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The explosive growth in integration technology and the parallel nature of rasterization-based graphics APIs (Application Programming Interface) changed the panorama of consumer-level graphics: today, GPUs (Graphics Processing Units) are cheap, fast and ubiquitous. We show how to harness the computational power of GPUs and solve the incompressible Navier-Stokes fluid equations significantly faster (more than one order of magnitude in average) than on CPU solvers of comparable cost. While past approaches typically used Stam's implicit solver, we use a variation of SMAC (Simplified Marker and Cell). SMAC is widely used in engineering applications, where experimental reproducibility is essential. Thus, we show that the GPU is a viable and affordable processor for scientific applications. Our solver works with general rectangular domains (possibly with obstacles), implements a variety of boundary conditions and incorporates energy transport through the traditional Boussinesq approximation. Finally, we discuss the implications of our solver in light of future GPU features, and possible extensions such as three-dimensional domains and free-boundary problems.

Abstract. We present a new algorithm to compute the QR factorization of a matrix Am×n intended for use when m n. The algorithm uses a reduction strategy to perform the factorization which in turn allows a good degree of parallelism. It is then integrated into a parallel implementation of the QR factorization with column pivoting algorithm due to Golub and Van Loan, which allows the determination of the rank of A. The algorithms were coded in Fortran 90 using the MPI library. Results are presented for several different problem sizes on an IBM 9076 SP/2 parallel computer.

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