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- W4301800361 abstract "We present both, theory and an algorithm for solving time-harmonic wave problems in a general setting. The time-harmonic solutions will be achieved by computing time-periodic solutions of the original wave equations. Thus, an exact controllability technique is proposed to solve the time-dependent wave equations. We discuss a first order Maxwell type system, which will be formulated in the framework of alternating differential forms. This enables us to investigate different kinds of classical wave problems in one fell swoop, such as acoustic, electro-magnetic or elastic wave problems. After a sufficient theory is established, we formulate our exact controllability problem and suggest a least-squares optimization procedure for its solution, which itself is solved in a natural way by a conjugate gradient algorithm operating in the canonical Hilbert space. Therefore, it might be one of the biggest advances of this approach that the proposed conjugate gradient algorithm does not need any preconditioning." @default.
- W4301800361 created "2022-10-05" @default.
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- W4301800361 date "2011-05-20" @default.
- W4301800361 modified "2023-09-27" @default.
- W4301800361 title "Theoretical Considerations on the Computation of Generalized Time-Periodic Waves" @default.
- W4301800361 doi "https://doi.org/10.48550/arxiv.1105.4095" @default.
- W4301800361 hasPublicationYear "2011" @default.
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