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Sparse matrix solvers on the GPU: conjugate gradients and multigrid

Jeff Bolz,Ian Farmer,Eitan Grinspun,Peter Schrooder
Caltech
ACM Transactions on Graphics (TOG) – Proceedings of ACM SIGGRAPH 2003, Volume 22 Issue 3, July 2003

@conference{bolz2003sparse,

   title={Sparse matrix solvers on the GPU: conjugate gradients and multigrid},

   author={Bolz, J. and Farmer, I. and Grinspun, E. and Schr{\”o}oder, P.},

   booktitle={ACM SIGGRAPH 2003 Papers},

   pages={917–924},

   isbn={1581137095},

   year={2003},

   organization={ACM}

}

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Many computer graphics applications require high-intensity numerical simulation. We show that such computations can be performed efficiently on the GPU, which we regard as a full function streaming processor with high floating-point performance. We implemented two basic, broadly useful, computational kernels: a sparse matrix conjugate gradient solver and a regular-grid multigrid solver. Real time applications ranging from mesh smoothing and parameterization to fluid solvers and solid mechanics can greatly benefit from these, evidence our example applications of geometric flow and fluid simulation running on NVIDIA’s GeForce FX.
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