Publications

Book (1): 

      1.   K. Zhao and J. -F. Lee, "A Domain Decomposition Method: A Finite Element Preconditioner for Time-Harmonic Maxwell's Equations", ISBN: 3639185927, VDM Verlag, 2009.

Patents (5):

      1.   K. Zhao and D. K. Sun, "Domain Decomposition Formulations for Simulating Electromagnetic Fields," US 8,510,091, Aug 2013.

      2.  K. Zhao, "Simulations of Physical Systems for Multiple Excitations", US 8,924,186, Dec 2014.

      3.  K. Zhao, "Matrix Preconditioners for Simulations of Physical Fields", US 9,063,882, Jun 2015.

     4.  K. Zhao, "Systems and Methods for Electromagnetic Field Analysis", US 10,423,738, Sept 2019.

     5.  K. Zhao, L. E. R. Petersson, and X. Fu, "Non-conformal domain decomposition with imprints at interfaces with boundaries for finite element analysis", US 11,699,008 B2, Jul 2023.

Thesis and Dissertation (2): 

      1.  K. Zhao, "Single Level Dual Rank SVD Algorithm for Solving Multilayer Radiation and Scattering Problems", MS Thesis, Electrical Engineering, Columbus, OH, Mar. 2003.

      2.  K. Zhao, "A Domain Decomposition Method for Solving Electrically Large Electromagnetic Problems", PhD Dissertation, Electrical Engineering, Columbus, OH, Sept. 2007.

Journal Publications (13) (Total citations: 1616):

1.  K. Zhao, and J. -F. Lee, "A Single-Level IE-QR Algorithm to Model Large Microstrip Antenna Arrays", IEEE Transactions on Antennas and Propagation, vol. 52, no. 10, pp. 2580-2585, Oct., 2004. (cited by 46)

2.  M. N. Vouvakis, S.-C. Lee, K. Zhao and J.-F. Lee, "A Symmetric FEM-IE Formulation with a Single-Level IE-QR Algorithm for Solving Electromagnetic Radiation and Scattering Problems", IEEE Transactions on Antennas and Propagation, vol. 52, no. 11, pp. 3060-3070, Nov., 2004. (cited by 110)

3.  S.-C. Lee, M. N. Vouvakis, K. Zhao and J.-F. Lee, "Analyzing Microwave Devices Using a Symmetric Coupling of Finite and Boundary Elements", International Journal for Numerical Methods in Engineering, vol. 64, no. 4, pp. 528-546, Sept., 2005. (cited by 14)

4.  K. Zhao, M. N. Vouvakis, and J. -F. Lee, "The Adaptive Cross-Approximation Algorithm for Accelerated Method of Moments Computations of EMC Problems", IEEE Transactions on Electromagnetic Compatibility, vol. 47, no. 4, pp. 763-773, Nov., 2005. (cited by 796)

5.  K. Zhao, M. N. Vouvakis, and J. -F. Lee, "Solving Electromagnetic Problems Using A Novel Symmetric FEM-BEM Approach", IEEE Transactions on Magnetic, vol. 42, no. 4, pp.583-587, Apr., 2006. (cited by 61)

6.  M. N. Vouvakis, K. Zhao, and J. -F. Lee, "FEM Analysis of Infinite Periodic Structures with Non-Matching Triangulations", IEEE Transactions on Magnetic, vol. 42, no. 4, pp.691-695, Apr., 2006. (cited by 40)

7.  M. N. Vouvakis, K. Zhao, S. M. Seo, and J. -F. Lee, "A Domain Decomposition Approach for Non-Conformal Couplings Between Finite and Boundary Elements for Unbounded Electromagnetic Problems in R3", Journal of Computational Physics,  vol. 225, no. 1, pp. 975-994, Jul. 2007. (cited by 95)

8.  K. Zhao, V. Rawat, S.-C. Lee, and J.-F. Lee, "A Domain Decomposition Method with Non-Conformal Meshes for Finite Periodic and Semi-Periodic Structures", IEEE Transactions on Antennas and Propagation, vol. 55, no. 9, pp. 2559-2570, Sept. 2007. (cited by 170)

9.  S.-C. Lee, K. Zhao, U. Navsariwala, and J.-F. Lee, "Modeling of Environmental Effects by Numerical Green’s Function in Electromagnetic Applications", IEEE Transactions on Magnetic, vol. 44, no. 6, pp.1334-1337, June, 2008. (cited by 9)

