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Imaging and Sensing (Waves) Seminar

March 10, 2022 - 2:00pm

Speaker: Daniel Appelö (Michigan State University)

Title talk: WaveHoltz: Parallel and Scalable Solution of the Helmholtz Equation via Wave Equation Iteration

Abstract: We introduce a novel idea, the WaveHoltz iteration, for solving the Helmholtz equation. Our method makes use of time domain methods for wave equations to design frequency domain Helmholtz solvers. We show that the WaveHoltz iteration we propose results in a symmetric and positive definite linear system even though we are solving the Helmholtz equation. As our method utilizes time-domain solvers we can exploit features such as local timestepping that are not present in the frequency domain. A unique “free lunch” property that WaveHoltz possesses allows us to solve for multiple frequencies at the cost of a single solve. We will present numerical examples, using various discretization techniques, that show that our method can be used to solve problems with rather high wave numbers.