Partial Differential Equation Toolbox

Solve partial differential equations using finite element analysis

Partial Differential Equation Toolbox provides functions for solving structural mechanics, heat transfer, and general partial differential equations (PDEs) using finite element analysis.

You can perform linear static analysis to compute deformation, stress, and strain. For modeling structural dynamics and vibration, the toolbox provides a direct time integration solver. You can analyze a component’s structural characteristics by performing modal analysis to find natural frequencies and mode shapes. You can model conduction-dominant heat transfer problems to calculate temperature distributions, heat fluxes, and heat flow rates through surfaces. You can perform electrostatic and magnetostatic analyses, and also solve other standard problems using custom PDEs.

Partial Differential Equation Toolbox lets you import 2D and 3D geometries from STL or mesh data. You can automatically generate meshes with triangular and tetrahedral elements. You can solve PDEs by using the finite element method, and postprocess results to explore and analyze them.

What Is Partial Differential Equation Toolbox?

A von Mises stress distribution plot in color on a 3D surface with title von Mises stress.

Structural Mechanics

Perform linear static, transient, modal, and frequency response analyses. Evaluate mechanical strength by computing displacement, stress, and strain or simulate dynamic behavior of mechanical systems.

Finite Element Analysis in MATLAB, Part 1: Structural Analysis Using Finite Element Method in MATLAB (7:33)

Documentation | Examples

A temperature distribution plot in color of a spherical surface with title Temperature at Time 50, xlabel x, ylabel y.

Heat Transfer

Perform steady-state, transient, or coupled thermal-stress analysis to compute temperature distributions and other thermal characteristics. Approximate dynamic characteristics using reduced-order models.

Finite Element Analysis in MATLAB, Part 2: Heat Transfer Using Finite Element Method in MATLAB (6:18)

Documentation | Examples

Magnetic potential plot in color with the equipotential lines as contours and the magnetic fields as arrows.

Electromagnetics

Perform electrostatic, magnetostatic, or harmonic analysis for the design of electrical and electronic components.

Documentation | Examples

A mesh surface plot in color that shows the values of the PDE solution as heights above a grid in the x-y plane. The surface has solid edge colors, which correspond to the heights, and no face colors.

General PDEs

Solve second-order linear and nonlinear PDEs for stationary, time-dependent, and eigenvalue problems commonly arising in engineering and science.

Documentation | Examples

3D geometry object created from an STL geometry file.

Geometry and Meshing

Define a 2D or 3D geometry by importing STL, STEP, or mesh data or by creating parameterized shapes using geometric primitives. Generate finite element mesh using triangular elements in 2D and tetrahedral elements in 3D.

Documentation | Examples

Figure contains an axes object. The axes object with xlabel x, ylabel y contains 385 objects of type patch.

Visualization and Postprocessing

Visualize models and solutions by creating plots and animations of geometry, mesh, results, and derived and interpolated quantities by leveraging powerful MATLAB graphics. Interactively create and explore visualizations of PDE results using the Visualize PDE Results Live Editor task.

Documentation | Examples

Workflow block diagram that illustrates the FEA workflow starting with Geometry and continuing to Develop Models, Analysis, Integrate and Scale, and Share.

Automate, Integrate, and Share FEA Workflows

Automate FEA simulations using MATLAB, integrate with other MATLAB products to build end-to-end workflows, and share custom applications using App Designer and MATLAB Compiler.

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