Helmholtz equation for a Neumann condition on a curved boundary: spurious resonances

Abstract

The 2D canonical case of a semi-circular canyon is addressed via two types of boundary-integral equations (BIE) methods which are shown, via Galerkin procedures, to lead to matrix equations with kernels that vanish at two different sets of (what appear as resonant) frequencies. This physically impossible result is interpreted as being the sign that the two BIE methods are generally defective and that the resonances are ‘spurious’. This ‘disease’ is cured by combining two BIE's into one which gives rise to a closed-form solution identical to the exact separation-of-variables solution devoid of resonances.

Keywords:

• Seismic response
• canyons
• spurious resonances
• combined boundary integral equations

2020 Mathematics Subject Classification:

• 45F99

Disclosure statement

No potential conflict of interest by the author.