Abstract
Present and future supercomputers offer many opportunities and advantages to attack complex and demanding industrial and applied mathematical problems, but provide also new challenges. In the Peta-Flops regime, these concern both, the way to exploit the increasingly available power and the need of designing algorithms which are scalable and fault-tolerant at the same time. An example of a probabilistic domain decomposition method, which is indeed scalable and naturally fault-tolerant, is presented. Grid computing should also be mentioned as an increasingly popular way to perform massively distributed computing: it represents a way to exploit computing power, aside the existing supercomputers. Beyond classical supercomputers there is the prospective quantum computer, in view of which it is advisable to start now a search for suitable algorithms for certain classes of problems.
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Acebrón, J.A., Spigler, R. Supercomputing applications to the numerical modeling of industrial and applied mathematics problems. J Supercomput 40, 67–80 (2007). https://doi.org/10.1007/s11227-006-0014-3
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DOI: https://doi.org/10.1007/s11227-006-0014-3