Partial Differential Equation Toolbox0 pages

Partial Differential Equation Toolbox
Solve partial differential equations using finite element methods
The Partial Differential Equation Toolbox™ product contains tools for the study and solution of partial differential
equations (PDEs) in two-space dimensions (2-D) and time. A set of command-line functions and a graphical user
interface let you preprocess, solve, and postprocess generic 2-D PDEs for a broad range of engineering and science
applications.
Key Features
▪ Complete GUI for pre- and post-processing 2-D PDEs
▪ Automatic and adaptive meshing
▪ Geometry creation using constructive solid geometry (CSG) paradigm
▪ Boundary condition specification: Dirichlet, generalized Neumann, and mixed
▪ Flexible coefficient and PDE problem specification using MATLAB syntax
▪ Fully automated mesh generation and refinement
▪ Nonlinear and adaptive solvers handle systems with multiple dependent variables
▪ Simultaneous visualization of multiple solution properties, FEM-mesh overlays, and animation
Working with the Partial Differential Equation Toolbox
The Partial Differential Equation Toolbox lets you work in six modes from the graphical user interface 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.

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