Abstract
This work addresses the numerical solution of timedomain boundary integral equations arising from acoustic and electromagnetic scattering in three dimensions. The semidiscretization of the timedomain boundary integral equations by RungeKutta convolution quadrature leads to a lower triangular Toeplitz system of size N. This system can be solved recursively in an almost linear time (O(Nlog^{2}N)), but requires the construction of O(N) dense spatial discretizations of the single layer boundary operator for the Helmholtz equation. This work introduces an improvement of this algorithm that allows to solve the scattering problem in an almost linear time. The new approach is based on two main ingredients: the nearfield reuse and the application of datasparse techniques. Exponential decay of RungeKutta convolution weights wnh(d) outside of a neighborhood of d≈. nh (where h is a time step) allows to avoid constructing the nearfield (i.e. singular and nearsingular integrals) for most of the discretizations of the single layer boundary operators (nearfield reuse). The farfield of these matrices is compressed with the help of datasparse techniques, namely, Hmatrices and the highfrequency fast multipole method. Numerical experiments indicate the efficiency of the proposed approach compared to the conventional RungeKutta convolution quadrature algorithm.
Original language  English 

Pages (fromto)  103126 
Number of pages  24 
Journal  Journal of Computational Physics 
Volume  279 
DOIs  
Publication status  Published  2014 
Keywords
 Boundary element method
 Fast multipole method
 Hmatrices
 RungeKutta convolution quadrature
 Timedomain boundary integral equations
 Wave scattering
Fingerprint Dive into the research topics of 'Fast convolution quadrature for the wave equation in three dimensions'. Together they form a unique fingerprint.
Profiles

Lehel Banjai
 School of Mathematical & Computer Sciences  Associate Professor
 School of Mathematical & Computer Sciences, Mathematics  Associate Professor
Person: Academic (Research & Teaching)