This paper by Dominik Göddeke, Robert Strzodka and Stefan Turek describes a preliminary algorithm to achieve double precision results by adding a CPU-based defect correction to iterative linear system solvers on the GPU. We demonstrate that identical accuracy as compared to a full CPU double precision solver is possible while still gaining a factor of 2 in speedup compared to a highly tuned cache-aware CPU reference implementation in double precision. (Accelerating Double Precision FEM Simulations with GPUs. Dominik Göddeke, Robert Strzodka and Stefan Turek. To appear in Proceedings of ASIM 2005 – 18th Symposium on Simulation Technique.)

This thesis by Robert Strzodka describes the design of robust quantized schemes and their hardware efficient implementation on data-stream-based architectures for PDE-based image processing. The focus lies on enhancing both performance and accuracy by an efficient use of appropriate hardware resources. Quantized schemes which, despite roundoff errors, preserve the qualitative behavior of the continuous models are constructed, and examined on different GPUs, a FPGA and a reconfigurable array processor. The pros and cons of the hardware designs and the memory gap problem are discussed in detail. (Hardware Efficient PDE Solvers in Quantized Image Processing. Robert Strzodka. PhD thesis, University of Duisburg-Essen, 2004.)