I am trying to solve following PDE：
$$ \frac{\partial^{2} \theta}{\partial x^{2}} + \frac{\partial^{2} \theta}{\partial y^{2}} - m^{2} \cdot \theta = 0 \\ 0 \leq x \leq a, 0 \leq y \leq b $$
with the given boundary conditions $$BC1: \frac{\partial }{\partial x}\theta(0,y) = \frac{\partial }{\partial x}\theta(a,y) =0 \\ BC2 : \frac{\partial }{\partial y}\theta(x,0) = \frac{\partial }{\partial x}\theta(x,b) =0 $$
$$ \theta(x,y) = \theta_{i} \textrm{ with} ( x -x_{i})^{2} + (y-y_{i})^{2} = r^{2} , r \textrm{ r is small } i= 1,2, \cdots , n $$
Generally speaking, the domain is a rectangular minus several small "interior" round holes. Actually, these holes are not necessary to be "round", they can be "square" if needed (both are simplification from real physics). I have no ideal how to deal with these holes. does anyone can help me with this? Either exact solution or analytical approximation(asymptotic) is acceptable. Thanks in advance.