# Coupling of finite element method with boundary algebraic equations

Recently, a combined approach of CFIE--BAE has been proposed by authors for solving external scattering problems in acoustics. CFIE stands for combined-field integral equations, and BAE is the method of boundary algebraical equation. The combined method is, essentially, a discrete analogue of the boundary element method (BEM), having none of its disadvantages. Namely, due to the discrete nature of BAE one should not compute quadratures of oversingular integrals. Moreover, due to CFIE formulation, the method does not possess spurious resonances. However, the CFIE--BAE method has an important drawback. Since the modelling is performed in a regular discrete space, the shape of the obstacle should be assembled of elementary "bricks", so smooth scatterers (like spheres, cylinders, etc) are approximated with a poor accuracy. This loss of accuracy becomes the bottleneck of the method. Here this disadvantage is overcome. The CFIE--BAE method developed for regular meshing of the outer space is coupled in a standard way with a relatively small irregular mesh enabling one to describe the shape of the obstacle accurately enough.

• 1 publication
• 2 publications
research
06/20/2023

### Solving acoustic scattering problems by the isogeometric boundary element method

We solve acoustic scattering problems by means of the isogeometric bound...
research
07/10/2021

### On the coupling of the Curved Virtual Element Method with the one-equation Boundary Element Method for 2D exterior Helmholtz problems

We consider the Helmholtz equation defined in unbounded domains, externa...
research
07/18/2023

### Finite element solution of a radiation/propagation problem for a Helmholtz equation with a compactly supported nonlinearity

A finite element method for approximating the solution of a mathematical...
research
01/24/2022

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

In d dimensions, approximating an arbitrary function oscillating with fr...
research
08/26/2020

### Caccioppoli-type estimates and ℋ-Matrix approximations to inverses for FEM-BEM couplings

We consider three different methods for the coupling of the finite eleme...
research
05/10/2021

### A shape optimisation with the isogeometric boundary element method and adjoint variable method for the three-dimensional Helmholtz equation

This paper presents a shape optimisation system to design the shape of a...
research
06/04/2022

### Implicit Neural Representation for Mesh-Free Inverse Obstacle Scattering

Implicit representation of shapes as level sets of multilayer perceptron...