ALTERNATIVE TIME DOMAIN BOUNDARY INTEGRAL EQUATIONS FOR THE SCALAR WAVE EQUATION USING DIVERGENCE-FREE REGULARIZATION TERMS

Georgios Natsiopoulos

ALTERNATIVE TIME DOMAIN BOUNDARY INTEGRAL EQUATIONS FOR THE SCALAR WAVE EQUATION USING DIVERGENCE-FREE REGULARIZATION TERMS
Journal article, 2009

In this short note alternative time domain boundary integral equations (TDBIE) for the scalar wave equation are formulated on a surface enclosing a volume. The technique used follows the traditional approach of subtracting and adding back relevant Taylor expansion terms of the field variable, but does not restrict this to the surface patches that contain the singularity only. From the divergence-free property of the added-back integrands, together with an application of Stokes' theorem, it follows that the added-back terms can be evaluated using line integrals defined on a cut between the surface and a sphere whose radius increases with time. Moreover, after a certain time, the line integrals may be evaluated directly. The results provide additional insight into the theoretical formulations, and might be used to improve numerical implementations in terms of stability and accuracy.

boundary integral equation

three-dimensional

theorem

Stokes'

hypersingular

scattering

stabilization

time domain

stability

divergence-free

numerical solution

closed surface

collocation

element method

singularity subtraction

Author

Georgios Natsiopoulos

Chalmers, Civil and Environmental Engineering, Applied Acoustics

Other publications Research

Journal of Computational Acoustics

0218-396X (ISSN)

Vol. 17 2 211-218

Subject Categories

Fluid Mechanics and Acoustics

More information

Created

10/6/2017