function U = lp_bexact(X, Y)
% LP_BEXACT  Ground truth for the interior Dirichlet problem on a curve.
%
% A sum of point sources placed outside the curve,
%
%     u(z) = sum_k c_k log|z - z_k| ,
%
% which is harmonic everywhere except at the sources and therefore harmonic on
% the whole of the interior. Its trace on the curve is the Dirichlet data, and
% it is the exact solution by construction, to full precision at every point.
zk = [1.8 + 0.9i, -1.5 - 1.7i, 0.2 + 2.4i];
ck = [1.0, -0.7, 0.5];
U = zeros(size(X));
for k = 1:numel(zk)
    U = U + ck(k) * 0.5 * log((X - real(zk(k))).^2 + (Y - imag(zk(k))).^2);
end
end