Question: What to do with lockup, lost kernel, crashes with big symbolic problem?

I am a retired physicist persuing independent mathematical research and don't fit into any of Maplesoft's four user catagories.

I am trying to develop a new finite element method for incompressible fluid dynamics in 3D. I must derive four vector functions which are mapped into the 84 degrees-of-freedom of the finite element. I expand each of the four functions in terms of multinomials with 192 unknown coefficients to be determined. I apply essential constraints to each function and solve the equations to evaluate/eliminate some of the coefficients. I then require that the now partially constrained Hermite functions interpolate vector functions through highest order possible, repeatedly solving for new values of the set of coefficients, reducing the number of unknowns at each step.

The problem is admittedly big, but I lose the kernel, or the problem locks up, or gets out of control at times. While executing successfuly, Maple is using about 6 to 8 MB memory, and may accumulate a half hour or more CPU time over several solution iterations. When it gets out of control, it may use up to 560 MB and claims to exceed the output limit of 1000000. On smaller problems there are fewer lockups and kernel losses. Lockups and overflows can only be terminated using Task Manager.

What can I do to increase the allowable program size so I can get an answer? I have larger problems in mind.

I am using Maple 11 on a dual processor Lenovo T61 laptop with 3 GB memory running Windows 7. I have been using Maple since version 6.

Also, why can't I enter tags that properly describe my Maple problem? Is Maple hiding problems with lockup?