@Article{IJNAM-20-1,
author = {Victoria, Mederos, Hernández and Ugalde, Isidro, Abellό and Rolando, M., Bruno, Alfonso and Lahaye, Domenico and Valia, Ones, Guerra},
title = {Isogeometric Solution of Helmholtz Equation with Dirichlet Boundary Condition in Regions with Irregular Boundary: Numerical Experiences},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2023},
volume = {20},
number = {1},
pages = {1--28},
abstract = {<p style="text-align: justify;">In this paper we use the Isogeometric Analysis (IgA) to solve the Helmholtz equation with Dirichlet boundary condition over a bounded physical 2D domain. Starting from the
variational formulation of the problem, we show how to apply IgA to obtain an approximated
solution based on biquadratic B-spline functions. We focus the attention on problems where the
physical domain has very irregular boundary. To solve these problems successfully a high quality
parametrization of the domain must be constructed. This parametrization is also a biquadratic
tensor product B-spline function, with control points computed as the vertices of a quadrilateral
mesh with optimal geometric properties. We study experimentally the influence of the wave number and the parametrization of the physical domain in the accuracy of the approximated solution.
A comparison with classical Finite Element Method is also included. The power of IgA is shown
solving several difficult model problems, which are particular cases of the Helmholtz equation and
where the solution has discontinuous gradient in some points, or it is highly oscillatory. For all
model 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. The results obtained with our implementation of the method prove that IgA approach is successful, even on regions with irregular
boundary, since it is able to offer smooth solutions having at the same time some singular points
and high number of oscillations.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2023-1001},
url = {https://global-sci.com/article/82883/isogeometric-solution-of-helmholtz-equation-with-dirichlet-boundary-condition-in-regions-with-irregular-boundary-numerical-experiences}
}