A PDE2D program is created during an interactive
session , or a GUI session , and all
documentation, including examples, is available on-line. Thus the user
does not have to work through a thick user's manual (there is no manual,
in fact!) to determine how to set up a problem. All the user has to do is
answer a series of questions about the region, partial differential equations
and boundary conditions, and select solution method and graphical output
options. Extensive error checking is done during the interactive session,
and also at execution time.
After all questions have been answered, the FORTRAN90 program created by the
driver is compiled, linked to the runtime routines which it calls, and
executed. The FORTRAN90 program contains copious
documentation and is highly readable (most of the questions asked during the
interactive session are repeated in the comments), so the user can make minor
changes directly to the program, and does not have to work through another
interactive session each time minor modifications to the problem or solution
method are desired.
There are 15 prepared example problems, and if the user selects one of these,
answers will be provided to each interactive question, appropriate to the
example. To see what the interactive sessions look like for these problems,
click on one of the following examples:
To see the FORTRAN90 program generated during the example 9 interactive
session, click on:
- A simply-supported elastic plate equation, with
a unit load concentrated at the midpoint of a square.
- A non-linear, steady-state PDE, solved in an
annulus. The initial triangulation is generated automatically, and
adaptive grid refinement is illustrated.
- An eigenvalue problem. The region has a curved
interface across which material properties vary abruptly, in this
- The first part of a thermal stress problem. In
this part, the temperature distribution in a V-notched block is calculated
by solving the time-dependent heat conduction equation, using adaptive
time step control.
- The second part of a thermal stress problem. In
this part, the stresses induced in the V-notched block by thermal
expansion are calculated using the temperature distribution output
by example 4.
- A 1D time-dependent integro-differential equation for
a financial math application. In this problem there is a
term involving an integral of the solution, which requires
that we use PDE2D's feature for interpolating the solution
at the last saved time step, for use in the integral term.
- A waveguide problem (an eigenvalue
problem in which the eigenvalue appears nonlinearly).
- The Navier-Stokes equations solved for
a fluid flowing around a bend in a pipe.
- A 3D elasticity problem, solved in a
torus. This example illustrates the use of user-defined coordinate
transformations to handle more general 3D regions.
- A 3D time-dependent wave equation
- A 3D eigenvalue problem: the Schrodinger
equation in a hydrogen atom. This example illustrates the use of
spherical coordinates and periodic boundary conditions.
- A 3D eigenvalue problem, solved in a
composite region consisting of two cylinders of different material
- The axisymmetric Navier-Stokes equations
solved in a non-rectangular channel, using the collocation FEM.
- A 1D saturated/unsaturated water flow
- A 1D version of the Schrodinger eigenvalue
equation of example 11.
Example 9 Fortran program