Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Amplitude-based Generalized Plane Waves: new Quasi-Trefftz functions for
  scalar equations in 2D   Generalized Plane Waves (GPWs) were introduced to take advantage of Trefftz
methods for problems modeled by variable coefficient equations. Despite the
fact that GPWs do not satisfy the Trefftz property, i.e. they are not exact
solutions to the governing equation, they instead satisfy a quasi-Trefftz
property: they are only approximate solutions. They lead to high order
numerical methods, and this quasi-Trefftz property is critical for their
numerical analysis.
  The present work introduces a new family of GPWs, amplitude-based. The
motivation lies in the poor behavior of the phase-based GPW approximations in
the pre-asymptotic regime, which will be tamed by avoiding high degree
polynomials within an exponential. The new ansatz is introduces higher order
terms in the amplitude rather than the phase of a plane wave as was initially
proposed. The new functions' construction and the study of their interpolation
properties are guided by the roadmap proposed in [16]. For the sake of clarity,
the first focus is on the two-dimensional Helmholtz equation with
spatially-varying wavenumber. The extension to a range of operators allowing
for anisotropy in the first and second order terms follows. Numerical
simulations illustrate the theoretical study of the new quasi-Trefftz
functions.

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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: stat