PDEase2D can handle initial- or boundary-value problems that involve
partial or ordinary differential equations; are primarily nonlinear in nature;
and are static or dynamic, including eigenvalue analysis. To insure proper
handling for each class of these problems, PDEase2D will use different types of
solvers. Model size in PDEase2D can include up to 32 simultaneous equations and
up to 10^{9} nodes for FEM model size.

The dimensionality of these problems is limited to 21/2 dimensions (that is, problems that cannot reference the third dimension as a dependent variable). However, you can still use the software at different locations of a 3-D model, provided that the geometry and boundary conditions (BCs) are adjusted accordingly. This version will not handle complex type and/or complex eigenvalue problems.

If you use Macsyma software's symbolic math capabilities to develop equations, you can still use them in their final form in PDEase2D. There is no bi-directional interface that can take advantage of Macsyma from within PDEase2D. The only way to pass information between Macsyma and PDEase2D is through the MFE notebook where all variables are accessible to both math engines.

A typical PDEase2D model-definition file is divided into sections. Using PDEase2D's natural language, the problem definition in the equation section can describe complex equations involving partial derivatives, in most cases on one command line. The equation section is where the model's mathematical definition is used, and it can be easily translated into PDEase's notation. PDEase2D is limited to first- or second-order space definition and first order in time.

PDEase2D gives you flexibility as to how BCs are entered. The section 'Boundaries' in the input file is based on a hierarchical structure that divides the model in regions. In every region you define the geometry over which BCs are applied. Regions can be handy in areas where you want to force a finer mesh. By breaking the model into regions in that area, PDEase2D will fine mesh the boundary in between.

With PDEase2D you don't have to specify node or element locations. Based on the geometrical outline you specify, PDEase2D will create nodes and elements inside and at the boundary of the model. With boundary segment words such as arc, you can define with relative ease the outline and any openings in your model. New in this version is the ability to import geometry directly from a CAD program in DXF format. PDEase2D interprets every region in the model, as long as you keep them in separate layers in the CAD and DXF files.

At this point, the majority of the model definition portion is complete. You can watch the program meshing the model, and can also use the "monitors" tool to keep an eye on the convergence of the solution. PDEase2D has an excellent mesh generator that minimizes the relative and converges to the solution. The created mesh is made of triangular isoparametric (quadratic) elements.

Unlike ordinary FEA mesh generators, PDEase2D will refine the mesh only where the error exceeds a user-supplied minimum figure. For unstable nonlinear problems, imposing a single-step convergence criterion will not yield an accurate solution. By breaking the problem into small linear sections, you can use the solution and its corresponding mesh density as the initial values for the next step.

The value of PDEase2D for the scientist or engineer is evident in three areas where it shines: ease in setting up the model, simple FEA node and element creation, and excellent resources and postprocessing tools. By implementing the MFE notebook in this version of PDEase2D, which features a bi-directional interface with Macsyma symbolic math package, Macsyma Inc. is providing the user with the best of both worlds in symbolic math and PDE solvers.

## Spec box: PDEase2D 3.0

PDEase2D is a front-end language that can model static and time-dependent problems involving partial differential equations using the Finite Element Method. The program requires a 80486 or better PC with 8 Mbytes of RAM, 10 Mbytes of Disk space, and Windows 95 or NT.

**List Price:** $999

*Macsyma, Inc., 20 Academy St., Arlington, MA 02174, ph: (617) 646-4550; fax: (617) 646-3161 *

**A similar product: **

MATLAB with PDE Toolbox - The Mathworks Inc., 24 Prime Park Way, Natick, MA 01760; ph: (508) 647-7000, e-mail: [email protected]

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