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A Plane Wave Discontinuous Galerkin Method with a Dirichlet-to-Neumann Boundary Condition for the Scattering Problem in Acoustics

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Shelvean Kapita, Peter Monk

Numerical Analysis · Submitted 22 Nov 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Numerical results suggest that the accuracy of the PWDG method for the acoustic scattering problem can be significantly improved by using DtN boundary conditions.

how it is stated · hedged possibility 1.00 read the record →

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arXiv ID1611.07337 (version 1)
Pith ID5GHBV6BA, Pith's permanent record of this paper and its review
CitationPeter Monk, Shelvean Kapita. "A Plane Wave Discontinuous Galerkin Method with a Dirichlet-to-Neumann Boundary Condition for the Scattering Problem in Acoustics." arXiv:1611.07337 (2016). https://pith.science/paper/5GHBV6BA
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,312 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.29 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We consider the numerical solution of an acoustic scattering problem by the Plane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded domain in $\mathbb{R}^2$. In order to apply the PWDG method, we introduce an artificial boundary to truncate the domain, and we impose a non-local Dirichlet-to-Neumann (DtN) boundary conditions on the artificial curve. To define the method, we introduce new consistent numerical fluxes that incorporate the truncated series of the DtN map. Error estimates with respect to the truncation order of the DtN map, and with respect to mesh width are derived. Numerical results suggest that the accuracy of the PWDG method for the acoustic scattering problem can be significantly improved by using DtN boundary conditions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider the numerical solution of an acoustic scattering problem by the Plane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded domain in $\mathbb{R}^2$. contribution 0.54 0.61 0.03 asserted 0.84
s1 In order to apply the PWDG method, we introduce an artificial boundary to truncate the domain, and we impose a non-local Dirichlet-to-Neumann (DtN) boundary conditions on the artificial curve. method 0.95 0.92 0.04 asserted 0.99
s2 To define the method, we introduce new consistent numerical fluxes that incorporate the truncated series of the DtN map. method 0.91 0.92 0.04 asserted 0.98
s3 Error estimates with respect to the truncation order of the DtN map, and with respect to mesh width are derived. contribution 0.51 0.93 0.08 asserted 0.99
s4 Numerical results suggest that the accuracy of the PWDG method for the acoustic scattering problem can be significantly improved by using DtN boundary conditions. result 0.77 0.89 0.83 hedged possibility 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.56.

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  • references and citing sentences
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  • S sections
  • T body sentences
  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider the numerical solution of an acoustic scattering problem by the Plane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded domain in $\mathbb{R}^2$. In order to apply the PWDG method, we introduce an artificial boundary to truncate the domain, and we impose a non-local Dirichlet-to-Neumann (DtN) boundary conditions on the artificial curve. To define the method, we introduce new consistent numerical fluxes that incorporate the truncated series of the DtN map. Error estimates with respect to the truncation order of the DtN map, and with respect to mesh width are derived. Numerical results suggest that the accuracy of the PWDG method for the acoustic scattering problem can be significantly improved by using DtN boundary conditions.

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