Next: Symmetrization and reduction of
Up: Appendix J: Helmholtz basis
Previous: Real plane waves (RPWs)
Evanescent plane waves (EPWs) are given a good introduction in [26].
Vergini [194] developed a set of EPWs for the stadium
which involved `families' with increasing evanescence parameter,
which he arranged to become increasingly localized at the stadium
curvaturediscontinuity point P (see Fig. J.1).
I found a single such family to be sufficient.
Following Vergini's recipe, the EPWs are

(J.5) 
for
.
For each , the propagation direction
(parallel to the wavevector ) points along
, and the growth and decay directions are perpendicular to this.
The evanescence parameters are given by an algebraic progression,

(J.6) 
The angles (restricted to the 2nd quadrant )
are chosen so as to `balance' the EPW to roughly
equal weight on the boundary either side of the point P:

(J.7) 
where the balancing is controlled by the constant .
I found optimal (Vergini reports and uses a second
family at ).
The impact parameters (see Fig. J.1) are such that the
maximum value of on the boundary is unity.
The number
is chosen so that the maximum is about 3
(the limit on is discussed in Section 6.3.3).
At ,
is sufficient.
So even though the EPW functions take longer to evaluate than RPWs
(especially when symmetrized, see below),
there are so few that their computational effort remains small.
Next: Symmetrization and reduction of
Up: Appendix J: Helmholtz basis
Previous: Real plane waves (RPWs)
Alex Barnett
20011003