Isogeometric simulation of acoustic radiation

In this paper we discuss the numerical solution on a simple 2D domain of the Helmoltz equation with mixed boundary conditions. The so called radiation problem depends on the wavenumber constant parameter k and it is inspired here by medical applications, where a transducer emits a pulse at a given frequency. This problem has been successfully solved in the past with the classical Finite Element Method (FEM) for relative small values of k. But in modern applications the values of k can be of order of thousands and FEM faces up several numerical difficulties. To overcome these difficulties we solve the radiation problem using the Isogeometric Analysis (IgA), a kind of generalization of FEM. Starting with the variational formulation of the radiation problem, we show with details how to apply the isogeometric approach in order to compute the coefficients of the approximated solution of radiation problem in terms of the B-spline basis functions. Our implementation of IgA using GeoPDEs software shows that isogeometric approach is superior than FEM, since it is able to reduce substantially the pollution error, especially for high values of k, producing additionally smoother solutions which depend on less degrees of freedom.


page 13

page 16


A new mixed finite-element method for the biharmonic problem

Fourth-order differential equations play an important role in many appli...

Isogeometric solution of Helmholtz equation with Dirichlet boundary condition: numerical experiences

In this paper we use the Isogeometric method to solve the Helmholtz equa...

A C^0 finite element algorithm for the sixth order problem with simply supported boundary conditions

In this paper, we study the sixth order equation with the simply support...

The Helmholtz boundary element method does not suffer from the pollution effect

In d dimensions, approximating an arbitrary function oscillating with fr...

Adaptive modelling of variably saturated seepage problems

In this article we present a goal-oriented adaptive finite element metho...

Isogeometric Analysis of Bound States of a Quantum Three-Body Problem in 1D

In this paper, we initiate the study of isogeometric analysis (IGA) of a...

Isogeometric Analysis of Acoustic Scattering with Perfectly Matched Layers (IGAPML)

The perfectly matched layer (PML) formulation is a prominent way of hand...

Please sign up or login with your details

Forgot password? Click here to reset