In real-coded genetic algorithms, some crossover operators do not work well on functions which have their optimum at the corner of the search space. To cope with this problem, we have proposed a boundary extension methods which allows individuals to be located within a limited space beyond the boundary of the search space. In this paper, we give an analysis of the boundary extension methods fro...

We consider the exact controllability of a wave equation by means of dynamical boundary control. Unlike the classical control, a difficulty is due to the presence of the dynamical type. First, we establish a new weak observability results. Next, by the HUM method, we prove that the system is exactly controllable by means of regular dynamical boundary control.

The paper presents main results of the investigation of the coupled BEM and FEM applied to a nonlinear generally nonmonotone exterior boundary value problem. The problem consists of a nonlinear diier-ential equation considered in an annular bounded domain and the Laplace equation outside. These equations are equipped with boundary and transmission conditions. The problem is reformulated in a we...

In order to overcome the difficulties of low computational efficiency and high memory requirement in the conventional boundary element method for solving large-scale potential problems, a fast multipole boundary element method for the problems of Laplace equation is presented. through the multipole expansion and local expansion for the basic solution of the kernel function of the Laplace equati...

We analyze adaptive mesh-refining algorithms in the frame of boundary element methods (BEM) and the coupling of finite elements and boundary elements (FEM-BEM). Adaptivity is driven by the two-level error estimator proposed by Ernst P. Stephan, Norbert Heuer, and coworkers in the frame of BEM and FEM-BEM or by the residual error estimator introduced by Birgit Faermann for BEM for weakly-singula...

The boundary knot method (BKM) is a recent boundary-type radial basis function (RBF) collocation scheme for general PDE’s. Like the method of fundamental solution (MFS), the RBF is employed to approximate the inhomogeneous terms via the dual reciprocity principle. Unlike the MFS, the method uses a non-singular general solution instead of a singular fundamental solution to evaluate the homogeneo...

Sliding mode control is a nonlinear control technique, which is robust against some classes of uncertainties and disturbances. However, this control produces chattering which can cause instability due to unmodeled dynamics and can also cause damage to actuators or the plant. There are essentially two ways to counter the chattering phenomenon. One way is to use higher order sliding mode, and the...

We consider a problem of stabilization of the linearized Schrödinger equation using boundary actuation and measurements. We propose two different control designs. First, a simple proportional collocated boundary controller is shown to exponentially stabilize the system. However, the decay rate of the closed-loop system cannot be prescribed. The second, full-state feedback boundary control desig...

Peskin’s Immersed Boundary (IB) method is one of the most popular numerical methods for many years and has been applied to problems in mathematical biology, fluid mechanics, material sciences, and many other areas. Peskin’s IB method is associated with discrete delta functions. It is believed that the IB method is first order accurate in the L∞ norm. But almost none rigorous proof could be foun...

Boundary control of time-fractional order diffusion-wave systems is becoming an active research area. However, there is no readily available simulation tool till now for researchers to analyze and design controllers. In this paper, a simulation method for some typical boundary control problems, combining symbolic mathematics and numerical method, is presented with two application examples. In t...