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# How Does It Do It?

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# How Does It Do It?

FlexPDE is a fully integrated PDE solver, combining several internal facilities to provide a complete problem solving system:

 • A script editing facility with syntax highlighting provides a full text editing facility and a graphical domain preview.

 • A symbolic equation analyzer expands defined parameters and equations, performs spatial differentiation, and symbolically applies integration by parts to reduce second order terms to create symbolic Galerkin equations.  It then symbolically differentiates these equations to form the Jacobian coupling matrix.

 • A mesh generation facility constructs a triangular or tetrahedral finite element mesh over a two or three-dimensional problem domain. In two dimensions, an arbitrary domain is filled with an unstructured triangular mesh.  In three-dimensional problems, an arbitrary two-dimensional domain is extruded into a the third dimension and cut by arbitrary dividing surfaces.  The resulting three-dimensional figure is filled with an unstructured tetrahedral mesh.

 • A Finite Element numerical analysis facility selects an appropriate solution scheme for steady-state, time-dependent or eigenvalue problems, with separate procedures for linear and nonlinear systems.  The finite element basis may be linear, quadratic or cubic.

 • An adaptive mesh refinement procedure measures the adequacy of the mesh and refines the mesh wherever the error is large.  The system iterates the mesh refinement and solution until a user-defined error tolerance is achieved.

 • A dynamic timestep control procedure measures the curvature of the solution in time and adapts the time integration step to maintain accuracy.

 • A graphical output facility accepts arbitrary algebraic functions of the solution and plots contour, surface, vector or elevation plots.

 • A data export facility can write text reports in many formats, including simple tables, full finite element mesh data, CDF,  VTK or TecPlot compatible files.