Table 7 Convergence study for scattering by a bean shaped scatterer with \(\kappa _e a = 6.0\), \(\kappa _i = \sin (\pi x_1)\cos (\pi x_2)\) and \(\rho _i = 2.0 + \sin (\pi x_1)\cos (\pi x_2)\) where 5-point Newton-Cotes quadrature is used for integration in \(t\)-direction over the boundary region
From: Fast rapidly convergent penetrable scattering computations
\({\varvec{N}}^{\mathcal B}_{\varvec{u}}\) | \({\varvec{N}}^{\mathcal B}_{\varvec{t}}\) | \({\varvec{N}}^{\mathcal I}_{\varvec{u}}\) | \({\varvec{N}}^{\mathcal I}_{\varvec{t}}\) | Iter | \({\varvec{\varepsilon }}_{\varvec{2}}\) | Order | \({\varvec{\varepsilon }}_{\varvec{\infty }}\) | Order |
|---|---|---|---|---|---|---|---|---|
\(17\) | \(9\) | \(17\) | \(17\) | \(4\) | \(4.17\times {10}^{-1}\) | − | \(3.26\times {10}^{-1}\) | − |
\(33\) | \(17\) | \(33\) | \(33\) | \(5\) | \(6.20\times {10}^{-2}\) | \(2.74\) | \(6.97\times {10}^{-2}\) | \(2.23\) |
\(65\) | \(33\) | \(65\) | \(65\) | \(7\) | \(4.77\times {10}^{-3}\) | \(3.70\) | \(5.20\times {10}^{-3}\) | \(3.74\) |
\(129\) | \(65\) | \(129\) | \(129\) | \(10\) | \(8.07\times {10}^{-5}\) | \(5.89\) | \(1.03\times {10}^{-4}\) | \(5.66\) |