Calderón projector explained

In applied mathematics, the Calderón projector is a pseudo-differential operator used widely in boundary element methods. It is named after Alberto Calderón.

Definition

The interior Calderón projector is defined to be:[1]

l{C}=\left(\begin{array}{cc}(1-\sigma)Id-K&V\\W&\sigmaId+K'\end{array}\right),

where

\sigma

is

\tfrac12

almost everywhere,

Id

is the identity boundary operator,

K

is the double layer boundary operator,

V

is the single layer boundary operator,

K'

is the adjoint double layer boundary operator and

W

is the hypersingular boundary operator.

The exterior Calderón projector is defined to be:[1]

l{C}=\left(\begin{array}{cc}\sigmaId+K&-V\\-W&(1-\sigma)Id-K'\end{array}\right).

References

  1. Book: Steinbach, Olaf . 2008 . Numerical Approximation Methods for Elliptic Boundary Value Problems . limited . Springer . 978-0-387-31312-2.