Table 2 Convergence study for scattering in the setting of Example 2. The 5-point Newton-Cotes quadrature is used for integration in the \(t\)-direction over the boundary region
From: Fast rapidly convergent penetrable scattering computations
\({\varvec{N}}^{\mathcal B}_{\varvec{u}}\) | \({\varvec{N}}_{\varvec{t}}^{\mathcal B}\) | \({\varvec{N}}^{\mathcal I}_{\varvec{u}}\) | \({\varvec{N}}^{\mathcal I}_{\varvec{t}}\) | Iter | \({\varvec{\varepsilon }}_{\varvec{2}}\) | Order | \({\varvec{\varepsilon }}_{\varvec{\infty }}\) | Order |
|---|---|---|---|---|---|---|---|---|
\(17\) | \(9\) | \(17\) | \(17\) | \(3\) | \(4.20\times 10^{-1}\) | − | \(5.98\times 10^{-1}\) | − |
\(33\) | \(17\) | \(33\) | \(33\) | \(6\) | \(7.40\times 10^{-2}\) | \(2.51\) | \(6.01\times 10^{-2}\) | \(3.32\) |
\(65\) | \(33\) | \(65\) | \(65\) | \(10\) | \(5.94\times 10^{-3}\) | \(3.64\) | \(4.57\times 10^{-3}\) | \(3.72\) |
\(129\) | \(65\) | \(129\) | \(129\) | \(14\) | \(1.37\times 10^{-4}\) | \(5.43\) | \(1.1\times 10^{-4}\) | \(5.38\) |
\(257\) | \(129\) | \(257\) | \(257\) | \(18\) | \(4.86\times 10^{-6}\) | \(4.85\) | \(3.92\times 10^{-6}\) | \(4.81\) |