### Table 3. Relative size of characteristic variables in a plane wave calculation. See text for details.

2000

"... In PAGE 77: ... The following variables are used to denote quantities that measure system size. Nat number of atoms Np number of projectors Nb number of electronic bands or states NPW number of plane-waves ND number of plane-waves for densities and potentials Nx, Ny, Nz number of grid points in x, y, and z direction N = NxNyNz total number of grid points In Table3 the relative size of this variables are given for two systems. The example for a silicon crystal assumes an energy cuto of 13 Rydberg and s non-locality for the pseudopotential.... ..."

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### TABLE 1. DSO and OLS plane-wave inversion experiments performed on Gulf of Mex- ico eld data.

1997

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### Table 2: Scattering of an incident plane wave on a circular cylinder of radius a

"... In PAGE 6: ... 7 Numerical results A matrix free iterative solver has been implemented by utilizing the two-dimensional version of the high-frequency integrator described in the preceding sections in conjunction with the GMRES algo- rithm [15]. Table2 shows results produced by means of this two-dimensional solver on a 1:5 GHz PC, applied to a circular cylinder of radius a. Errors were computed by comparison with an exact solution for the integral equation, and de ned as Z @ j exact slow (r) slow(r)j2 ds(r) 1=2 .... ..."

### Table 3. Scattering of an incident plane wave on a circular cylinder of radius a

"... In PAGE 12: ... Numerical results A matrix free iterative solver has been implemented by utilizing the two-dimensional version of the high-frequency integrator described in the preceding sections in con- junction with the GMRES algorithm (Saad amp; Schultz 1986). Table3 shows results produced by means of this two-dimensional solver on a 1.5 GHz PC, applied to a circular cylinder of radius a.... ..."

### Table 4.1 Iteration counts for the exterior scattering problem with Dirichlet or Neumann plane wave data on the boundaryof an ellipse for various wave numbers, grid sizes, and numbers of levels. A dash denotes divergence.

2001

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### Table 4.1 Iteration counts for the exterior scattering problem with Dirichlet or Neumann plane wave data on the boundary of an ellipse for various wave numbers, grid sizes and numbers of levels.

2001

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### Table 4.1 Iteration counts for the exterior scattering problem with Dirichlet or Neumann plane wave data on the boundary of an ellipse for various wave numbers, grid sizes and numbers of levels.

2001

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### (Table iii) the errors are much larger on the coarse grid because there are insu cient mesh points to resolve the transmitted wave. Our convergence analysis for the 1-D case (not presented here) is in close agreement with these 2-D results. These results verify the e ectiveness of the method for problems with discontin- uous coe cients on nonsmooth, nonorthogonal grids. 7.2. Scattering of a Plane Wave on Perfect Conductor. Our next example is an in nite domain problem modeling the scattering of a plane wave on a perfect conductor [34], [38]. We consider a plane wave

"... In PAGE 36: ...12-b) In Table i, we see that at t = 2 10?9, the L2 and max norm convergence rates for both smooth and random grids are between rst- and second-order. At t = 4 10?9 (Table ii) the convergence rates are similar, but the solution is less accurate because of a errors introduced when the wave interacted with the discontinuity. At t = 6 10?9 (Table iii) the errors are much larger on the coarse grid because there are insu cient mesh points to resolve the transmitted wave.... ..."

### Table II: Parities, boundary conditions of the separated wave functions s, periods of the separated wave functions and , and Cartesian nodal planes.

1999

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### Table 3: Relaxation parameters speci ed in Fig. 3 (in A) for the (110) surface as calculated by siesta,incomparisonwithearliercalculationsby ab initio plane-wave method (PW) and by a tight-binding method (TB).

"... In PAGE 5: ... The values of structural parameters as introduced in Fig. 3 are listed in Table3 according to our present calculation and two earlier ones. In all cases, our calculations essentially con rm the plane wave pseudopotential results by Rantala, Rantala and Lantto (1999), even when they di er from tight-binding calculation results by Godin and LaFemina (1993).... ..."