10.  K. Zhao, V. Rawat, and J.-F. Lee, "A Domain Decomposition Method for Electromagnetic Radiation and Scattering Analysis of Multi-Target Problems", IEEE Transactions on Antennas and Propagation, vol. 56, no. 8, pp. 2211-2221, Aug. 2008. (cited by 112)

11.  J. Silvestro, K. Zhao and A. Sligar, "Hybrid Finite Element-Boundary Integral Technique for Efficient Simulation of Radiation and Scattering", Microwave Journal, vol. 54, no. 1, pp.74, Jan, 2011. (cited by 12)

12.  J. Manges, J. Silvestro and K. Zhao, "Finite Element Analysis of Infinite and Finite Arrays", International Journal of Microwave and Wireless Technologies, vol. 4, no. 3, pp. 357-364, 2012. (cited by 4)

13.  I. Bardi, K. Zhao, R. Petersson, J. Silvestro, and N. Lambert, "Multi-Domain Multi-Scale Problems in High Frequency Finite Element Methods", COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 32, no. 5, pp.1471 - 1483, 2013.

Recent Publications (14):

1. J. Silvestro, K. Zhao and A. Sligar, "Hybrid Finite Element-Boundary Integral Technique for Efficient Simulation of Radiation and Scattering", Microwave Journal, vol. 54, no. 1, pp.74, Jan, 2011.

2. K. Zhao, M. H. Commens, and N. Lambert, "Hybridization of Different Numerical Methods Using Domain Decomposition Method", International Conference on Electromagnetics in Advanced Applications, Torino, Italy, Sept, 2011.

3. K. Zhao and M. H. Commens, " Efficient Full-Wave Electromagnetic Simulation with Hybrid Finite Element - Boundary Integral", EuMW, Manchester, UK, Oct. 9-14, 2011.

4. K. Zhao, D.-K. Sun, and N. Lambert, "Recent Advances in HFSS for Electromagnetic Radiation and Scattering Analysis", ACES, Columbus, Ohio, Apr. 2012.

5. J. Silvestro, J. Manges, and K. Zhao, "The New Finite Array Tool in ANSYS HFSS", ACES, Columbus, Ohio, Apr. 2012.

6. M. H. Commens and K. Zhao, "Efficient Large Scale Simulations with a Hybrid Finite Element Boundary Integral Technique", WAMICON, Cocoa Beach, FL, Apr. 2012.

7. K. Zhao and N. Lambert, "Modeling of Antennas and Arrays Using Domain Decomposition Method", International Workshop on Finite Elements for Microwave Engineering, Estes Park, Colorado, June, 2012.

8. M. H. Commens and K. Zhao, "Finite Antenna Array Analysis with Unit-cell Domain Decomposition Method", EuMW, Amsterdam RAI, The Netherlands, Oct. 2012.

9. J. Manges, J. Silvestro and K. Zhao, "Finite Element Analysis of Infinite and Finite Arrays", International Journal of Microwave and Wireless Technologies, vol. 4, no. 3, pp. 357-364, 2012.

10. I. Bardi, K. Zhao, R. Petersson, J. Silvestro, and N. Lambert, "Multi-Domain Multi-Scale Problems in High Frequency Finite Element Methods", (invited paper) The 15th International IGTE Symposium on Numerical Field Calculation, Graz, Austria, Sept. 2012.

11. L. E. R. Petersson, K. Zhao, and I. Bardi, "HFSS Hybrid---The Advent of 3D System Simulation", The 7th European Conference on Antennas and Propagation, Gothenburg, Sweden, Apr. 2013.

12. K. Zhao and M.H. Commens, "A Fast and Efficient Domain Decomposition Approach for Finite Antenna Arrays", IEEE MTT-S, Seattle, WA, June, 2013.

13. K. Zhao and L. E. R. Petersson, "Solving Challenging Problems Using Domain Decomposition Problem", International Workshop on Finite Elements for Microwave Engineering, Chengdu, China, June, 2014.

14. K. Zhao and L. E. R. Petersson, "AHybrid FEBI-MoM-PO Formulation for the Analysis of Radiation and Scattering Problems", EuMW, Paris, France, 2015.

Technical Reports (1):

1.  K. Zhao, R. J. Burkholder, and J.-F. Lee, "Radiation Pattern Analysis of an Antenna Enclosed in an Aerodynamic Radome Using a Domain Decomposition Method", Rep. #60009498-1, ElectroScience Lab, Ohio State Univ., 2007.

