into a larger system of equations that models the entire domain.
A typical finite element analysis workflow includes the following tasks:
- Import or create a geometry
- Preprocess the geometry by meshing and defining physics (loads, boundary, and initial conditions)
- Postprocess results
You can use design of experiments or optimization techniques along with FEA to perform trade-off studies or design an optimal product for specific applications. You can also create a reduced order model from the finite element simulations to incorporate it in a physical or system-level model.
MATLAB® helps you apply FEA in several ways:
- Solve PDEs with Partial Differential Equation Toolbox™
- Apply design of experiments and other statistics and machine learning techniques with FEA simulation data using Statistics and Machine Learning Toolbox™.
- Apply optimization techniques on FEA simulations to come up with an optimum design with Optimization Toolbox™
- Speed up your analysis by distributing multiple FEA simulations to run in parallel using Parallel Computing Toolbox™.
Examples and How To
See also: physical modeling, mathematical modeling, dimensional analysis