112:, the construction of a coarse problem follows the same principles as in multigrid methods, but the coarser problem has much fewer unknowns, generally only one or just a few unknowns per subdomain or substructure, and the coarse space can be of a quite different type that the original finite element space, e.g. piecewise constants with averaging in
143:, the coarse problem is generally obtained by the Galerkin approximation on a subspace. In mathematical economics, the coarse problem may be obtained by the aggregation of products or industries into a coarse description with fewer variables. In Markov chains, a coarse Markov chain may be obtained by aggregating states.
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for the solution of a given larger system of equations. A coarse problem is basically a version of the same problem at a lower resolution, retaining its essential characteristics, but with fewer variables. The purpose of the coarse problem is to propagate information throughout the whole problem
264:
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without a coarse problem deteriorates with decreasing mesh step (or decreasing element size, or increasing number of subdomains or substructures), thus making a coarse problem necessary for a
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or mapped coarse model. It permits fast, but more accurate, harnessing of the underlying coarse model in the exploration of designs or in design optimization.
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62:, the coarse problem is typically obtained as a discretization of the same equation on a coarser grid (usually, in
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82:, the Galerkin approximation is typically used, with the coarse space generated by larger elements on the same
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is unusual in that it is not obtained as a
Galerkin approximation of the original problem, however.
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This article deals with a component of numerical methods. For coarse space in topology, see
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344:Multiscale modeling
40:numerical analysis
56:multigrid methods
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152:scalable
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