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Here are the new PDE2D 9.0 features:
- There is now a PDE2D Graphical User Interface (GUI), which can be used to access the PDE2D collocation methods (0d,1d,2d,3d). The GUI is an alternative to the Interactive Driver for generating your Fortran program, which is then executed using RUNPDE2D as before. Users can still create their input through the Interactive Driver if they prefer; in fact, for a problem involving a complicated 2D region, which requires the PDE2D Galerkin method, or a problem involving a system of more than 8 PDEs, they will still have to use the Interactive Driver program.
However, for 0D or 1D problems, and for 2D and 3D problems in "a wide range of simple regions", the PDE2D GUI is exceptionally easy to use. Less important options are assigned default values (which can later be modified in the Fortran program, as usual), and PDE2D GUI users can set up a system of PDEs in an extraordinarily short time.
- When the PDE2D collocation methods are used to solve 2D and 3D problems, the region must be parameterized. In previous versions, the parameters were called X,Y,Z and the Cartesian coordinates were X1,X2,X3. It really makes no sense to call the parameters X,Y,Z, that was done for historical reasons only. With version 9.0, the parameters are called P1,P2,P3 and the Cartesian coordinates are X,Y,Z. Thus now Laplace's equation, for example, is written Uxx+Uyy+Uzz=0, no matter what 3D region is used.
Unfortunately this may be a bit confusing to old users, because this means the meanings of, say, U11 and Uxx are exactly reversed from before! The change really makes the documentation much simpler and less confusing, though, and is easily worth the transitional pain. Despite the reversal in notation, edition 9.0 will be backward compatible with versions 8.0 to 8.6, because all the relevant changes are in the (automatically generated) user's program.
- In previous editions, the MATLAB graphics programs generated by PDE2D (written from POSTPR) ran very slowly when the number of output points was large (usually 3D problems), because the output matrices were assigned element by element in the M-file. Now the matrices are read in from a file, and the large graphics programs run MUCH faster.
- For 2D Galerkin problems, NTF has been moved from a PARAMETER statement to an assignment statement, making it easy to do multiple runs (NPROB>1) with different size triangulations, in the same program.
- The boundary arc number IARC can now be referenced in boundary integrals, for 2D Galerkin problems (useful in limiting a boundary integral to a single arc, or selected arcs).
- Now the boundary integrals for all 2D and 3D problems, and the boundary conditions for 2D and 3D collocation problems, can all reference the normal derivative of each unknown. For example, if an unknown is named "Q", you can reference its normal derivative as "Qnorm". Previously, users had to form the normal derivative using the boundary normal vector.
- A minor bug was fixed which gave incorrect answers for 0D eigenvalue problems, when NEQN was 2 or less, and when all eigenvalues were requested (ITYPE=4). Of course, PDE2D is not the recommended method for finding eigenvalues of a 2 by 2 matrix (0D problem), but it is supposed to work, and now does!
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