Flexible LU linear solver using low-level CUDA algorithms

Abstract

This specic research involved the initial analysis, design, and coding of a CUDA based LU decomposition linear solver with partial pivoting with the intention of being compact and flexible. A block based approach to decomposition and substitution was derived and applied to produce desirable GPU based algorithms. The result was a properly working linear solver with reasonable but less than desired performance due to lack of optimization. Developing CUDA based programs at the kernel (lowest) level is an extensive process with complex optimization requirements and thus, as a foundation, this work maintained the basic goal of producing a functional but not necessarily refined solver. This goal was achieved and the resulting code is thoroughly described and documented in the body of the article.

Detailed plans for future work with regard to integration into the modeling package and optimization are also discussed.

The primary motivation for this work was the acceleration of a here unnamed nonlinear modeling package whose current computational performance is limited by it's current MATLAB based platform. As a rst step toward an independent implementation it was decided to develop in-house GPU accelerated numerical solvers using the NVIDIA CUDA platform.