10/15/05

BOOKS, THESES, BOOK CHAPTERS AND REFEREED JOURNAL PUBLICATIONS

1. Kotiuga, P. R., Topology-Based Inequalities and Inverse Problems for Near Force-Free Magnetic Fields. IEEE Transactions on Magnetics, Vol. 40, (2), March 2004, pp 1108-1111.

Gross, P.W., Kotiuga, P.R., Electromagnetic Theory and Computation: A Topological Approach. MSRI Monograph series, Vol. 48; Cambridge University Press, 2004. ISBN 0 521 801605 hardback.

3.      Kotiuga, P. R., Bellamine, F. H., Fast Impedance Formulation and Numerical Computation Associated with Ratios of Confluent Hypergeometric Functions. IEEE Transactions on Magnetics, Vol. 39, (5), September 2003, pp. 3355-3357.

4.      Suuriniemi, S., Kettunen, L., Kotiuga, P.R., Techniques for Systematic Treatment of Certain Coupled Problems. IEEE Transactions on Magnetics, MAG-39, (3), May 2003, pp 1737-1740.

5.      Crager, J.C., Kotiuga P.R., Cuts for the Magnetic Scalar Potential in Knotted Geometries and Force-Free Magnetic Fields. IEEE Transactions on Magnetics, MAG-38, (2), March 2002, pp 1309-1312.

6.      Gross, P.W., Kotiuga, P.R., Data Structures for Geometric and Topological Aspects of Finite Element Algorithms. Geometric Methods for Computational Electromagnetics, Teixeira, F.L. editor, Progress in Electromagnetics Res., 32, Kong, J.A. chief editor, EMW Publishing, Cambridge MA, 2001, pp151-169. (ISBN 09668143-6-3)

7.      Gross, P.W., Kotiuga, P.R., Finite Element-based Algorithms to Make Cuts for Magnetic Scalar Potentials:  Topological Constraints and Computational Complexity.  Geometric Methods for Computational Electromagnetics, Teixeira, F.L. editor, Progress in Electromagnetics Res., 32, Kong, J.A. chief editor, EMW Publishing, Cambridge MA, 2001, pp 207-245. (ISBN 0966143-6-3)

8.      Kotiuga, P.R., Toffoli, T., Potential for Computation in Micromagnetics via Topological Conservation Laws, Physica D, 120, 1998, pp. 139-161.

9.      Gross, P.W., Kotiuga, P.R., A Challenge for Magnetic Scalar Potential Formulations of 3-D Eddy Current Problems: Multiply Connected Cuts in Multiply Connected Regions Which Necessarily Leave the Cut Complement Multiply Connected. Electric and Magnetic Fields, Nicolet, A., Belmans, R., eds., Plenum Press, New York, 1995, pp. 1-20. (ISBN 0-306-44991-9)

10.  Kotiuga, P.R., Metric Dependent Aspects of Inverse Problems and Functionals Based Helicity.  Journal of Applied Physics, 70(10), May 1993, pp. 5437-5439.

11.  Kotiuga, P.R., Arithmetic for Evaluating Three-Dimensional h vs. p Finite Element Refinement Strategies.  Journal of Applied Physics, 70(10), May 1993, pp. 6778-6780.

12.  Kotiuga, P.R., Essential Arithmetic for Evaluating Three Dimensional Vector Finite Element Interpolation Schemes. IEEE Transactions on Magnetics, MAG-27, (6), November, 1991, pp. 5208-5210.

13.   Kotiuga, P.R., Clebsch Potentials and the Visualization of Three Dimensional Solenoidal Vector Fields. IEEE Transactions on Magnetics, MAG-27, (5), September, 1991, pp. 3986-3989.

14.  Giles, R.C., Kotiuga, P.R., Mansuripur, M., Parallel Micromagnetic Simulations Using Fourier Methods on a Regular Hexagonal Lattice. IEEE Transactions on Magnetics, MAG-27, (5), September 1991, pp. 3815-3818.

15.  Giles, R.C., Patterson, G., Bagneres, A., Kotiuga, P.R., Humphrey, F.B., Mansuripur, M., Micromagnetic Simulations on the Connection Machine, Very Large Scale Computation in the 21st Century, Jill P. Mesirov, Editor.  Published by the Society for Industrial and Applied Mathematics, 1991, ISBN 0-89871-279-3, Chapter 3, pp. 33-40.

16.  Kotiuga, P.R., Correspondence on paper 6437A: Magnetostatics with scalar potentials in multiply connected regions, Proceedings of the IEE, 37, Pt. A, (4), July 1990, pp. 231-232.

17.  Kotiuga, P.R., Is Three-Dimensional Electromagnetic Field Analysis Incompatible with Node-Based Finite Element Interpolation?, Advances in Electrical Engineering Software, P.P. Silvester, Editor, Jointly published by Computational Mechanics Publications and Springer-Verlag, 1990, ISBN: 1-85312-088-X,  pp. 187-190.

18.  Kotiuga, P.R., Giles, R.C., A Topological Invariant for the Accessibility Problem of Micromagnetics, Journal of Applied Physics, 67(9), May 1990, pp. 5347-5349.

