Using Graphics Cards for Quantized FEM Computations.
Martin Rumpf, Robert Strzodka · 2001
Graphics cards exercise increasingly more computing power and are highly optimized for high data transfer volumes. In contrast typical workstations perform badly when data exceeds their processor caches. Performance of scientific computations very often is wrecked by this deficiency. Here we present a novel approach by shifting the computational load from the CPU to the graphics card. We represent data in images and operations on vectors in graphics operations on images. Broad access to graphics memory and parallel processing of image operands thus turns the graphics card into an ultrafast vector coprocessor. The presented strategy opens up a wide area of numerical applications for hardware acceleration. The implementations of Finite Element solvers for the linear heat equation and the anisotropic diffusion method in image processing underline its practicability. We explain the vector processor usage of graphics cards in detail. An extensive correspondence of vector and graphics operations is given and the decomposition of complex operations into hardware supported is explicated. We also sketch the realization of arbitrary number formats in graphics hardware and the consequences of the restricted precision. Finally, we propose slight modifications and extensions which would further improve computational benefits and extend the range of applicability of the proposed approach. Computing in image processing at ms for an Jacobi iteration on images is exemplarily depicted as an ideal field, where Finite Element methods can be greatly accelerated and ultimate number precision is not required. KEY WORDS graphics hardware computing, hardware accelerated numerical methods, anisotropic diffusion 1.