Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isogeometric solution of Helmholtz equation with Dirichlet boundary
  condition: numerical experiences   In this paper we use the Isogeometric method to solve the Helmholtz equation
with nonhomogeneous Dirichlet boundary condition over a bounded physical
domain. Starting from the variational formulation of the problem, we show with
details how to apply the isogeometric approach to obtain an approximation of
the solution using biquadratic B-spline functions. To illustrate the power of
the method we solve several difficult problems, which are particular cases of
the Helmholtz equation, where the solution has discontinuous gradient in some
points, or it is highly oscillatory. For these problems we explain how to
select the knots of B-spline quadratic functions and how to insert knew knots
in order to obtain good approximations of the exact solution on regions with
irregular boundary. The results, obtained with our Julia implementation of the
method, prove that isogeometric approach produces approximations with a
relative small error and computational cost.

29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci