# Eliminating the fictitious frequency problem in BEM solutions of the external Helmholtz equation

@article{Klaseboer2019EliminatingTF, title={Eliminating the fictitious frequency problem in BEM solutions of the external Helmholtz equation}, author={Evert Klaseboer and F. Charlet and Boo Cheong Khoo and Qiang Sun and Derek Y. C. Chan}, journal={Engineering Analysis with Boundary Elements}, year={2019} }

## 7 Citations

### Including monopoles to a fully desingularized boundary element method for acoustics

- PhysicsArXiv
- 2021

The inclusion of domain (point) sources into a three dimensional boundary element method while solving the Helmholtz equation is described. The method is fully desingularized which allows for the use…

### Helmholtz equation and non-singular boundary elements applied to multi-disciplinary physical problems

- MathematicsCommunications in Theoretical Physics
- 2022

It is reviewed here how a recently developed singularity-free 3D boundary element framework with superior accuracy can be used to tackle problems only using one or more Helmholtz equations with higher order (quadratic) elements which can tackle complex shapes.

### Field-only surface integral equations: scattering from a perfect electric conductor.

- MathematicsJournal of the Optical Society of America. A, Optics, image science, and vision
- 2020

A field-only boundary integral formulation of electromagnetics is derived without the use of surface currents that appear in the Stratton-Chu formulation, which allows high-order elements with fewer degrees of freedom to represent surface features to a higher precision than the traditional planar elements.

### A non-singular boundary element method for interactions between acoustical field sources and structures

- Physics
- 2021

. Localized point sources (monopoles) in an acoustical domain are implemented to a three dimensional non-singular Helmholtz boundary element method in the frequency domain. It allows for the…

### Solution of the 3D Helmholtz equation using barycentric Lagrange interpolation collocation method

- Physics
- 2021

PurposeThis meshless collocation method is applicable not only to the Helmholtz equation with Dirichlet boundary condition but also mixed boundary conditions. It can calculate not only the high…

## References

SHOWING 1-10 OF 38 REFERENCES

### The numerical solution of exterior neumann problem for Helmholtz's equation via modified green's functions approach☆

- Mathematics
- 2004

### Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

- MathematicsRoyal Society Open Science
- 2015

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically, resulting in a significant reduction in the problem size with improved precision.

### The numerical solution of the exterior dirichlet problem for Helmholtz's equation via modified green's functions approach

- Mathematics
- 2002

### On the exterior problems of acoustics

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1973

Abstract The method of integral equations is the most familiar method of proving existence theorems for the Helmholtz equation of acoustics. The wave potentials are expressed as surface distributions…

### A regularized approach evaluating origin intensity factor of singular boundary method for Helmholtz equation with high wavenumbers

- MathematicsEngineering Analysis with Boundary Elements
- 2019

### On modified Green functions in exterior problems for the Helmholtz equation

- MathematicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1982

The question of non-uniqueness in boundary integral equation formulations of exterior problems for the Helmholtz equation has recently been resolved with the use of additional radiating multipoles in…