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WaveHoltz: iterative solution of the Helmholtz equation via the wave equation. (English) Zbl 1453.65396

The authors present and analyze the WaveHoltz iteration which is a new iterative method for solving the Helmholtz equation. WaveHoltz is a fixed point iteration that filters the solution to the solution of a wave equation with time periodic forcing and boundary data. The iteration results in positive definite and sometimes symmetric matrices that are more amenable for iterative solution by Krylov subspace methods. The solutions of the systems of equations corresponding to these matrices approximate the Helmholtz solutions. Full analysis for both the continuous and discrete cases is presented. Some numerical tests are presented. The article is very interesting, useful, and well detailed.

MSC:

65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65F10 Iterative numerical methods for linear systems

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References:

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