Numerical Methods for Maxwell Equations
نویسنده
چکیده
The Maxwell equations describe the interaction of electric and magnetic fields. Important applications are electric machines such as transformers or motors, or electromagnetic waves radiated from antennas or transmitted in optical fibres. To compute the solutions of real life problems on complicated geometries, numerical methods are required. In this lecture we formulate the Maxwell equations, and discuss the finite element method to solve them. Involved topics are partial differential equations, variational formulations, edge elements, high order elements, preconditioning, a posteriori error estimates. 1 Maxwell Equations In this chapter we formulate the Maxwell equations. 1.1 The equations of the magnetic fields The involved field quantities are B V s m2 magnetic flux density (germ: Induktion) H A m magnetic field intensity (germ: magn. Feldstärke) jtot A m2 electric current density (germ: elektrische Stromdichte) We state the magnetic equations in integral form. The magnetic flux density has no sources, i.e., for any volume V there holds ∫
منابع مشابه
Resolution of the time-harmonic Maxwell equations using discontinuous Galerkin methods and domain decomposition algorithms
We present numerical results relative to the resolution of the time-harmonic Maxwell equations discretized by discontinuous Galerkin methods. First, a numerical study of the convergence of discontinuous Galerkin methods which compares different strategies proposed in the literature for the elliptic Maxwell equations, is performed in the two-dimensional case. We also introduce a Schwarz-type dom...
متن کاملON MAXWELL'S STRESS FUNCTIONS FOR SOLVING THREE DIMENSIONAL ELASTICITY PROBLEMS IN THE THEORY OF ELASTICITY
The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...
متن کاملModelling, Analysis and Simulation Numerical integration of damped Maxwell equations
We study the numerical time integration of Maxwell's equations from electromagnetism. Following the method of lines approach we start from a general semi-discrete Maxwell system for which a number of time-integration methods are considered. These methods have in common an explicit treatment of the curl terms. Central in our investigation is the question how to efficiently raise the temporal con...
متن کاملDiscontinuous Galerkin Methods for the Vlasov-Maxwell Equations
Discontinuous Galerkin methods are developed for solving the Vlasov–Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov–Maxwell system. The proposed scheme employs discontinuous Galerki...
متن کاملNumerical methods for the bidimensional Maxwell-Bloch equations in nonlinear crystals
Two numerical schemes are developed for solutions of the bidimensional Maxwell-Bloch equations in nonlinear optical crystals. The Maxwell-Bloch model was recently extended [1] to treat anisotropic materials like nonlinear crystals. This semiclassical model seems to be adequate to describe the wave-matter interaction of ultrashort pulses in nonlinear crystals [2] as it is closer to the physics t...
متن کامل