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Sarah Palfreyman, MathWorks
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Solve partial differential equations using finite element analysis with Partial Differential Equation Toolbox™.

Partial Differential Equation Toolbox provides functionality for using finite element analysis to solve applications such as thermal analysis, structural analysis, and custom partial differential equations.

The first step in the FEA workflow is to define the geometry. You can import from 2D or 3D CAD files in STL format or create geometries using parameterized shapes. Next, you can mesh geometries using 2D triangular or 3D tetrahedral elements or import mesh data from existing meshes from complex geometries. To ensure accurate simulation results, you can inspect the mesh quality and perform refinement.

Partial Differential Equation Toolbox makes it easy to set up your simulation. In this thermal analysis example, material properties like thermal conductivity and boundary conditions including convection, fixed temperature, and heat flux are applied using only a few lines of code.

Next, you can solve and visualize results, including temperature distributions, heat fluxes, and heat flow rates and see how transients vary over time. You can run multiple simulations in parallel to perform Design of Experiment studies. You can perform structural analysis such as:

- static analysis to compute stress and strain from an applied load,
- evaluate resonance with modal analysis to compute vibration modes and frequencies,
- and dynamic simulation to compute time varying displacements and reaction forces.

In addition, Partial Differential Equation Toolbox documentation has many examples for solving custom PDEs. For more information, return to the Partial Differential Equation Toolbox page or choose a link below.