Typical Steps to Solve PDEs

Partial Differential Equation Toolbox™ provides the PDE app that you can use to:

  1. Define the 2-D geometry.

    You create Ω, the geometry, using the constructive solid geometry (CSG) model paradigm. A set of solid objects (rectangle, circle, ellipse, and polygon) is provided. You can combine these objects using set formulas.

  2. Define the boundary conditions.

    You can have different types of boundary conditions on different boundary segments. See Classification of Boundary Conditions.

  3. Define the PDE coefficients. See Scalar PDE Coefficients and Coefficients for Systems of PDEs.

    You interactively specify the type of PDE and the coefficients c, a, f, and d. You can specify the coefficients for each subdomain independently. This may ease the specification of, e.g., various material properties in a PDE model.

  4. Create the triangular mesh.

    Generate the mesh to a fineness that adequately resolves the important features in the geometry, but is coarse enough to run in a reasonable amount of time and memory.

  5. Solve the PDE.

    You can invoke and control the nonlinear and adaptive solvers for elliptic problems. For parabolic and hyperbolic problems, you can specify the initial values, and the times for which the output should be generated. For the eigenvalue solver, you can specify the interval in which to search for eigenvalues.

  6. Plot the solution and other physical properties calculated from the solution (post processing).

After solving a problem, you can return to the mesh mode to further refine your mesh and then solve again. You can also employ the adaptive mesh refiner and solver, adaptmesh. This option tries to find a mesh that fits the solution.

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