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This article deals with a component of numerical methods. For coarse space in topology, see coarse structure. In numerical analysis, coarse problem is an auxiliary system of equations used in an iterative method for the solution of a given larger system of equations. A coarse problem is basically a version of the same problem at a lower ...
(More generally, coarse grid unknowns can be particular linear combinations of fine grid unknowns.) Thus, AMG methods become black-box solvers for certain classes of sparse matrices . AMG is regarded as advantageous mainly where geometric multigrid is too difficult to apply, [ 20 ] but is often used simply because it avoids the coding necessary ...
A coarse structure on a set is a collection of subsets of (therefore falling under the more general categorization of binary relations on ) called controlled set s, and so that possesses the identity relation, is closed under taking subsets, inverses, and finite unions, and is closed under composition of relations.
Granularity (also called graininess) is the degree to which a material or system is composed of distinguishable pieces, "granules" or "grains" (metaphorically). It can either refer to the extent to which a larger entity is subdivided, or the extent to which groups of smaller indistinguishable entities have joined together to become larger distinguishable entities.
A coarse mesh may provide an accurate solution if the solution is a constant, so the precision depends on the particular problem instance. One can selectively refine the mesh in areas where the solution gradients are high, thus increasing fidelity there. Accuracy, including interpolated values within an element, depends on the element type and ...
Another definition of granularity takes into account the communication overhead between multiple processors or processing elements. It defines granularity as the ratio of computation time to communication time, wherein computation time is the time required to perform the computation of a task and communication time is the time required to ...
The Fineness Modulus (FM) is an empirical figure obtained by adding the total percentage of the sample of an aggregate retained on each of a specified series of sieves, dividing the sum by 100.
Coarse graining and fine graining in statistical mechanics addresses the subject of entropy , and thus the second law of thermodynamics. One has to realise that the concept of temperature T {\displaystyle T} cannot be attributed to an arbitrarily microscopic particle since this does not radiate thermally like a macroscopic or " black body ".