Multilevel augmentation methods for nonlinear boundary integral equations II: Accelerated quadratures and Newton iterations
The authors improve their multilevel augmentation method (MAM) previously analyzed in Part I [SIAM J. Numer. Anal. 49, No. 6, 2231--2255 (2011; Zbl 1236.65147)]. They use a product integration scheme in order to accurately evaluate the singular integrals involved in the matrices of MAM. Then, they introduce an efficient approximation technique in implementing the usual Newton scheme which avoids repeated computation in Jacobian matrices. Some numerical experiments are carried out in order to underline the accuracy as well as the efficiency of the modified MAM.
scientific article; zbMATH DE number 6144973
scientific article