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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.
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 ...
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.
A continuous map f : X → Y remains continuous if the topology on Y becomes coarser or the topology on X finer. An open (resp. closed) map f : X → Y remains open (resp. closed) if the topology on Y becomes finer or the topology on X coarser. One can also compare topologies using neighborhood bases.
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 ...
(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 ...
All tagged cells are then refined, meaning that a finer grid is overlaid on the coarse one. After refinement, individual grid patches on a single fixed level of refinement are passed off to an integrator which advances those cells in time. Finally, a correction procedure is implemented to correct the transfer along coarse-fine grid interfaces ...
In general, however, a smaller value indicates a finer aggregate. Fine aggregates range from an FM of 2.00 to 4.00, and coarse aggregates smaller than 38.1 mm range from 6.75 to 8.00. Combinations of fine and coarse aggregates have intermediate values. [1]