Special ACM Seminar

We have constructed and successfully applied high order local Farfield Expansions absorbing

boundary conditions (FEABC) for time-harmonic single acoustic scattering in two– and three–

dimensions in previous works. A computational advantageous aspect of the FEABC is its local

character. It means only few boundary points or elements are needed to compute the approximate

solution at the different stages of the computation. This constitutes a significant improvement over

well-known high order absorbing boundary conditions such as the Dirichlet to Neumann whose

global nature requires computation over all the nodes or elements at the artificial boundary. In

this work, we extend the formulation of FEABC to scattering from multiple obstacles. We will

present some numerical results for two-dimensional multiple scattering from obstacles of arbitrary

shape by coupling second order finite differences with the FEABC. We will also discuss weak

formulations of these multiple scattering problems with FEABC as our first step to derive high

order general curvilinear finite element methods in the context of Isogeometric Analysis (IGA) for

multiple scattering.