High-Order Nonreflecting Boundary Conditions without High-Order Derivatives |
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Authors: | Dan Givoli |
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Institution: | Department of Aerospace Engineering and Asher Center for Space Research, Technion–Israel Institute of Technology, Haifa, 32000, Israelf1 |
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Abstract: | A wave problem in an unbounded domain is often treated numerically by truncating the infinite domain via an artificial boundary
, imposing a so-called nonreflecting boundary condition (NRBC) on
, and then solving the problem numerically in the finite domain bounded by
. A general approach is devised here to construct high-order local NRBCs with a symmetric structure and with only low (first- or second-) order spatial and/or temporal derivatives. This enables the practical use of NRBCs of arbitrarily high order. In the case of time-harmonic waves with finite element discretization, the approach yields a symmetric C0 finite element formulation in which standard elements can be employed. The general methodology is presented for both the time-harmonic case (Helmholtz equation) and the time-dependent case (the wave equation) and is demonstrated numerically in the former case. |
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Keywords: | Abbreviations: wavesAbbreviations: high-orderAbbreviations: artificial boundaryAbbreviations: nonreflecting boundary conditionAbbreviations: finite element |
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