In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asy...

The paper will review the art, craft and science of modelling cavitation bubbles near boundaries through the use of the boundary integral method. The presentation will come in four parts, namely, a discussion of recent experimental studies that have motivated our current research, understanding the physics associated with the phenomena, a detailed presentation on the boundary integral method an...

Acoustic scattering by three-dimensional obstacles is considered, using boundary integral equations, null-field equations and the T-matrix. Connections between these techniques are explored. It is shown that solving a boundary integral equation by a particular Petrov–Galerkin method leads to the same algebraic system as obtained from the null-field equations. It is also emphasised that the T-ma...

Since meshless methods have been introduced to alleviate the difficulties arising in conventional finite element method, many papers on applications of meshless methods to boundary element method have been published. However, most of these papers use moving least squares approximation functions that have difficulties in prescribing essential boundary conditions. Recently, in order to strengthen...

We describe a boundary integral method for computing time-dependent, doubly periodic, three-dimensional water waves. This method has been proved to converge to the exact solution. We discuss several analytical issues, including the quadrature of singular integrals, such as single and double layer potentials on surfaces, and stability estimates for discrete versions of operators such as the laye...

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...

A new method called Boundary Integral-based Domain Decomposition is proposed for the fast solution of the Laplace equation on regular and irregular regions. The idea of the method is to adopt the domain decomposition approach by partitioning into subdomains and use an integral equation formulation to compute the interface values. The method provides a particularly eecient algorithm for parallel...

Boundary spanning systemic innovations such as building information modeling (BIM) are difficult to implement. Literature suggests that vertical integration facilitates the implementation of systemic innovations. This study examines the role of vertical integration in the implementation of BIM as an example of a systemic innovation. It analyzes and compares two opposite case studies from the Fi...

In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...

Elastic boundary eigensolution problems are converted into boundary integral equations by potential theory. The kernels of the boundary integral equations have both the logarithmic and Hilbert singularity simultaneously. We present the mechanical quadrature methods for solving eigensolutions of the boundary integral equations by dealing with two kinds of singularities at the same time. The meth...