In physics and applied mathematics, analytical regularization is a technique used to convert boundary value problems which can be written as Fredholm integral equations of the first kind involving singular operators into equivalent Fredholm integral equations of the second kind. The latter may be easier to solve analytically and can be studied with discretization schemes like the finite element method or the finite difference method because they are pointwise convergent. In computational electromagnetics, it is known as the method of analytical regularization. It was first used in mathematics during the development of operator theory before acquiring a name.

Method

Analytical regularization proceeds as follows. First, the boundary value problem is formulated as an integral equation. Written as an operator equation, this will take the form

representing boundary conditions and inhomogeneities, the equation becomes

or

is compact on the Hilbert space is a member.

will be possible for each problem.

See also

• Method of moments (electromagnetics)

References

• , Paperpack (also available online). Read Chapter 8 for Analytic Regularization.

External links

• E-Polarized Wave Scattering from Infinitely Thin and Finitely Width Strip Systems