MATLAB Examples

Solve Poisson's equation using the programmatic workflow. For the PDE Modeler app solution, see docid:pde_ug.bvhf75n. The problem formulation is in , on , where is the unit disk. The exact

Solve the wave equation using command-line functions. It solves the equation with boundary conditions u = 0 at the left and right sides, and at the top and bottom. The initial conditions are

Perform one-level domain decomposition for complicated geometries, where you can decompose this geometry into the union of more subdomains of simpler structure. Such structures are

Calculate eigenvalues and eigenvectors using the programmatic workflow. For the PDE Modeler app solution, see Eigenvalues and Eigenmodes of the L-Shaped Membrane: PDE App .

Compute the eigenvalues and eigenmodes of a square domain using the programmatic workflow. For the PDE Modeler app solution, see Eigenvalues and Eigenmodes of a Square .

Solve for the heat distribution in a block with cavity using the programmatic workflow. For the PDE Modeler app solution, see Heat Equation for a Block with Cavity: PDE App .

The calculation of the vibration modes of a circular membrane. The calculation of vibration modes requires the solution of the eigenvalue partial differential equation (PDE). In this

Solve the heat equation with a source term using the Partial Differential Equation Toolbox™.

How a 3-D axisymmetric model can be analyzed using a 2-D model. The model geometry, material properties, and boundary conditions must all be symmetric about a single axis for this

Perform a heat transfer analysis of a thin plate using the Partial Differential Equation Toolbox™.

An idealized thermal analysis of a rectangular block with a rectangular cavity in the center. One of the purposes of this example is to show how temperature-dependent thermal conductivity

Perform a 3-D transient heat conduction analysis of a hollow sphere made of three different layers of material, subject to a nonuniform external heat flux.

Solve a nonlinear elliptic problem.

Create a cardioid geometry using four distinct techniques. The techniques are ways to parametrize your geometry using arc length calculations. The cardioid satisfies the equation .

A PDE model stores initial conditions in its InitialConditions property. Suppose model is the name of your model. Obtain the initial conditions:

Import 3-D geometry from a point cloud.

Import a 3-D mesh into a PDE model. Importing a mesh creates the corresponding geometry in the model.

Use a geometry function to create a circular region. Of course, you could just as easily use a circle basic shape.

A PDE model stores coefficients in its EquationCoefficients property. Suppose model is the name of your model. Obtain the coefficients:

Create a geometry file for a region with subdomains and a hole. It uses the “Analytic” cardioid example from "Arc Length Calculations for a Geometry Function" and a variant of the circle

A PDE model stores boundary conditions in its BoundaryConditions property. To obtain the boundary conditions stored in the PDE model called model , use this syntax:

There are two types of boundaries:

Numerically solve a Poisson's equation using the assempde function in the Partial Differential Equation Toolbox™ in conjunction with domain decomposition.

Create contour slices in various directions through a solution in 3-D geometry.

Solves a Poisson's equation with a delta-function point source on the unit disk using the adaptmesh function in the Partial Differential Equation Toolbox™.

Numerically solve a Poisson's equation using the solvepde function in Partial Differential Equation Toolbox™.

Calculate the approximate gradients of a solution, and how to use those gradients in a quiver plot or streamline plot.

Obtain a surface plot of a solution with 3-D geometry and N > 1.

Obtain plots from 2-D slices through a 3-D geometry.

Calculate the deflection of a structural plate acted on by a pressure loading using the Partial Differential Equation Toolbox™.

Solve a coupled elasticity-electrostatics problem using Partial Differential Equation Toolbox™. Piezoelectric materials deform when a voltage is applied. Conversely, a voltage is

Include damping in the transient analysis of a simple cantilever beam analyzed with the Partial Differential Equation Toolbox™. The beam is modeled with a plane stress elasticity

Analyze an idealized 3-D mechanical part under an applied load using Finite Element Analysis (FEA). The objective of the analysis is to determine the maximal deflection caused by the load.

Calculate the vibration modes and frequencies of a 3-D simply supported, square, elastic plate. The dimensions and material properties of the plate are taken from a standard finite element

The Partial Differential Equation Toolbox™ analysis of the dynamic behavior of a beam clamped at both ends and loaded with a uniform pressure load. The pressure load is suddenly applied at

Perform a 2-D plane-stress elasticity analysis.

Solve the wave equation using the solvepde function in the Partial Differential Equation Toolbox™.

Solve a Helmholtz equation using the solvepde function in Partial Differential Toolbox™.

Analyze an idealized 3-D mechanical part under an applied loading using Finite Element Analysis (FEA). The objective of the analysis is to determine the maximum deflection caused by the

This examples conducts a parametric study in which heat conduction simulation is performed over a set of similar geometries to determine which geometry "best" meets an average temperature

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