Related papers: Spectral formulation of the boundary integral equa…
We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication…
There is scientific and industrial interest in understanding how geologic faults respond to transient sources of fluid. Natural and artificial sources can elevate pore fluid pressure on the fault frictional interface, which may induce slip.…
We analyse a problem of anti-plane shear in a bi-material plane containing a semi-infinite crack situated on a soft imperfect interface. The plane also contains a small thin inclusion (for instance an ellipse with high eccentricity) whose…
We model a slip boundary condition at fluid-solid interface of an arbitrary geometry in smoothed particle hydrodynamics and smoothed dissipative particle dynamics simulations. Under an assumption of linear profile of the tangential velocity…
This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect…
Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method…
Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical…
We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…
We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…
Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this…
We develop numerical methods to simulate the fluid-mechanical erosion of many bodies in two-dimensional Stokes flow. The broad aim is to simulate the erosion of a porous medium (e.g. groundwater flow) with grain-scale resolution. Our fluid…
A boundary element formulation is developed to determine the complex stress intensity factors associated with cracks on the interface between dissimilar materials. This represents an extension of the methodology developed previously by the…
We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…
This paper describes a novel numerical model aiming at solving moving-boundary problems such as free-surface flows or fluid-structure interaction. This model uses a moving-grid technique to solve the Navier--Stokes equations expressed in…
This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…
This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…
Turbulent flows over blunt bodies with distributed roughness present a class of problems relevant to hypersonic atmospheric entry systems. However, accurate predictions of shear stress on such bodies remains elusive. This work presents a…
In this paper, we extend the recently proposed extended scaled boundary finite element method (xSBFEM)~\cite{natarajansong2013} to study fracture parameters of interfacial cracks and cracks terminating at the interface. The approach is also…
This paper proposes a Cartesian grid-based boundary integral method for efficiently and stably solving two representative moving interface problems, the Hele-Shaw flow and the Stefan problem. Elliptic and parabolic partial differential…
For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation…