PDEsim

Synopsis

PDEsim is a Monte Carlo partial differential equation solver. It's still in development, but is already able to put out some nifty graphics.

Sample Output

This should be the graph of the solution $Φ (x, y)$ to the elliptical partial differential equation $(1 + y) \frac{\partial^{2} Φ}{\partial x^{2}} + 2 x \frac{\partial^{2} Φ}{\partial x \partial y} + (1 - y) \frac{\partial^{2} Φ}{\partial y^{2}} - \frac{\partial Φ}{\partial x} = 0$ with boundary values given by $f (x, y) = x + 2 y$ on the unit circle $x^{2} + y^{2} = 1$ .

(That was in MathML; probably illegible to most everybody right now...)

The Algorithm

Short summary goes here.

Development Roadmap

Currently, all of the parameters PDEsim needs (for example, the actual equation it's solving) are compiled in. Changing them is easy, but may require understand both the algorithm and C programming; this rather limits PDEsim's audience. Clearly, the next step for PDEsim is adding the ability to read from the command line the numerical parameters (easy) and the PDE to be solved (hard?).

Why the latter might be hard: Reading a PDE off the command line first requires some description language that works as text; it's hard to type in those partial derivatives. (How does MATLAB handle this?) Also, the random_walk() probabilities are dependent on the PDE; it may be difficult to automate the conversion of PDE coefficients into probabilities. Got to check...

Getting The Source

If you'd like to get your hands dirty with C code, you can browse the CVS repository on the PDEsim project page, hosted by Sourceforge. I'm still working on it; I'd also welcome improvements from anyone who wants to contribute. Compiling PDEsim requires the GNU plotutils package; specifically, the libplot library. Also available is a fairly recent snapshot that will compile even when the most recent version doesn't, and doesn't require CVS to set up.

Mark Jeffcoat
jeffcoat@alumni.rice.edu

Last Updated October 15, 2000.