Award-Winning Papers (5):

Fourth Place, 2003 USRI Student Paper Contest

K. Zhao, and J. -F. Lee, “An O(N3/2) MoM Computation of Electromagnetic Radiation and Scattering Problems Using A Novel 2-Level IE-SVD Algorithm”

Best Poster Award, 2006 CEFC

F. Gundes, K. Zhao, and J.-F. Lee, “Implementation of Higher Order Absorbing Boundary Conditions in Vector Finite Element Methods”

First Place, 2006 EMC-Zurich Student Paper Contest

K. Zhao and J.-F. Lee, “An Accelerated Non-Conforming DP-FETI Domain Decomposition Method for the Analysis of EMC Problems”

Finalist, 2006 IEEE-APS Student Paper Contest

K. Zhao and J.-F. Lee, “On the Solution of Large EM Problems Using a Fast Geometrically Non-Conforming Domain Decomposition Method”

Second Place, 2007 IEEE-APS Student Paper Contest

K. Zhao, and J.-F. Lee, “Domain Decomposition Framework to Hybridize Different Numerical Methods for Solving Electrically Large Problems”

Conference Publications (44):

Integral Equation Methods (7):

1. K. Zhao and J.-F. Lee, “A Novel 2-Level IE-SVD Algorithm to Model Large Microstrip Antenna Arrays”, ACES, Monterey, CA, Mar. 24-28, 2003.

2. K. Zhao and J. -F. Lee, “Using Star Loop Method of Moments to Model Arbitrary Shaped Microstrip Antennas”, Compumag, Saratoga Springs, New York, July 14-17, 2003.

3.  K. Zhao, and J. -F. Lee, “An O(N3/2) MoM Computation of Electromagnetic Radiation and Scattering Problems Using A Novel 2-Level IE-SVD Algorithm”, IEEE Antennas Propagat. Symposium, Columbus, OH, July, 2003.

4. K. Zhao, N. A. Ozdemir, S. M. Seo, and J.-F. Lee, “Single Level O(N1.5) IE-QR Algorithm-One Algorithm Fits All”, EMCC, NASA Langley Research Center, Hampton Virginia, May 20-22, 2003.

5.  K. Zhao, M. N. Vouvakis, and J.-F. Lee, “Application of the Multilevel Adaptive Cross-Approximation on Ground Plane Designs”, IEEE EMC Symposium, Santa Clara, CA, vol. 1, pp. 124-127, Aug. 9-14, 2004. (cited by 19)

6. K. Zhao, M. N. Vouvakis, and J.-F. Lee, “The Multilevel Adaptive Cross-Approximation Algorithm For Modeling Electromagnetic Radiation and Scattering Problems”, PIERs, Nanjing, China, Aug. 28-31, 2004.

7. K. Yuan, K. Zhao, and J.-F. Lee, “A SVD Based BCG Algorithm for Speeding Up Monostatic RCS Computations”, IEEE Antennas Propagat. Symposium, Washington D. C, July, 2005.

Finite Element Methods (13):

1. S. M. Seo, S.-C. Lee, K. Zhao, and J.-F. Lee, “A Symmetric FEM-IE Formulation with a Multi-Level IE-FFT Algorithm for Solving Electromagnetic Radiation and Scattering Problems”, IEEE Antennas Propagat. Symposium, Monterey, CA, June, 2004.

2.  M. N. Vouvakis, S.-C. Lee, K. Zhao, and J.-F. Lee, “Speed Up the Hybrid FEM+IE Formulation Using a Low-Rank Matrix Approximation”, IEEE Antennas Propagat. Symposium, Columbus, OH, vol. 2, pp. 124-127, July, 2003.

3.  M. N. Vouvakis, S.-C. Lee, K. Zhao, and J.-F. Lee, “Hybrid FEM/IE Formulation using a Single Level QR Algorithm”, EMCC, NASA Langley Research Center, Hampton Virginia, May 20-22, 2003.

4. M. N. Vouvakis, S.-C. Lee, K. Zhao, and J.-F. Lee, “Hybrid FEM/IE Formulation using a Single-Level Low-Rank IE-QR Algorithm”, Mathematics of Finite Elements and Applications (MAFELAP), Brunel Institute of Computational Mathematics, UK, pp. 109, June 21-24, 2003.

5.  M. N. Vouvakis, S.-C. Lee, K. Zhao, and J.-F. Lee, “A Symmetric FEM-IE Formulation using a Single Level IE-QR Algorithm”, International Conference on Electromagnetics in Advanced Applications, Torino, Italy, vol. 1, pp.111-114, Sept, 2003.

