On 4/3/19 6:53 AM, solee wrote:
> I am a beginner of deal.ii and some problem happened. I want to solve the
> Maxwell equations in the 2D cylindrical coordinates with axis-symmetry.
> When I create a weak form of the equation (see attached formula), I want to
> remove 1 / r from the first term. When I refer to other posts, they are
> asked to multiply 2 pi r by both sides. But I do not understand this. Why
> do you multiply by 2 pi? Multiplying both sides yields r in the other
> terms.
You want to think of integrating over a domain Omega that in cylindrical
coordinates is r=(0..R), phi=(0..2pi), z=[0..Z]:
\int_\Omega f(r,z)
= \int_0^Z \int_0^R \int_0^{2pi} f(r,phi,z) r dphi dr dz
But in your case the integrand you want to integrate over only depends on r,z.
So you get
\int_\Omega f(r,z)
= \int_0^Z \int_0^R \int_0^{2pi} f(r,z) r dphi dr dz
= \int_0^Z \int_0^R [2 pi f(r,z) r] dr dz
= 2 pi \int_0^Z \int_0^R [f(r,z) r] dr dz
Of course, in your weak formulation, *every* term is an integral, and so will
have the factor 2*pi. You can divide the entire equation by 2*pi if you want
to get rid of this factor.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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