This paper aims at introducing new approaches for designing and optimising induction heat treatment processes. Although the final objectives of induction heating processes may deal with some specific mechanical or metallurgical properties for manufactured parts, we shall primarily focus here on achieving an accurate control of temperature distribution and evolution in the Heat Affected Zone (HA...

In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving Schrödinger equation. In order to pass the information among grids we use the values of the fields only at the contact point between them. Surprisingly we obtain a convergent methods which is third order accurate with respect to the spatial resolution. In test cases, at the minima...

The numerical treatment of boundary integral equations in the form of boundary element methods has became very popular and powerful tool for engineering computations of boundary value problems, in addition to finite difference and finite element methods. Here, we present some of the most important analytical and numerical aspects of the boundary integral equation. The concept of the principle s...

Let u denote a quasiminimal surface (QMS) bounded by a polygon ? 2 IR q (q 2) with N+3 distinct vertices in the sense of Shiiman. A linear nite element method is presented for the approximation of u. Furthermore, an error estimation in terms of the angles at the vertices of ? and some examples of computed quasiminimal surfaces are given.

In this paper we are concerned with oscillatory functional differential equations (that is, those equations where all solutions oscillate) under numerical approximation. Our interest is in the preservation of qualitative properties of solutions under numerical discretisation. We give conditions under which an equation is oscillatory, and consider whether the discrete schemes derived using linea...

• The architecture of chaos oscillator should be similar to classical second order sine wave oscillator, e.g. LC or Wien-bridge based circuit. • The oscillator should not be higher than the third order system. • The circuit should be an autonomous oscillator. • The active unit should be linear and separated from the nonlinear element(s). • The nonlinear element should be single and simple, e.g....

This report is part of PATH Task Order 4141 and shows how moving obstructions can be modeled numerically with kinematic wave theory. It shows that if a moving obstruction is replaced by a sequence of fixed obstructions at nearby locations with the same “capacity”, then the error in vehicle number converges uniformly to zero as the maximum separation between the moving and fixed bottlenecks is r...

This paper surveys techniques for calculating eigenvalues and eigenvectors of very large matrices.