greenWithTensionRBF

% Green's RBF with tension as defined by Wessel and Bercovici in:
 
 Wessel, P., Bercovici, D., 1998. Interpolation with splines in tension: a
 Green’s function approach. Mathematical Geology 30 (1), 77–93.
 
 When tension (e) == 0, defaults to greenRBF(r)

0001 function fx = greenWithTensionRBF(r, e)
0002 %% Green's RBF with tension as defined by Wessel and Bercovici in:
0003 %
0004 % Wessel, P., Bercovici, D., 1998. Interpolation with splines in tension: a
0005 % Green’s function approach. Mathematical Geology 30 (1), 77–93.
0006 %
0007 % When tension (e) == 0, defaults to greenRBF(r)
0008 %
0009 
0010 if e == 0
0011     % Regular Green function
0012     fx = (r.^2) .* (log(r)-1);
0013 else
0014     % Green function with tension
0015     g0 = 0.115931515658412420677337; % log(2) - 0.5772156...
0016     fx = besselk(0, e*r)+log(e*r)-g0;    
0017 end
0018 fx(r==0) = 0; % Fix singularity of Green's function at 0
0019 
0020 end
0021