Calderon-preconditioned BEMs for frequency-differentiated boundary-value problems of Helmholtz’ equation

抄録

This paper presents an efficient numerical scheme for solving frequency-differentiated boundary-value problems related to scalar wave scattering. The proposed method simultaneously solves linear algebraic equations derived from Burton–Miller-type boundary integral equations for both the original solution and its high-order derivatives using a Krylov-based linear solver. Calderon’s formulae are utilised to construct preconditioning matrices for the linear system, resulting in a reduction in the number of Krylov iterations. The assembly of the linear system and the matrix-vector multiplication in the Krylov solver, both involving frequency derivatives, are managed through automatic differentiation of forward mode, which is straightforward to implement. Through numerical examples for the Neumann and transmission problems of the three-dimensional Helmholtz equation, we demonstrate that the proposed method can efficiently evaluate the frequency derivatives of their solutions.