Abstract
Helmholtz equation is widely used in physics and engineering. We present the sixth-order fast algorithm of the threedimensional Helmholtz equation with large wave numbers. For the difference scheme of the equation, a three-diagonal structure is generated by the fast Fourier transform which transforms the original problem into an independent small system. The novel feature of the high-order algorithm lies in its accurate numerical solution and shorter computation time. The method makes it possible to solve the Helmholtz equation with large wave numbers. Finally, the feasibility and accuracy of the proposed algorithm are verified by several numerical experiments.
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