The programming models presented by parallel computers are diverse and changing. We study a new parallel programming model-cooperative shared memory (CSM)-with a collaborative effort between chemical engineers and computer scientists. Since CSM machines do not (yet) exist we evaluate our applications and machine designs with the Wisconsin Wind Tunnel (WWT), which runs CSM programs and calculates the performance of hypothetical parallel computers. The application considered is the class of three-dimensional elliptic partial differential equations (Laplace, Stokes, Navier) with solutions represented by boundary integral equations. The parallel algorithm follows naturally from our use of the Completed Double Layer Boundary Integral Equation Method (CDLBIEM). A major result is the demonstration that coding CDLBIEM is much simpler under CSM than with the message passing model, and yet performance (computational times and speed ups) is comparable, a fact that may be of great interest to designers of future machines. With WWT, we can also examine performance as a function of machine parameters such as cache size and network bandwidth and latency. The possibility of tweaking simultaneously the algorithm and architecture to outline pathways of evolution for future parallel machines is an important concept explored in this work.