Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 69, 2016 - Issue 3
125
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Mixed-dimensional elements in transient thermal analysis of gradient coils

, , , , &
Pages 265-282 | Received 15 Apr 2015, Accepted 30 May 2015, Published online: 02 Dec 2015

References

  • W. J. Minkowycz, E. M. Sparrow, and J. Y. Murthy, eds., Handbook of Numerical Heat Transfer, John Wiley & Sons Ltd, Hoboken, NJ, 2006.
  • L. Krähenbül and D. Muller, Thin Layers in Electrical Engineering. Example of Shell Models in Analysing Eddy-Currents by Boundary and Finite Element Methods, IEEE Trans. Magn., vol. 29, no. 2, pp. 1450–1455, 1993.
  • H. T. Hu, F. M. Lin, and Y. Y. Jan, Nonlinear Finite Element Analysis of Reinforced Concrete Beams Strengthened by Fiber-Reinforced Plastics, Compos. Struct., vol. 63, pp. 271–281, 2004.
  • K. S. Surana and R. K. Phillips, Three Dimensional Solid-Shell Transition Finite Elements for Heat Conduction, Comput. & Struct., vol. 26, no. 6, pp. 941–950, 1987.
  • H. Wang, S. Wang, X. Wang, and E. Li, Development of a 3D/1D Round Patched Transient Heat Transfer Model for Simulations of Heat Transfer Through the Casting-Mold Interface, Numer. Heat Transfer, Part A: Appl., vol. 67, no. 4, pp. 401–413, 2015.
  • E. Tonti, The Mathematical Structure of Classical and Relativistic Physics, Modeling and Simulation in Science, Engineering and Technology, Springer, New York, 2013.
  • M. Clemens and T. Weiland, Discrete Electromagnetism with the Finite Integration Technique, Prog. Electromagn. Res., vol. 32, pp. 65–87, 2001.
  • P. Alotto, F. Freschi, and M. Repetto, Multiphysics Problems via the Cell Method: The Role of Tonti Diagrams, IEEE Trans. Magn., vol. 46, no. 8, pp. 2959–2962, 2010.
  • F. Freschi, L. Giaccone, and M. Repetto, Educational Value of the Algebraic Numerical Methods in Electromagnetism, COMPEL – Int. J. Comput. Math. Electr. Electron. Eng., vol. 27, no. 6, pp. 1343–1357, 2008.
  • P. T. While, L. K. Forbes, and S. Crozier, Calculating Temperature Distributions for Gradient Coils, Concepts Magn. Reson. Part B, vol. 37B, pp. 146–159, 2010.
  • D. A. Field, Qualitative Measures for Initial Meshes, Int. J. Numer. Methods Eng., vol. 47, pp. 887–906, 2000.
  • R. E. Bank and L. R. Scott, On the Conditioning of Finite Element Equations with Highly Refined Meshes, SIAM J. Numer. Anal., vol. 26, no. 3, pp. 1383–1394, 1989.
  • J. R. Shewchuk, What is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures, Eleventh International Meshing Roundtable, pp. 115–126, Sandia National Laboratories, Ithaca, NY, 2002.
  • O. Axelsson, Iteration Number for the Conjugate Gradient Method, Math. Comput. Simul., vol. 61, no. 3–6, pp. 421–435, 2003.
  • P. T. While, M. S. Poole, L. K. Forbes, and S. Crozier, Minimum Maximum Temperature Gradient Coil Design, Magn. Reson. Med., vol. 70, pp. 584–594, 2013.
  • J. M. Bergheau and R. Fortunier, Finite Element Simulation of Heat Transfer, John Wiley & Sons Ltd, Hoboken, NJ, 2008.
  • R. H. Pletcher, Finite-Difference Method, in W. J. Minkowycz, E. M. Sparrow, and J. Y. Murthy (eds.), Handbook of Numerical Heat Transfer, pp. 53–90. John Wiley & Sons Ltd, Hoboken, NJ, 2000.
  • B. R. Baliga and N. Atabaki, Control-Volume-Based Finite-Difference and Finite-Element Methods, in W. J. Minkowycz, E. M. Sparrow, and J. Y. Murthy (eds.), Handbook of Numerical Heat Transfer, pp. 191–224. John Wiley & Sons Ltd, Hoboken, NJ, 2000.
  • A. Singh, I. V. Singh, and R. Prakash, Numerical Solution of Temperature-Dependent Thermal Conductivity Problems Using a Meshless Method, Numer. Heat Transfer, Part A: Appl., vol. 50, no. 2, pp. 125–145, 2006.
  • P. Alotto, F. Freschi, M. Repetto, and C. Rosso, The Cell Method for Electrical Engineering and Multiphysics Problems, An Introduction, Springer Verlag, Berlin-Heidelberg, 2013.
  • M. Clemens and T. Weiland, Discrete Electromagnetics: Maxwell’s Equations Tailored to Numerical Simulations, Int. Compumag Soc. Newsl., vol. 8, no. 2, pp. 13–20, 2001.
  • L. Codecasa, R. Specogna, and F. Trevisan, Base Functions and Discrete Constitutive Relations for Staggered Polyhedral Grids, Comput. Methods Appl. Mech. Eng., vol. 198, pp. 1117–1123, 2009.
  • P. Alotto, R. Specogna, and F. Trevisan, A θ-Method for Eddy Currents in Time-Domain with a Discrete Geometric Approach, IEEE Trans. Magn., vol. 42, no. 4, pp. 779–782, 2006.
  • A. Bossavit, Computational Electromagnetism, Academic Press, San Diego, CA, 1998.
  • J. Jin, Electromagnetic Analysis and Design in Magnetic Resonance Imaging, CRC Press, Boca Raton, FL, 1998.
  • K. C. Chu and B. K. Rutt, MR Gradient Coil Heat Dissipation, Magn. Reson. Med., vol. 34, pp. 125–132, 1995.
  • L. Liu, H. Sanchez Lopez, M. Poole, F. Liu, and S. Crozier, Simulation and Analysis of the Interactions Between Split Gradient Coils and a Split Magnet Cryostat in an MRI–PET System, J. Magn. Reson., vol. 222, pp. 8–15, 2012.
  • L. S. Petropoulos and M. Morich, Novel Gradient Coil Set with an Interstitial Gap for Interventional Nuclear Magnetic Resonance Applications, IEEE Trans. Magn., vol. 33, no. 5, pp. 4107–4109, 1997.
  • S. Shvartsman, G. DeMeester, T. Eagan, S. Bates, and M. Savill, A Split Gradient Coil for High Speed Imaging with Application to MRI-RT, in Proceedings of the International Society for Magnetic Resonance in Medicine, p. 3939, Stockholm, Sweden, 2010.
  • H. Sanchez Lopez, F. Liu, M. Poole, and S. Crozier, Equivalent Magnetization Current Method Applied to the Design of Gradient Coils for Magnetic Resonance Imaging, IEEE Trans. Magn., vol. 45, no. 2, pp. 767–775, 2009.
  • A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics, 2nd ed., Springer-Verlag, Berlin Heidelberg, 2007.
  • S. Ilie, G. Söderlind, and R. M. Corless, Adaptivity and Computational Complexity in the Numerical Solution of {ODEs}, J. Complexity, vol. 24, no. 3, pp. 341–361, 2008.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.