Hardware-oriented numerics and concepts for PDE software

Processor technology is still dramatically advancing and promises further enormous improvements in processing data for the next decade. On the other hand, much lower advances in moving data are expected such that the efficiency of many numerical software tools for partial differential equations (PDEs) are restricted by the cost for memory access. We demonstrate how data locality and pipelining can achieve a significant percentage of the available huge computing power, and we explain the influence of processor technology on recent and future numerical PDE simulation tools. Exemplarily, we describe hardware-oriented concepts for adaptive error control, multigrid/domain decomposition schemes and incompressible flow solvers and discuss their numerical and computational characteristics.