19.  Kotiuga, P.R. Analysis of Finite Element Matrices Arising from Discretizations of Helicity Functionals, Journal of Applied Physics, 67(9), May 1990, pp. 5815-5817.

20.  Giles, R.C., Kotiuga, P.R., Humphrey, F.B., Three Dimensional Micromagnetic Simulations on the Connection Machine, Journal of Applied Physics, 67(9), May 1990, pp. 5821-5823.

21.  Kotiuga, P.R., Topological Duality in Three-Dimensional Eddy-Current Problems and its Role in Computer-Aided Problem Formulation, Journal of Applied Physics, 67(9), May 1990, pp. 4717-4719.

22.  Kotiuga, P.R., The Algebraic Topology of Bloch Points, IEEE Transactions on Magnetics, MAG-25, (5), September 1989, pp. 3476-3478.

23.  Kotiuga, P.R., An Algorithm to Make Cuts for Magnetic Scalar Potentials in Tetrahedral Meshes Based on the Finite Element Method, IEEE Transactions on Magnetics, MAG-25, (5), September 1989, pp. 4129-4131.

24.  Kotiuga, P.R., Helicity Functionals and Metric Invariance in Three Dimensions, IEEE Transactions on Magnetics, MAG-25, (4), July 1989, pp. 2813-2815.

25.  Kotiuga, P.R., Topological Considerations in Coupling Magnetic Scalar Potentials to Stream Functions Describing Surface Currents, IEEE Transactions on Magnetics, MAG-25, (4), July 1989, pp. 2925-2927.

26.  Kotiuga, P.R., Variational Principles for Three-Dimensional Magnetostatics Based on Helicity, Journal of Applied Physics, 63(8), April 1988, pp.3360-3362.

27.  Kotiuga, P.R., Toward an Algorithm to Make Cuts for Magnetic Scalar Potentials in Finite Element Meshes, Journal of Applied Physics, Vol. 63(8), April 1988, pp. 3357-3359. Erratum: 64(8), 4257, 1988.

28.  Kotiuga, P.R., On Making Cuts for Magnetic Scalar Potentials in Multiply Connected Regions, Journal of Applied Physics, 61(8), April 1987, pp. 3916-3918.

29.  Kotiuga, P.R., Hodge Decompositions and Computational Electromagnetics, Ph.D. Thesis, McGill University, Montreal, Canada, 1985.

30.  Kotiuga, P.R., Well-Posed Three Dimensional Magnetostatics Formulations, M.Eng. Thesis, McGill University Montreal, Canada, 1982.

31.   Kotiuga, P.R., Silvester, P.P., Vector Potential Formulation for Three Dimensional Magnetostatics, Journal of Applied Physics, 53, (11), November 1982, pp. 8399-8401.

 SIGINIFCANT CONFERENCE PAPERS AND PAPERS APPEARING IN NEWSLETTERS (i.e. not in appearing in refereed journals or books with ISBN data).

1.      Kotiuga, P. R.., The Idea of an Electromagnetic Field, Numerical Electromagnetism, and the Geometric Perspective, International Compumag Society Newsletter, Vol. 12, No. 2., 1 July 2005, ISSN 1026-0854.

2.      Kotiuga, P. R., Tonti Diagrams and Natural Elliptic Complexes: A Framework for Uniquely Relating Helicity Functionals and Inverse Problems, 4th International Workshop on Electric and Magnetic Fields, Marseille, France, May 12-15, 1998.  See pp. 313-318 of proceedings.

3.      Chammas, P., Kotiuga, P. R., Sparsity Vis A Vis Lanczos Methods for Discrete Helicity Functionals, 3rd International Workshop on Electric and Magnetic Fields, Liege, Belgium, May 5-9, 1996. See pp.333-339 of proceedings.

AN ODDITY:

1.  Hallaj, I.M., Kotiuga, P.R., An Efficient Method for Calculating the Impedance of a Round Wire. Was to be submitted to the IEEE Trans. CAS, Pt. I (electronic copy lost; only a hard copy exists).

PUBLISHED ABSTRACTS (AMS abstracts can be found at the AMS web site)

1.      Kotiuga, P.R., On the Formal Analogy Between Multi-Particle Quantum Entanglement and Entanglement in Link Theory.  AMS abstract number 971-81-26.

2.      Kotiuga, P.R., Topological Aspects of Electromagnetic Design Problems Requiring Noncommutative Functors.  AMS abstract number 959-57-99.

3.      Kotiuga, P.R., The Indirect Influence of André Weil on Computational Electromagnetics.  AMS abstract number 947-78-142.

4.      Kotiuga, P.R., Discrete Abelian Chern-Simons TQFT via Whitney Forms and Finite Element Discretizations. AMS abstract number 924-57-60.

5.      Kotiuga, P.R., Retakh, V., Complexity, Computability, and Critical Point Theory.  AMS abstract number 924-57-61.

6.      Kotiuga, P.R., A Generalized Harmonic Map Equation for Micromagnetics, Journal of Applied Physics, 69(8), April 1991, p. 4617.