Sparsity of Runge–Kutta convolution weights for the three-dimensional wave equation

@article{Banjai2014SparsityOR,
  title={Sparsity of Runge–Kutta convolution weights for the three-dimensional wave equation},
  author={L. Banjai and M. Kachanovska},
  journal={BIT Numerical Mathematics},
  year={2014},
  volume={54},
  pages={901-936}
}
Wave propagation problems in unbounded homogeneous domains can be formulated as time-domain integral equations. An effective way to discretize such equations in time are Runge–Kutta based convolution quadratures. In this paper the behaviour of the weights of such quadratures is investigated. In particular approximate sparseness of their Galerkin discretization is analyzed. Further, it is demonstrated how these results can be used to construct and analyze the complexity of fast algorithms for… Expand

Figures from this paper

Fast convolution quadrature for the wave equation in three dimensions
Dissipation free low order convolution quadrature for TDBIE
  • L. Banjai
  • Mathematics
  • 2015 International Conference on Electromagnetics in Advanced Applications (ICEAA)
  • 2015
Efficient Solution of Two-Dimensional Wave Propagation Problems by CQ-Wavelet BEM: Algorithm and Applications
Time-dependent electromagnetic scattering from thin layers
...
1
2
...

References

SHOWING 1-10 OF 31 REFERENCES
RUNGE-KUTTA METHODS FOR PARABOLIC EQUATIONS AND CONVOLUTION QUADRATURE
Rapid Solution of the Wave Equation in Unbounded Domains
Fast convolution quadrature for the wave equation in three dimensions
Time-domain Dirichlet-to-Neumann map and its discretization
Stability and Convergence of Collocation Schemes for Retarded Potential Integral Equations
Multistep and Multistage Convolution Quadrature for the Wave Equation: Algorithms and Experiments
  • L. Banjai
  • Computer Science, Mathematics
  • SIAM J. Sci. Comput.
  • 2010
...
1
2
3
4
...