Numerical Integration

In the Boundary Element Method we have to evaluate integrals of the type 6.1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaWGjbGaeyypa0Zaa8qua8aabaWdbiaacIcacaGG3cGaaiyka8aa % daahaaWcbeqaa8qacaGGQaaaaaWdaeaapeGaeu4KdC0damaaCaaame % qabaWdbiaacIcacaWGLbGaaiykaaaaaSqab0Gaey4kIipakiaacIca % caWG4bGaaiilaiabe67a4jaacMcacqaHvpGzcaGGOaGaamiEaiaacM % cacaWGKbGaeu4KdCeaaa!4D38! $$I = \int\limits_{{\Gamma ^{(e)}}} {{{(\cdot )}^*}} (x,\xi )\phi (x)d\Gamma $$ over the boundary elements Γ_(e) whose integrands are products of fundamental solutions (•)* and shape functions Φ, cf. (5.67). Depending on the relative position of the load point ξ to the element Γ_(e) over which the integration is carried out, we have to distinguish between three types of integrals, see Figure 6.1.