scholarly journals Sparse convolution quadrature for time domain boundary integral formulations of the wave equation

2008 ◽  
Vol 29 (1) ◽  
pp. 158-179 ◽  
Author(s):  
W. Hackbusch ◽  
W. Kress ◽  
S. A. Sauter
Keyword(s):  
Wave Equation ◽  
Time Domain ◽  
Domain Boundary ◽  
Boundary Integral ◽  
Convolution Quadrature

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

2009 ◽  
Vol 17 (02) ◽  
pp. 211-218
Author(s):  
GEORGIOS NATSIOPOULOS
Keyword(s):  
Wave Equation ◽  
Integral Equations ◽  
Time Domain ◽  
Boundary Integral Equations ◽  
Domain Boundary ◽  
Short Note ◽  
Boundary Integral ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Divergence Free

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.

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