T. Malas, L. Gürel, "Schur complement preconditioners
for surface integral-equation formulations of dielectric problems solved with
the multilevel fast multipole algorithm," SIAM
J. Sci. Comput. (2011).

Ö. Ergül, L. Gürel, "Efficient solution of the electric
and magnetic current combined-field integral equation with the multilevel
fast multipole algorithm and block-diagonal preconditioning," Radio Sci. 44, RS6001-1-RS6001-15 (2009) RS6001, doi:10.1029/2009RS004143.

Ö. Ergül, L. Gürel, "Comparison of integral-equation
formulations for the fast and accurate solution of scattering problems involving
dielectric objects with the multilevel fast multipole algorithm," IEEE Trans. Antennas Prop. 57, 176-187 (2009).

Ö. Ergül, L. Gürel, "Discretization error due to
the identity operator in surface integral equations," Comput.
Phys. Comm. 180, 1746-1752 (2009).

J. Yuan, Y. Y. Lu, X. Antoine, "Modeling photonic crystals by boundary integral
equations and Dirichlet-to-Neumann maps," J.
Comput. Phys. 227, 4617-4629 (2008).

P. Ylä-Oijala, M. Taskinen, S. Järvenpää, "Analysis of surface integral
equations in electromagnetic scattering and radiation problems," Eng. Anal. Boundary Elem. 32, 196-209 (2008).

T. Malas, L. Gürel, "Incomplete LU preconditioning
with multilevel fast multipole algorithm for electromagnetic scattering," J. Sci. Comput. 29, 1476-1494 (2007).

D. Pissoort, E. Michielssen, D. V. Ginste, F. Olyslager, "Fast-multipole analysis of
electromagnetic scattering by photonic crystal slabs," J.
Lightw. Technol. 25, 2847-2863 (2007).

W. Kuang, W. J. Kim, J. D. O'Brien, "Finite-difference time domain
method for nonorthogonal unit-cell two-dimensional photonic crystals," J. Lightw. Technol. 25, 2612-2617 (2007).

C. Siefert, E. de Sturler, "Preconditioners for generalized
saddle-point problems," J. Numer. Anal. 44, 1275-1296 (2006).

M. Benzi, G. H. Golub, J. Liesen, "Numerical solution of saddle
point problems," Acta Numer. 14, 1-137 (2005).

P. Ylä-Oijala, M. Taskinen, S. Järvenpää, "Surface integral equation formulations
for solving electromagnetic scattering problems with iterative methods," Radio Sci. 40, (2005) doi:10.1029/2004RS003169.

P. Ylä-Oijala, M. Taskinen, "Well-conditioned Müller
formulation for electromagnetic scattering by dielectric objects," IEEE Trans. Antennas Propag. 53, 3316-3323 (2005).

P. Ylä-Oijala, M. Taskinen, "Application of combined field
integral equation for electromagnetic scattering by dielectric and composite
objects," IEEE Trans. Antennas Propag. 53, 1168-1173 (2005).

S. Boscolo, M. Midrio, "Three-dimensional multiple-scattering
technique for the analysis of photonic-crystal slabs," J.
Lightw. Technol. 22, 2778-2786 (2004).

T.-L. Wu, J.-S. Chiang, C.-H. Chao, "A novel approach for calculating
the dispersions of photonic crystal fibers," IEEE
Photon. Technol. Lett. 16, 1492-1494 (2004).

A. Mekis, J. D. Joannopoulos, "Tapered couplers for efficient
interfacing between dielectric and photonic crystal waveguides," J. Lightw. Technol. 19, 861-865 (2001).

M. Koshiba, "Wavelength division multiplexing
and demultiplexing with photonic crystal waveguide couplers," J. Lightw. Technol. 19, 1970-1975 (2001).

R. Stoffer, H. J. W. M. Hoekstra, R. M. De Ridder, E. Van Groesen, F. P. H. Van Beck Um, "Numerical studies of 2-D photonic
crystals: Waveguides, coupling between waveguides and filters," Opt. Quantum Electron. 32, 947-961 (2000).

S. Venakides, M. A. Haider, V. Papanicolaou, "Boundary integral calculations
of two-dimensional electromagnetic scattering by photonic crystal Fabry–Perot
structures," J. Appl. Math. 60, 1686-1706 (2000).

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).

P. Loschialpo, D. W. Forester, J. Schelleng, "Anomalous transmission through
near unit index contrast dielectric photonic crystals," J.
Appl. Phys. 86, 5342-5347 (1999).

J. Song, C.-C. Lu, W. C. Chew, "Multilevel fast multipole algorithm
for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propagat. 45, 1488-1493 (1997).

E. Chow, Y. Saad, "Approximate inverse techniques for block-partitioned
matrices," J. Sci. Comput. 18, 1657-1675 (1997).

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in
photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).

S. M. Rao, D. R. Wilton, A. W. Glisson, "Electromagnetic scattering
by surfaces of arbitrary shape," IEEE Trans.
Antennas Propag. AP-30, 409-418 (1982).

T. K. Wu, L. L. Tsai, "Scattering from arbitrarily-shaped
lossy dielectric bodies of revolution," Radio
Sci. 12, 709-718 (1977).

Y. Chang, R. F. Harrington, "A surface formulation for characteristic
modes of material bodies," IEEE Trans. Antennas
Propagat. AP-25, 789-795 (1977).

M. Benzi, G. H. Golub, J. Liesen, "Numerical solution of saddle
point problems," Acta Numer. 14, 1-137 (2005).

Ö. Ergül, L. Gürel, "Discretization error due to
the identity operator in surface integral equations," Comput.
Phys. Comm. 180, 1746-1752 (2009).

