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 also solve standard problems such as diffusion, electrostatics, and magnetostatics, as well as 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.

Get Started:

Structural Mechanics

Solve linear static, transient, modal analysis, and frequency response problems.

Linear Static Analysis

Compute displacement, stress, and strain under load and boundary conditions, and evaluate a component’s mechanical strength and behavior.

Modal and Frequency Response Analysis

Find natural frequencies and mode shapes to identify and prevent potential resonances, and simulate dynamic behavior of a structure using its frequency responses.

First six mode shapes of a robotic arm.

Transient Analysis

Compute displacement, velocity, acceleration, stress, and strain under time-varying loads.

Deflection of a beam center as function of time.

Heat Transfer

Analyze temperature distributions of components to address thermal management challenges.

Steady-State Thermal Analysis

Find temperature distributions and other thermal characteristics under constant thermal loads.

Transient Thermal Analysis

Find temperature distributions and other thermal characteristics under time-varying thermal loads.

Contour plots of temperature distribution with respect to time.

Coupled Thermal-Stress Analysis

Analyze mechanical behavior under coupled thermal and mechanical loads.

Stress distribution under combined mechanical and thermal loads.

General PDEs

Solve PDEs that occur in common applications in engineering and science.

Second-Order PDEs

Solve second-order linear and nonlinear PDEs for stationary, time-dependent, and eigenvalue problems.

L-shaped membrane with zero Dirichlet Boundary condition.


Solve electrostatics, magnetostatics, DC conduction, and wave propagation problems.

Electrostatic simulation of MEMS device.

Geometry and Meshing

Define geometry and discretize it to build finite element models.

Import/Create Geometry

Reconstruct 2D and 3D geometry from imported STL or mesh data, or create simple parameterized shapes using geometric primitives.

Import or create geometry in MATLAB.

Generate Mesh

Generate finite element mesh using triangular elements in 2D and tetrahedral elements in 3D. Inspect and analyze mesh quality to assess accuracy of results.

Generate mesh and ensure its quality for accuracy of results.

Visualization and Postprocessing

Compute derived and interpolated data from results as well as create plots and animations

Plot and Animate Solutions

Visualize models and solutions by creating plots and animations of geometry, mesh, results, and derived and interpolated quantities by leveraging powerful MATLAB graphics. Create multiple subplots and easily customize plot properties.

Contour plot slices in 3D.


Analyze solutions and its gradients at mesh nodes and other interpolated locations. Leverage MATLAB’s extensive functionalities for further statistical postprocessing and data analysis using Statistics and Machine Learning Toolbox and Optimization Toolbox.

Fast Fourier Transform of tip displacement.

Automate, Integrate, and Share FEA Workflows

Automate, Integrate, and Share Finite Element Analysis (FEA) Workflows in MATLAB.

FEA Workflows

Create a typical FEA workflow in MATLAB – import or create geometries, generate mesh, define physics with load, boundary, and initial conditions, solve, and visualize results – all from one user interface.

MATLAB helps automate and integrate FEA workflows.

Latest Features

3-D Geometry Creation

Extrude a 2-D geometry into a 3-D geometry

Finite Element Matrices

Assemble finite element matrices for time-dependent and nonlinear modeling

See release notes for details on any of these features and corresponding functions.

Finite Element Analysis in MATLAB Video Series

Watch the videos in this series to learn how to perform finite element analysis in MATLAB® using Partial Differential Equation Toolbox™.