A finite element code on
the Connection Machine

Dave Nichols

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ABSTRACT

I have written a finite element code for the Connection Machine (CM) that models heat flow in a circuit element. The code uses the conjugate gradient method to solve the global Galerkin matrix associated with the finite element problem. The design of the algorithm depends on the connectivity of the elements. For regularly connected elements, the application of the global matrix can be coded as a banded matrix multiply. This is very efficient on the CM. If a regular mesh is used the solution of the finite element system runs at 275MFlops on 4K CM. For irregularly connected elements the communication is more complicated and the global data transfer is much more difficult to implement efficiently on the CM. The basic design considerations that apply to this simple problem should be the same for more complicated problems such as solution of the wave equation.