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
  • electromagnetics
  • diffusion
  • vibration

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.

Geometry discretization for finite element analysis.

A typical finite element analysis workflow includes the following tasks:

  1. Import or create a geometry
  2. Preprocess the geometry by meshing and defining physics (loads, boundary, and initial conditions)
  3. Solve
  4. Postprocess results

A typical finite element analysis workflow.

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:

See also: physical modeling, mathematical modeling, dimensional analysis