6. K. Zhao, M. N. Vouvakis, S.-C. Lee, and J.-F. Lee, “Solving Electromagnetic Problems Using a Novel Symmetric FEM-BEM Approach”, Compumag, Shengyang, China, vol. 1, pp. 156-157, Jun. 26-30, 2005.

7. S. M. Seo, K. Zhao, M. N. Vouvakis, and J.-F. Lee, “A Symmetric FEM-BEM Approach for Solving Electromagnetic Problems”, IEEE Antennas Propagat. Symposium, Washington D. C, July, 2005.

8. S. M. Seo, K. Zhao, M. N. Vouvakis, and J.-F. Lee, “A Domain Decomposition Symmetric FEM-BEM Formulation, Free of Internal Resonances, for Solving Electromagnetic Problems”, PIERs, Hangzhou, China, Aug, 22-26, 2005.

9. K. Zhao, M. N. Vouvakis, S. M. Seo, S.-C. Lee, and J.-F. Lee, “A Symmetric Domain Decomposition Formulation of Hybrid FEM-BEM Coupling for Electromagnetic Analysis”, EMC Zurich, Singapore, pp.45-48, Feb. 28-Mar. 3, 2006.

10. K. Zhao, and J.-F. Lee, “Multi-Level Multiplicative Schwarz Preconditioner for Solving Matrix Equations from DD-FE-BEM Formulation”, PIERs, Cambridge, MA, Mar. 26-29, 2006.

11.  F. Gundes, K. Zhao, and J.-F. Lee, “Implementation of Higher Order Absorbing Boundary Conditions in Vector Finite Element Methods”, CEFC, Miami, FL, pp. 400-400, Apr. 30 - May 3 2006.

12.  F. Gundes, K. Zhao, and J.-F. Lee, “Implementation of Higher Order Absorbing Boundary Conditions in Vector Finite Element Methods”, International Workshop on Finite Elements for Microwave Engineering, Stellenbosch, South Africa, May 25-26, 2006.

13.  F. Gundes, K. Zhao, and J.-F. Lee, “Implementing Higher Order Absorbing Boundary Conditions in Vector Finite Element Methods”, IEEE Antennas Propagat. Symposium, Albuquerque, New Mexico, pp.1787-1790, July 9-12, 2006.

Domain Decomposition Methods (19):

1. K. Zhao, M. N. Vouvakis, S.-C. Lee, and J.-F. Lee, “An Ultimate DDM with Mortar Techniques for Solving Large EM Problems --1 billion Unknowns on a PC”, PIERs, Pisa, Italy, Mar. 28-31, 2004.

2. M. N. Vouvakis, K. Zhao, and J.-F. Lee, “Modeling Large Almost Periodic Structures Using a Non-Overlapping Domain Decomposition Method”, IEEE Antennas Propagat. Symposium, Monterey, CA, vol. 1, pp. 343-346, June, 2004.

3. K. Zhao, M. N. Vouvakis, S.-C. Lee, and J.-F. Lee, “Domain Decomposition Method in Conjuction with DP-FETI for Modeling RCS Computation of Large Finite Arrays”, IEEE Antennas Propagat. Symposium, Monterey, CA, June, 2004.

4. K. Zhao, M. N. Vouvakis, S. -C. Lee, and J.-F. Lee, “Domain Decomposition Method in Conjunction with DP-FETI for Modeling Large Finite Arrays”, PIERs, Nanjing, China, Aug. 28-31, 2004.

5.  M. N. Vouvakis, K. Zhao, and J.-F. Lee, “FEM Analysis of Infinite Periodic Structures with Non-Matching Triangulations”, Compumag, Shengyang, China, vol. 4, pp. 190-191, Jun. 26-30, 2005.

6.  K. Zhao, M. N. Vouvakis, and J.-F. Lee, “Application of DP-FETI Domain Decomposition Method for the Negative Index of Refraction Materials”, IEEE Antennas Propagat. Symposium, Washington D. C, vol. 3B, pp. 26-29, Jul. 3-8, 2005.

7.  K. Zhao and J.-F. Lee, “An Accelerated Non-Conforming DP-FETI Domain Decomposition Method for the Analysis of EMC Problems”, EMC Zurich, Singapore, pp.200-203, Feb. 28-Mar. 3, 2006.

