From classical numerical mathematics to scientific computing (Q1129846)

The author discusses the ways in which the evolution of computer hardware impacts the evolution of numerical mathematics. We are doing ever more elaborate and detailed computations, and this requires efficient local error estimation as well as the ability to do local adaptation of grids and algorithms. The increasing size of the computational problems also pushes us toward the development of algorithms which scale nearly linearly. In some respects these trends are compatible with the use of parallel computers, but we must beware of difficulties with load balancing.