In the case of arbitrary grid (3) [[bar.D].sub.h] (4.1), using a priori estimate (3.2), we obtain the estimate
The solution of difference scheme (4.2) on arbitrary grid (4.1) is written out in the recurrent form:
Here [z.sub.[epsilon]](x) is the solution of difference scheme (4.2), (6.2) on the arbitrary grid [[bar.D].sub.h(4.1)] with number of intervals equal to N, and [u.sub.[epsilon]](x) is the exact solution in nodes x of the corresponding grid.
In numerical experiments, we use as an arbitrary grid either the uniform grid (4.4), or the special piecewise-uniform grid (5.1): the maximum point-wise errors E([epsilon], N) and [bar.E](N) in the solutions of the standard scheme (4.2) on the uniform grid (4.4) and on the special piecewise-uniform grid (5.1) are given in Tables 1 and 2, respectively.
When a new node is added to arbitrary grid
V(i), the DTN node ID allocation method is used to allocate a node ID for the new node.
v is an arbitrary grid
within XY, V is the sum of all grids, and, therefore, v [member of] V.
FIAFTA is valid for all kinds of antennas and is able to process the near-field data collected on an arbitrary grid. Furthermore, full probe correction without increase in numerical complexity makes FIAFTA an attractive choice.
The coupling matrix [parallel]C[parallel] takes care of the plane wave translations to the measurement points of the arbitrary grid. Therefore, the estimated error in the plane wave spectrum for the same inaccuracy in the probe output can differ for different measurement surfaces.
Since FIAFTA can handle measurements on arbitrary grids, the valid angle of the radiation pattern can be significantly increased by utilizing adaptive sampling in planar and cylindrical measurements [33, 34].
The problem of finding the domination number of a arbitrary grid
graph (= subgraph of [P.sub.k] x [P.sub.n]) is NP-complete (CLARK et al., 1990).
Even FEM programs that use arbitrary grid
element sizes require an increase in the number of elements around small structures.
A comparative analysis between the arbitrary grids
was then conducted to interpret morphological changes across space.