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In this paper we use the Isogeometric method to solve the Helmholtz equationwith nonhomogeneous Dirichlet boundary condition over a bounded physicaldomain. Starting from the variational formulation of the problem, we show withdetails how to apply the isogeometric approach to obtain an approximation ofthe solution using biquadratic B-spline functions. To illustrate the power ofthe method we solve several difficult problems, which are particular cases ofthe Helmholtz equation, where the solution has discontinuous gradient in somepoints, or it is highly oscillatory. For these problems we explain how toselect the knots of B-spline quadratic functions and how to insert knew knotsin order to obtain good approximations of the exact solution on regions withirregular boundary. The results, obtained with our Julia implementation of themethod, prove that isogeometric approach produces approximations with arelative small error and computational cost.

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