Table 6 Convergence study for scattering by a bean shape with \(\kappa _i = \sin (\pi x_1)\cos (\pi x_2)\) and \(\rho _i/\rho _e = 5\), where \(5\)-point Newton-Cotes quadrature is used for integration in the \(t\)-direction
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 |
|---|---|---|---|---|---|---|---|---|
\(9\) | \(5\) | \(9\) | \(9\) | \(2\) | \(3.43\times 10^{-1}\) | − | \(4.23\cdot 10^{-1}\) | − |
\(17\) | \(9\) | \(17\) | \(17\) | \(2\) | \(1.66\times 10^{-1}\) | \(1.05\) | \(1.97\times 10^{-1}\) | \(1.10\) |
\(33\) | \(17\) | \(33\) | \(33\) | \(3\) | \(4.79\times 10^{-2}\) | \(1.80\) | \(3.62\times {10}^{-2}\) | \(2.44\) |
\(65\) | \(33\) | \(65\) | \(65\) | \(4\) | \(2.51\times 10^{-3}\) | \(4.25\) | \(2.64\times {10}^{-3}\) | \(3.78\) |
\(129\) | \(65\) | \(129\) | \(129\) | \(6\) | \(6.28\times 10^{-5}\) | \(5.34\) | \(5.86\times {10}^{-5}\) | \(5.63\) |