A semilinear Schrödinger equation in the presence of a by Arioli G., Szulkin A. PDF

By Arioli G., Szulkin A.

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Additional info for A semilinear Schrödinger equation in the presence of a magnetic field

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In a field map such as Fig. 3 the field lines and the equipotentials are always at right angles to each other. We can therefore imagine a second problem whose field pattern is identical to the first except that the roles of the field lines and the equipotentials have been exchanged. Two problems related to each other in this way are called duals of each other. Sometimes it is easier to solve the dual of a problem and then to deduce the required answer from that solution. 57 3. 7 Calculation of resistance by energy methods It has already been observed that capacitances can be calculated by energy methods to an accuracy which is adequate for many purposes.

The very limited range of problems which can be solved by elementary methods can be extended by the use of the principle of superposition and the method of images. In most real problems, however, the electric field can be calculated only by solving Laplace’s or Poisson’s equations. Cases which have not been solved before generally have to be tackled using numerical methods. 31 2. Dielectric materials and capacitance Electromagnetism for Electronic Engineers 2. Dielectric materials and capacitance Objectives x x x x x x x To discuss how and why an electric field is affected by the presence of dielectric materials To introduce the electric flux density vector D as a useful tool for solving problems involving dielectric materials.

In large three-dimensional problems the number of variables can be very large indeed and the computation time correspondingly long. Very often the result required from a field calculation is not the detailed field information but only a single number such as the capacitance. For problems of this kind an alternative method, the boundary element method, is useful because it only requires mesh points and potentials to be specified on the boundaries. This has the benefit that the number of variables in the solution is less than in the corresponding finite difference or finite element solution by two or three orders of magnitude.

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A semilinear Schrödinger equation in the presence of a magnetic field by Arioli G., Szulkin A.

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