Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A geometric optics ansatz-based plane wave method for two dimensional
  Helmholtz equations with variable wave numbers   In this paper we develop a plane wave type method for discretization of
homogeneous Helmholtz equations with variable wave numbers. In the proposed
method, local basis functions (on each element) are constructed by the
geometric optics ansatz such that they approximately satisfy a homogeneous
Helmholtz equation without boundary condition. More precisely, each basis
function is expressed as the product of an exponential plane wave function and
a polynomial function, where the phase function in the exponential function
approximately satisfies the eikonal equation and the polynomial factor is
recursively determined by transport equations associated with the considered
Helmholtz equation. We prove that the resulting plane wave spaces have high
order $h$-approximations as the standard plane wave spaces (which are available
only to the case with constant wave number). We apply the proposed plane wave
spaces to the discretization of nonhomogeneous Helmholtz equations with
variable wave numbers and establish the corresponding error estimates of their
finite element solutions. We report some numerical results to illustrate the
efficiency of the proposed method.

15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph