In this paper, we are concerned with the error analysis for the finite element solution of the
two-dimensional exterior Neumann boundary value problem in acoustics. In particular, we …

Boundary perturbation methods, in which the deviation of the problem geometry from a
simple one is taken as the small quantity, have received considerable attention in recent …

We present a high-order spectral element method for solving layered media scattering
problems featuring an operator that can be used to transparently enforce the far-field …

As one of the most popular artificial boundary conditions, the Dirichlet-to-Neumann (DtN)
boundary condition has been widely developed and investigated for solving the exterior …

Standard numerical methods often fail to solve the Helmholtz equation accurately near
reentrant corners, since the solution may become singular. The singularity has an …

The quadrature method for Hadamard finite-part integral on a circle is discussed and the
emphasis is placed on the pointwise superconvergence phenomenon of the composite …

Numerical resolution of exterior Helmholtz problems requires some approach to domain
truncation. As an alternative to approximate nonreflecting boundary conditions and …

The most successful equations for the modeling of ocean wave phenomena are the free–
surface Euler equations. Their solutions accurately approximate a wide range of physical …

For exterior scattering problems one of the chief difficulties arises from the unbounded
nature of the problem domain. Inhomogeneous obstacles may require a volumetric …

We study the general (composite) Newton–Cotes rules for the computation of Hadamard
finite-part integral on a circle with the hypersingular kernel\sin^-2 xs 2 and focus on their …