Table 1 Convergence study for the forward map of the operator \(\mathcal L\psi \) for a unit disc with \(\kappa /\kappa _e = \sqrt{2.0}\) and \(\rho /\rho _e = 1.0\) using \(5\)-point Newton-Cotes quadrature for integration in the \(t\)-direction over the boundary region
From: Fast rapidly convergent penetrable scattering computations
\(\varvec{N}^{\mathcal B}_{\varvec{u}}\) | \(\varvec{N}^{\mathcal B}_{\varvec{t}}\) | \({\varvec{N}}^{\mathcal I}_{\varvec{u}}\) | \({\varvec{N}}^{\mathcal I}_{\varvec{t}}\) | \({\varvec{\varepsilon }}_{\varvec{2}}\) | Order | \({\varvec{\varepsilon }_\infty }\) | Order |
|---|---|---|---|---|---|---|---|
\(17\) | \(9\) | \(17\) | \(17\) | \(1.92\times 10^{-1}\) | − | \(2.72\times 10^{-1}\) | − |
\(33\) | \(17\) | \(33\) | \(33\) | \(4.12\times 10^{-2}\) | \(2.22\) | \(7.34\times 10^{-2}\) | \(1.89\) |
\(65\) | \(33\) | \( 65\) | \(65\) | \(5.78\times 10^{-3}\) | \(2.83\) | \(1.35\times 10^{-2}\) | \(2.44\) |
\(129\) | \(65\) | \( 129\) | \(129\) | \(2.56\times 10^{-4}\) | \(4.50\) | \(3.65\times 10^{-4}\) | \(5.21\) |
\(257\) | \(129\) | \( 257\) | \(257\) | \(4.53\times 10^{-6}\) | \(5.82\) | \(5.37\times 10^{-6}\) | \(6.09\) |