We consider the numerical solution of the wave equation in a two-dimensional domain and start from a boundary integral formulation for its discretization. We employ the convolution quadrature (CQ) for the temporal and a Galerkin boundary element method (BEM) for the spatial discretization. Our main focus is the sparse approximation of the arising sequence of boundary integral operators by panel...

From trivial edge-detection techniques to the use of a quadrature pair of Gabor filters, the status quo in orientation analysis entails some form of convolution over a window of interest. Although Gabor filters have increased in popularity, most likely due to its computational efficiency as well as being a viable model for the human visual system, it is not without its shortcomings. Most promin...

This paper presents a new and efficient approach for optimization and implementation of filter banks e.g. velocity channels, orientation channels and scale spaces. The multi layered structure of a filter network enable a powerful decomposition of complex filters into simple filter components and the intermediary results may contribute to several output nodes. Compared to a direct implementation...

We study stability of a numerical method in which the backward Euler method is combined with order one convolution quadrature for approximating the integral term of the linear Volterra integrodifferential equation u′(t) + ∫ t 0 β(t − s)Au(s) ds = 0, t ≥ 0, u(0) = u0, which arises in the theory of linear viscoelasticity. Here A is a positive self-adjoint densely defined linear operator in a real...

This paper presents a new and efficient approach for optimization and implementation of filter banks e.g. velocity channels, orientation channels and scale spaces. The multi layered structure of a filter network enable a powerful decomposition of complex filters into simple filter components and the intermediary results may contribute to several output nodes. Compared to a direct implementation...

We study the Rayleigh-Stokes problem for a generalized second-grade fluid which involves a Riemann-Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations. We establish the Sobolev regularity of the homogeneous problem for both smooth and nonsmooth initial data [Formula: see text], including [Formula: ...

An incoming elastodynamic wave impinges on an elastic obstacle is embedded in infinite medium. The objective of the paper to examine subsequent fields scattered by and transmitted into obstacle. By applying a boundary-field equation method, we are able formulate nonlocal boundary problem (NBP) Laplace transformed domain, using field equations inside integral exterior Existence, uniqueness stabi...

Chave presents an excellent algorithm and computer subprogram that evaluate Hankel transforms by quadrature and continued fraction summation. This subprogram would be a valuable addition to any mathematical computer library. Chave refers to digital filter (convolution) methods as “the standard numerical approach to the computation of Hankel transforms,” and makes numerous references to my publi...