P. Ylä-Oijala, M. Taskinen, S. Järvenpää, "Analysis of surface integral
equations in electromagnetic scattering and radiation problems," Eng. Anal. Boundary Elem. 32, 196-209 (2008).

T.-L. Wu, J.-S. Chiang, C.-H. Chao, "A novel approach for calculating
the dispersions of photonic crystal fibers," IEEE
Photon. Technol. Lett. 16, 1492-1494 (2004).

S. M. Rao, D. R. Wilton, A. W. Glisson, "Electromagnetic scattering
by surfaces of arbitrary shape," IEEE Trans.
Antennas Propag. AP-30, 409-418 (1982).

Y. Chang, R. F. Harrington, "A surface formulation for characteristic
modes of material bodies," IEEE Trans. Antennas
Propagat. AP-25, 789-795 (1977).

Ö. Ergül, L. Gürel, "Comparison of integral-equation
formulations for the fast and accurate solution of scattering problems involving
dielectric objects with the multilevel fast multipole algorithm," IEEE Trans. Antennas Prop. 57, 176-187 (2009).

P. Ylä-Oijala, M. Taskinen, "Well-conditioned Müller
formulation for electromagnetic scattering by dielectric objects," IEEE Trans. Antennas Propag. 53, 3316-3323 (2005).

P. Ylä-Oijala, M. Taskinen, "Application of combined field
integral equation for electromagnetic scattering by dielectric and composite
objects," IEEE Trans. Antennas Propag. 53, 1168-1173 (2005).

J. Song, C.-C. Lu, W. C. Chew, "Multilevel fast multipole algorithm
for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propagat. 45, 1488-1493 (1997).

P. Loschialpo, D. W. Forester, J. Schelleng, "Anomalous transmission through
near unit index contrast dielectric photonic crystals," J.
Appl. Phys. 86, 5342-5347 (1999).

J. Yuan, Y. Y. Lu, X. Antoine, "Modeling photonic crystals by boundary integral
equations and Dirichlet-to-Neumann maps," J.
Comput. Phys. 227, 4617-4629 (2008).

S. Boscolo, M. Midrio, "Three-dimensional multiple-scattering
technique for the analysis of photonic-crystal slabs," J.
Lightw. Technol. 22, 2778-2786 (2004).

D. Pissoort, E. Michielssen, D. V. Ginste, F. Olyslager, "Fast-multipole analysis of
electromagnetic scattering by photonic crystal slabs," J.
Lightw. Technol. 25, 2847-2863 (2007).

S. Venakides, M. A. Haider, V. Papanicolaou, "Boundary integral calculations
of two-dimensional electromagnetic scattering by photonic crystal Fabry–Perot
structures," J. Appl. Math. 60, 1686-1706 (2000).

A. Mekis, J. D. Joannopoulos, "Tapered couplers for efficient
interfacing between dielectric and photonic crystal waveguides," J. Lightw. Technol. 19, 861-865 (2001).

M. Koshiba, "Wavelength division multiplexing
and demultiplexing with photonic crystal waveguide couplers," J. Lightw. Technol. 19, 1970-1975 (2001).

W. Kuang, W. J. Kim, J. D. O'Brien, "Finite-difference time domain
method for nonorthogonal unit-cell two-dimensional photonic crystals," J. Lightw. Technol. 25, 2612-2617 (2007).

C. Siefert, E. de Sturler, "Preconditioners for generalized
saddle-point problems," J. Numer. Anal. 44, 1275-1296 (2006).

T. Malas, L. Gürel, "Incomplete LU preconditioning
with multilevel fast multipole algorithm for electromagnetic scattering," J. Sci. Comput. 29, 1476-1494 (2007).

E. Chow, Y. Saad, "Approximate inverse techniques for block-partitioned
matrices," J. Sci. Comput. 18, 1657-1675 (1997).

R. Stoffer, H. J. W. M. Hoekstra, R. M. De Ridder, E. Van Groesen, F. P. H. Van Beck Um, "Numerical studies of 2-D photonic
crystals: Waveguides, coupling between waveguides and filters," Opt. Quantum Electron. 32, 947-961 (2000).

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in
photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).

T. K. Wu, L. L. Tsai, "Scattering from arbitrarily-shaped
lossy dielectric bodies of revolution," Radio
Sci. 12, 709-718 (1977).

P. Ylä-Oijala, M. Taskinen, S. Järvenpää, "Surface integral equation formulations
for solving electromagnetic scattering problems with iterative methods," Radio Sci. 40, (2005) doi:10.1029/2004RS003169.

Ö. Ergül, L. Gürel, "Efficient solution of the electric
and magnetic current combined-field integral equation with the multilevel
fast multipole algorithm and block-diagonal preconditioning," Radio Sci. 44, RS6001-1-RS6001-15 (2009) RS6001, doi:10.1029/2009RS004143.

T. Malas, L. Gürel, "Schur complement preconditioners
for surface integral-equation formulations of dielectric problems solved with
the multilevel fast multipole algorithm," SIAM
J. Sci. Comput. (2011).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals, Molding the
Flow of Light (Princeton Univ. Press, 2008).

Y. Saad, Iterative Methods for Sparse Linear
Systems (SIAM, 2003).

C. Müller, Foundations of the Mathematical
Theory of Electromagnetic Waves (Springer-Verlag, 1969).

A. J. Poggio, E. K. Miller, Computer
Techniques for Electromagnetics (Pergamon, 1973).