Analysis of the Boundary Knot Method for 3D Helmholtz-Type Equation

الملخص EN

Numerical solutions of the boundary knot method (BKM) always perform oscillatory convergence when using a large number of boundary points in solving the Helmholtz-type problems.

The main reason for this phenomenon may contribute to the severely ill-conditioned full coefficient matrix.

In order to obtain admissible stable convergence results, regularization techniques and the effective condition number are employed in the process of simulating 3D Helmholtz-type problems.

Numerical results are tested for the 3D Helmholtz-type equation with noisy and non-noisy boundary conditions.

It is shown that the BKM in combination with the regularization techniques is able to produce stable numerical solutions.