Fast and Oblivious Convolution Quadrature

Authors:
Achim Schädle;María López-Fernández;Christian Lubich
Affiliations:
-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2006

Citing 0
Cited 11

Multistep collocation methods for Volterra Integral Equations

Applied Numerical Mathematics
On some explicit Adams multistep methods for fractional differential equations

Journal of Computational and Applied Mathematics
An extension of the ' 1/9 '-problem

Journal of Computational and Applied Mathematics
A variable step size numerical method based on fractional type quadratures for linear integro-differential equations

Advances in Engineering Software
Solution of time-convolutionary Maxwell's equations using parameter-dependent Krylov subspace reduction

Journal of Computational Physics
Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation

Numerical Algorithms
A Fast Time Stepping Method for Evaluating Fractional Integrals

SIAM Journal on Scientific Computing
Efficient long-time computations of time-domain boundary integrals for 2D and dissipative wave equation

Journal of Computational and Applied Mathematics
Two-step diagonally-implicit collocation based methods for Volterra Integral Equations

Applied Numerical Mathematics
A Bootstrap Method for Sum-of-Poles Approximations

Journal of Scientific Computing
Fast convolution quadrature based impedance boundary conditions

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.01

Visualization

Abstract

We give an algorithm to compute $N$ steps of a convolution quadrature approximation to a continuous temporal convolution using only $O(N\, \log N)$ multiplications and $O(\log N)$ active memory. The method does not require evaluations of the convolution kernel but instead uses $O(\log N)$ evaluations of its Laplace transform, which is assumed sectorial. The algorithm can be used for the stable numerical solution with quasi-optimal complexity of linear and nonlinear integral and integro-differential equations of convolution type. In a numerical example we apply it to solve a subdiffusion equation with transparent boundary conditions.