Hybrid preconditioned algorithms for boundary hypersingular integral equations

Three preconditioners for solving boundary hypersingular integral equations of the first kind are proposed. The first and the second preconditioners are based on circulant operators. The third is a hybrid of iterative substructuring techniques and circulant operators. Although this class of preconditioners are composition of circulant operators but we have shown that the condition number of the third preconditioner dose not exceed the condition number of two preconditioners. Numerical results are included.