Summary The Dirichlet-to-Neumann (DtN) Finite Element Method is a general technique for
the solution of problems in unbounded domains, which arise in many fields of application. Its …

This volume reviews and discusses the main numerical methods used today for solving
problems in infinite domains. It also presents in detail one very effective method in this class …

In various areas of applied mechanics, there are instances where it is necessary or
beneficial to represent the behavior of a mechanical system on an artificial boundary, or …

While numerically solving a problem initially formulated on an unbounded domain, one
typically truncates this domain, which necessitates setting the artificial boundary conditions …

We present an iterative domain decomposition method to solve the Helmholtz equation and
related optimal control problems. The proof of convergence of this method relies on energy …

" Artificial Boundary Method" systematically introduces the artificial boundary method for the
numerical solutions of partial differential equations in unbounded domains. Detailed …

We give a numerical method for the computation of heteroclinic orbits connecting two saddle
points in ℝ 2. These can be computed to very high period due to an integral phase condition …

In applications, solitary-wave solutions of semilinear elliptic equationsΔu+ g (u,∇ u)= 0 (x,
y)∈ R× Ω in infinite cylinders frequently arise as travelling waves of parabolic equations. As …

Anomalous diffusion behavior in many practical problems can be described by the nonlinear
time-fractional parabolic problems on unbounded domain. The numerical simulation is a …

Dirichlet-to-Neumann (DtN) boundary conditions for unbounded wave guides in two and
three dimensions are derived and analyzed, defining problems that are suitable for finite …