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Published February 11, 2023 | Accepted Version
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Sparse Matrix Solvers on the GPU: Conjugate Gradients and Multigrid


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.

Additional Information

This work was supported in part by NSF (DMS-0220905, DMS-0138458, ACI-0219979), the DOE (W-7405-ENG-48/B341492), NVIDIA, the Center for Integrated Multiscale Modeling and Simulation, Alias|Wavefront, Pixar, and the Packard Foundation. Special thanks to Matt Papakipos, Nick Triantos, David Kirk, Paul Keller, Mark Meyer, Mika Nyström, Niles Pierce, Burak Aksoylu, Michael Holst, Jason Hickey, André DeHon, Ian Buck, Mark Harris and all the speakers and students in the "Hacking the GPU" class (Caltech, Fall 2002).

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Accepted Version - cit-asci-tr175.pdf


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August 19, 2023
January 15, 2024