Analysis of nonlinear microstrip lattice with metamaterial substrate using method of integral equations

2015 ◽  
Author(s):  
D. V. Semenikhina ◽  
A. I. Semenikhin ◽  
N. I. Chikov
Keyword(s):  
Integral Equations ◽  
Method Of Integral Equations

Digital Modeling of Electromagnetic Processes in Technological Induction Devices

2021 ◽  
Vol 7 (7) ◽  
pp. 26-32
Author(s):  
Viktor B. DEMIDOVICH ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Integral Equations ◽  
Transverse Magnetic ◽  
Combined Method ◽  
Method Of Integral Equations ◽  
Leading Role ◽  
Casting Aluminum ◽  
Point To Point ◽  
Element Method

Development of an electrical calculation method plays the leading role in simulating induction devices. In modeling electrical devices and complexes, it is often necessary to simultaneously solve both chain and field problems, i.e., to deal with both lumped and distributed parameters. The article considers the method of integral equations for induction systems with non-magnetic and ferromagnetic loading, which is based on the theory of long-range action. The method’s key statement is that the field at any point is determined as the sum of the fields produced by all sources, including primary and secondary ones. Another finite element method is based on the theory of short-range action, which describes the electromagnetic wave propagation from point to point, its refraction and reflection at the boundaries of media. The article substantiates the development of a combined method based on using the method of integral equations for calculating the input parameters of inductors (an external problem) and the finite element method for calculating the field distribution in the load (an internal problem). The combined method has well proven itself in modeling induction heating and melting of metals and oxides, heating a tape in a transverse magnetic field, induction plasmatrons, and casting aluminum into an electromagnetic crystallizer.

On the Heaving Motion of Cylinders of Shallow Draft

1961 ◽  
Vol 5 (04) ◽  
pp. 34-43
Author(s):  
R. C. MacCamy
Keyword(s):  
Integral Equations ◽  
Circular Disk ◽  
Finite Width ◽  
Two Dimensional ◽  
Virtual Mass ◽  
Method Of Integral Equations ◽  
First Approximation ◽  
Strip Theory ◽  
Considerable Simplification ◽  
Special Case

A perturbation procedure is developed for the two-dimensional motion produced by a long ship in heave when the draft is assumed small. The procedure reduces the shallow draft problem to a series of problems for a "raft" of zero draft. A considerable simplification in the method of integral equations is found to occur. For the first approximation, that is, a raft of finite width, the integral equations are solved numerically to determine pressure, virtual mass and damping. The problem of heave of a circular disk of zero draft is treated by the same methods so that an evaluation of strip theory in this special case is possible.

An integral-equation method for determining the fluid motion due to a cylinder heaving on water of finite depth

1980 ◽  
Vol 372 (1748) ◽  
pp. 93-110 ◽  
Keyword(s):  
Integral Equation ◽  
Fundamental Solution ◽  
Integral Equations ◽  
Fluid Motion ◽  
Integral Equation Method ◽  
Finite Depth ◽  
The Body ◽  
Wave Source ◽  
Method Of Integral Equations ◽  
Infinite Set

The method of integral equations is used here to calculate the virtual mass of a half-immersed cylinder heaving periodically on water of finite constant depth. For general sections this method is more appropriate than the method of multipoles; particular sections that are considered are the circle and the ellipse. Green’s theorem is applied to the potential and to a fundamental solution (wave source) satisfying the conditions at the free surface, at the bottom and at infinity, but not necessarily on the body. An integral equation for the potential on the body only is thus obtained. For the simplest choice of fundamental solution the method breaks down at a discrete infinite set of frequencies, as is well known. When the fundamental solution was modified, however, a different integral equation could be obtained for the same unknown function and this was found not to break down for the circle and ellipse. The present numerical results are in good agreement with those obtained by the method of multipoles which for the circle is more efficient than the method of integral equations but which is not readily applicable to other sections. Much effort now goes into such calculations.

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