The fast Hankel transform (FHT) implemented with digital filters has been the algorithm of choice in EM geophysics for a few decades. However, other disciplines have predominantly relied on methods that break up the Hankel transform integral into a sum of partial integrals that are each evaluated with quadrature. The convergence of the partial sums is then accelerated through a nonlinear sequen...

We describe how time-discretized wave equation in a homogeneous medium can be solved by boundary integral methods. The time discretization can be a multistep, Runge-Kutta, or a more general multistep-multistage method. The resulting convolutional system of boundary integral equations belongs to the family of convolution quadratures of Ch. Lubich. The aim of this work is two-fold. It describes a...

We derive a new “convolution spline” approximation method for convolution Volterra integral equations. This shares some properties of convolution quadrature, but instead of being based on an underlying ODE solver is explicitly constructed in terms of basis functions which have compact support. At time step tn = nh > 0, the solution is approximated in a “backward time” manner in terms of basis f...

We propose two hybrid convolution quadrature based discretizations of the wave equation on interior domains with broadband Neumann boundary data or source terms. The method transforms time-domain problem into a series Helmholtz problems complex-valued wavenumbers, in which and solutions are connected to those original through

We consider initial/boundary value problems for the subdiffusion and diffusionwave equations involving a Caputo fractional derivative in time. We develop two fully discrete schemes based on the piecewise linear Galerkin finite element method in space and convolution quadrature in time with the generating function given by the backward Euler method/second-order backward difference method, and es...

In this paper we consider the (2D and 3D) exterior problem for the non homogeneous wave equation, with a Dirichlet boundary condition and non homogeneous initial conditions. First we derive two alternative boundary integral equation formulations to solve the problem. Then we propose a numerical approach for the computation of the extra “volume” integrals generated by the initial data. Finally, ...