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Publication# Moore's law and numerical modeling

Abstract

An estimate of the rate of increase in numerical simulation grid sizes with time is obtained by counting the grids (measured in terms of number of node points) reported in the nine volumes of an established proceedings on the numerical modeling of solidification phenomena dating back to 1980. It is shown that the largest grids used in a given year increase at a rate consistent with the well-known Moore's law on computing power, i.e., the number of nodes in the grids double every 18 months. Front this observation, approximate bounds on the available grid size in a current year are established. This approximation is used to provide projections as to when, assuming Moore's law continues to hold, direct simulations of physical phenomena, which resolve to the smallest scale present, will be achievable.

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Grid computing is the use of widely distributed computer resources to reach a common goal. A computing grid can be thought of as a distributed system with non-interactive workloads that involve many files. Grid computing is distinguished from conventional high-performance computing systems such as cluster computing in that grid computers have each node set to perform a different task/application. Grid computers also tend to be more heterogeneous and geographically dispersed (thus not physically coupled) than cluster computers.

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Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering.

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