# Partial Differential Equation Toolbox

## 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.

### Transient Analysis

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

## Heat Transfer

Analyze temperature distributions of components to address thermal management challenges.

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, and approximate dynamic characteristics using reduced-order models.

### Coupled Thermal-Stress Analysis

Analyze mechanical behavior under coupled thermal and mechanical loads.

## Electromagnetics

Perform electromagnetic analysis for design of electrical and electronic components.

### Electrostatics and Magnetostatics

Solve Maxwell’s equations modeling electrostatic and magnetostatic problems.

## 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.

## Geometry and Meshing

Define geometry and discretize it to build finite element models.

### Import/Create Geometry

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

### 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.

## 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.

### Postprocessing

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.

### Interactive Solution Plots

Plot and inspect results with the interactive controls in Visualize PDE Results Live Editor task

## 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.

• Automate FEA simulations by using MATLAB language, execute simulations faster leveraging Parallel Computing Toolbox
• Integrate with other MATLAB products such as Simscape Multibody and Simulink to build an end-to-end workflow
• Share custom applications using MATLAB Compiler and App Designer as a standalone application or as a web app