Partial Differential Equation Toolbox

Working with the Partial Differential Equation Toolbox

The Partial Differential Equation Toolbox lets you work in six modes from the PDE app or the command line. Each mode corresponds to a step in the process of solving PDEs using the Finite Element Method.

  • Draw mode lets you create Ω, the geometry, using the constructive solid geometry (CSG) model paradigm. The graphical interface provides a set of solid building blocks (square, rectangle, circle, ellipse, and polygon) that can be combined to define complex geometries.
  • Boundary mode lets you specify conditions on different boundaries or remove subdomain borders.
  • PDE mode lets you select the type of PDE problem and the coefficients c, a, f, and d. By specifying the coefficients for each subdomain independently, you can represent different material properties.
  • Mesh mode lets you control the fully automated mesh generation and refinement process.
  • Solve mode lets you invoke and control the nonlinear and adaptive solver for elliptic problems. For parabolic and hyperbolic PDE problems, you can specify the initial values and obtain solutions at specific times. For the eigenvalue solver, you can define the interval over which to search for eigenvalues.
  • Plot mode lets you select from different plot types, including surface, mesh, and contour. You can simultaneously visualize multiple solution properties using color, height, and vector fields. The FEM mesh can be overlaid on all plots and shown in the displaced position. For parabolic and hyperbolic equations, you can animate the solution as it changes with time.
PD Wrenches Image
Partial Differential Equation Toolbox Wrench Image

Using the PDE app to define the complex geometry of a wrench, generate a mesh, and analyze it for a given load configuration.

Next: Defining and Solving PDEs

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