Related Experiment Video
Updated: Oct 8, 2026

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
Published on: February 23, 2018
A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior
1Department of Naval Architecture, National Kaohsiung Institute of Marine Technology, Taiwan.
Abstract:
Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.
Related Concept Videos
Substitutions in Multiple Integrals
Standing Waves in a Cavity
Differential Form of Maxwell's Equations
Theorems of Pappus and Guldinus: Problem Solving
Theorem of Pappus
Second Uniqueness Theorem
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...