‘The Equator–Pole grid system’: an overset grid system for the sphere, with an optimal uniformity property

Table 5.

$re{l}_{\mathit{\text{mass}}}(1:7)$1.27e − 72.43e − 72.59e − 72.94e − 71.55e − 7−1.01e − 7−3.31e − 7$re{l}_{\mathit{\text{mass}}}(8:14)$−3.59e − 7−2.92e − 7−1.35e − 72.13e − 89.88e − 81.32e − 8−1.81e − 7$re{l}_{\mathit{\text{energy}}}(1:7)$4.24e − 41.70e − 33.32e − 34.47e − 35.01e − 35.46e − 35.70e − 3$re{l}_{\mathit{\text{energy}}}(8:14)$5.67e − 35.70e − 35.56e − 35.16e − 35.12e − 35.34e − 35.15e − 3

Table 3.

α${10}^8·c$2psstc, ${\ell }_{\infty }(\Psi )$stc,  ${\ell }_2(\Psi )$${10}^8·c$mstc,  ${\ell }_{\infty }(\Psi )$mstc,  ${\ell }_2(\Psi )$02.5427.4896e − 82.7333e − 82.02.3393e − 81.4434e − 84594.5424.5811e − 67.1803e − 715.09.8324e − 71.3341e − 7903.5423.3136e − 71.4239e − 73.53.3416e − 71.5007e − 700633.2131e − 101.0983e − 1001.7475e − 118.0196e − 12450634.9529e − 82.4985e − 903.7105e − 101.0249e − 10900635.7385e − 102.2245e − 1004.1246e − 102.0270e − 10

Table 2.

α${10}^8·c$2ps$\min H$$\max H$${\ell }_{\infty }(H)$${\ell }_2(H)$9098.542−7.44559.9906e + 27.4455e − 36.5382e − 387101.542−7.41759.9904e + 27.4175e − 36.5323e − 34543.042−6.29119.9758e + 26.2919e − 37.2938e − 39098.543−7.44419.9907e + 27.4452e − 36.5374e − 387102.043−7.41519.9904e + 27.4169e − 36.5313e − 39014.563−2.74159.9958e + 22.7466e − 32.3972e − 38712.063−2.73989.9956e + 22.7844e − 32.5172e − 38712.084−1.67301.0000e + 31.6995e − 32.2057e − 3

Table 1.

α${10}^8·c$2ps$\min \Psi$$\max \Psi$${\ell }_{\infty }(\Psi )$${\ell }_2(\Psi )$01.0420.462951.53704.9954e − 36.4872e − 4453.5420.462991.53704.9587e − 35.6236e − 4901.6420.462971.53707.5553e − 31.0074e − 300.25630.462951.53701.1315e − 31.2714e − 4450.35630.462991.53701.1612e − 31.0952e − 4900.45630.462971.53702.1246e − 32.4623e − 4

Table 4.

α${10}^8·c$2ps$\min \Psi$$\max \Psi$${\ell }_{\infty }(\Psi )$${\ell }_2(\Psi )$07.0422.0572e + 42.9401e + 44.4288e − 61.1233e − 66010.5422.0572e + 42.9401e + 42.0841e − 54.0558e − 600632.0572e + 42.9401e + 47.5006e − 81.3479e − 8600632.0572e + 42.9401e + 42.8129e − 75.3725e − 8