Multigrid Methods in Boundary Element Calculations

摘要

Multigrid iterative methods are advocated for the fast solution of algebraic systems occurring in boundary element calculations. Multigrid methods combine relaxation schemes for reducing high-frequency errors and coarse grid corrections for diminishing low-frequency errors. The choice of the relaxation scheme is found to be essential to attain a fast convergent iterative process. Asymptotically, the multigrid method needs only two iterations to obtain a result of the order of the truncation error. The fast convergence, however, may break down if the relaxation scheme does not account for boundary singularities such as corners and edges. This will be illustrated for the calculation of potential flow around an airfoil.