Numerical methods for maxwell equations

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Numerical methods for maxwell equations

Numerical Methods for Maxwell EquationsJoachim Schoberl SS05AbstractThe Maxwell equations dcscrilM? the interaction of electric and magnetic lields. I

Numerical methods for maxwell equations Important applications are electric machines such as transformers or motors, or electromagnetic waves radiated from antennas or transmitted in optical

fibres, 'lb compute t he solutions of real life problems on complicated geomet ries, numerical methods are required.In this lecture we formulate the Numerical methods for maxwell equations

Maxwell equations, and discuss the finite clement met hod to solve them. Involved topics arc partial differential equations, variational formulations,

Numerical methods for maxwell equations

edge elements, high order elements, preconditioning, a posteriori error estimates.1 Maxwell EquationsIn this chapter we formulate the Maxwell equatio

Numerical Methods for Maxwell EquationsJoachim Schoberl SS05AbstractThe Maxwell equations dcscrilM? the interaction of electric and magnetic lields. I

Numerical methods for maxwell equations (germ: magn. Fcldstarke)jtot $ electric current density (germ: clektrische Stromdichte)We state the magnet ic equations in integral form. The magneti

c flux density has no sources, i.c., for any volume V' there holds13 ■ n (is = 0<)VAmpere’s law gives a relations between the magnetic field and the e Numerical methods for maxwell equations

lectric current . A current through a wire generates a magnetic field around it. For any surface s in space there holds:/ H-rds = I jtotitdsJdsJs1Both

Numerical methods for maxwell equations

magnet ic fields are related by a material law, i.e., 13 — B(H). We assume a linear relation13 = /iH,where the scalar fl is called permeability. In g

Numerical Methods for Maxwell EquationsJoachim Schoberl SS05AbstractThe Maxwell equations dcscrilM? the interaction of electric and magnetic lields. I

Numerical methods for maxwell equations gral relations can be reformulated in differential form. Gauss' theorem givesi 13 • ft ds = i div 13 dr = 0 V V,JovJvwhich impliesdiv 13 = 0.Similar,

applying Stokes' theorem leads to/ II - 7 ds = / curl II ■ n ds = I jtot ■ n ds.Jif.s JsJ$orcurl 11 - jtat-Since div curl — 0, this identity can only Numerical methods for maxwell equations

hold t rue if div jM - 0 was assumed !Summing up, we havedivB = 0 curl//=jloi 13 = fill.-1The integral forms can also be used to derive interface cond

Numerical methods for maxwell equations

itions between different materials. In this case, we may expect piecewise smooth fields. Let. s be a surface in the material interface, i.e.,s c n+ ni

Numerical Methods for Maxwell EquationsJoachim Schoberl SS05AbstractThe Maxwell equations dcscrilM? the interaction of electric and magnetic lields. I