8.  S.-C. Lee, K. Zhao, M. N. Vouvakis, and J.-F. Lee, “Modeling Finite Periodic Structures using a Finite Element Domain Decomposition Technique with 2nd Order Transmission Conditions”, IWAT, White Plains, NY, Mar. 6-8, 2006.

9. S.-C. Lee, K. Zhao, and J.-F. Lee, “An Accelerated Non-Conforming DP-FETI Domain Decomposition Method for Analyzing Metamaterials in Electromagnetics”, ACES, Miami, Florida, Mar. 12-16, 2006.

10. K. Zhao and J.-F. Lee, “A Fast Domain Decomposition Method for Modeling Large Electromagnetic Problems”, International Workshop on Finite Elements for Microwave Engineering, Stellenbosch, South Africa, May 25-26, 2006.

11. K. Zhao, V. Rawat, and J.-F. Lee, “Modeling of Environmental Effects in EM Applications Using Domain Decomposition Method”, IEEE Antennas Propagat. Symposium, Albuquerque, New Mexico, pp. 309, July 9-12, 2006.

12. S.-C. Lee, K. Zhao, M. N. Vouvakis, and J.-F. Lee, “Analyzing Commercial Mobile Phones by a Domain Decomposition Approach”, IEEE MTT-S, San Francisco, CA, pp. 1061-1064, June 11-16, 2006.

13. K. Zhao and J.-F. Lee, “On the Solution of Large EM Problems Using a Fast Geometrically Non-Conforming Domain Decomposition Method”, IEEE Antennas Propagat. Symposium, Albuquerque, New Mexico, pp. 3981-3984, July 9-12, 2006.

14. K. Zhao and J.-F. Lee, “Modeling Complex EMC Problems Using Finite Element Tearing and Interconnecting Algorithm”, IEEE EMC, Portland, Oregon, vol. 3, pp. 586-590, Aug. 14-16, 2006.

15.  K. Zhao, S. -C. Lee, V. Rawat and J. -F. Lee, “Non-Conformal Domain Decomposition Methods for Maxwell Equations - Frequency Domain Approach”, Workshop on Computational Electromagnetism and Acoustics, Oberwolfach, Germany, Feb. 2-10, 2007.

16. K. Zhao, S.-C. Lee, V. Rawat, and J.-F. Lee, “Numerical Modeling of Metamaterials in Electromagnetics Using the Finite Element Method”, ACES, Verona, Italy, Mar. 19-23, 2007.

17.  V. Rawat, K. Zhao, S.-C. Lee, and J.-F. Lee, “A Finite Element Domain Decomposition Method fro the Analysis of Finite Antenna Arrays”, ACES, Verona, Italy, Mar. 19-23, 2007.

18.  S. C. Lee, K. Zhao, U. Navsariwala, and J.-F. Lee, “Modeling of Environmental Effects by Numerical Green’s Function in Electromagnetic Applications”, Compumag, Aachen, Germany, June 24-28, 2007.

19. V. Rawat, K. Zhao, S.-C. Lee, and J.-F. Lee, “On the Choice of Krylov Method for the Acceleration of the Domain Decomposition Method in Electromagnetics”, Compumag, Aachen, Germany, June 24-28, 2007.

Hybrid Methods (5):

1.  K. Zhao, and J.-F. Lee, “Domain Decomposition Framework to Hybridize Different Numerical Methods for Solving Electrically Large Problems”, IEEE Antennas Propagat. Symposium., Honolulu, Hawaii, June 10-15, 2007.

2. K. Zhao, V. Rawat, S.-C. Lee, and J.-F. Lee, “Hybrid Domain Decomposition Method and Boundary Element Method for the Solution of Large Array Problems”, IEEE Antennas Propagat. Symposium, Honolulu, Hawaii, June 10-15, 2007.

3.  Z. Jin, K. Zhao, P. H. Pathak, J. Zou, and J.-F. Lee, “A Hybrid FEM-DDM-PO Method for Electrically Large Objects”, IEEE Antennas Propagat. Symposium, Honolulu, Hawaii, June 10-15, 2007.

4. Z. Jin, K. Zhao, P. H. Pathak, and J.-F. Lee, “Hybridization of Finite Elements, Boundary Elements, and Physical Optics for Reflector Antenna Systems”, ICEAA, Torino, Italy, Sept. 17-21, 2007.

5. B. Donderici, K. Zhao, F. L. Teixeira, and J. -F. Lee, “Deferential Forms, Metrics, and the Electromagnetic Masking of Scattering Objects”, PIERs, Hangzhou, China, Mar. 24-28, 2008.