A meshless local Petrov-Galerkin method for magnetic diffusion in non-magnetic conductors

CMES - Computer Modeling in Engineering and Sciences

Volumn 22, Issue 3, 2007, Pages 165-188

  Johnson, J N ^a   Owen, J M ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Anisotropic; Conductivity; Conductor; Diffusion; Local weak form; Magnetic field; Magnetohydrodynamics; Maxwell's equations; Meshless method; Moving least squares; Resistivity

Indexed keywords

ELECTRIC CONDUCTIVITY; GALERKIN METHODS; LEAST SQUARES APPROXIMATIONS; MAGNETIC ANISOTROPY; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; MAXWELL EQUATIONS; SURFACE DIFFUSION;

LOCAL WEAK FORMS; MESHLESS METHOD; MOVING LEAST SQUARES; PETROV-GALERKIN METHOD;

ELECTRIC CONDUCTORS;

EID: 36448966434     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. Atluri, S. N. (2004): The Meshless Method (MLPG) for Domain and BIE Discretizations. Tech Science Press, Forsyth, GA.
2. Atluri, S. N.; Han, Z. D.; Rajendran, A. M. (2004): A New Implementation of the Meshless Finite Volume Method, Through the MLPG "Mixed" Approach. CMES: Computer Modeling in Engineering and Sciences, vol. 6, pp. 491-513.
3. Atluri, S. N.; Kim, H. G.; Cho, J. Y. (1999). A critical assessment of the truly Meshless Local Petrov-Galerkin (MLPG) and Local Boundary Integral Equation(LBIE) methods. Comput. Mech., vol. 24, pp. 348-372.
4. Atluri, S. N.; Liu, H. T.; Han, Z. D. (2006) : Meshless local Petrov-Galerkin (MLPG) mixed collocation method for elasticity problems. CMES: Computer Modeling in Engineering and Sciences, vol. 14, pp. 141-152.
5. Atluri, S. N.; Liu, H. T.; Han, Z. D. (2006): Meshless Local Petrov-Galerkin (MLPG) Mixed Finite Difference Method for Solid Mechanics. CMES: Computer Modeling in Engineering and Sciences, vol. 15, pp. 1-16.
6. Atluri, S. N.; Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics". Comput. Mech., vol. 22, pp. 117-127.
7. Balay, S.; Buschelman, K.; Gropp, W. D.; Kaushik, D.; Knepley, M. G.; Mclnnes, L. C.; Smith, B. E.; Zhang, H. (2001): PETSc Web page, 2001. http://www.mcs.anl.gov/petsc.
8. Belytschko, T.; Krogauz, Y.; Organ, D.; Fleming, M.; Krysl, P. (1996): Meshless methods: an overview and recent developments. Comp. Meth. Appl. Mech. Engn., vol. 139, pp. 3-47.
9. Bottauscio, O.; Chiampi, M.; Manzin, A. (2006): Element-free galerkin method in eddy-current problems with ferromagnetic media. IEEE Transactions on Magnetics, vol. 42, pp. 1577-1584.
10. Brauer, J. R.; Mayergoyz, I. D. (2004): Finiteelement computation of nonlinear magnetic diffusion and its effects when coupled to electrical, mechanical, and hydraulic systems. IEEE Transactions on Magnetics, vol. 40, pp. 537-540.
11. Chen, F. F. (1984): Introduction to Plasma Physics and Controlled Fusion. Plenum Publishing, New York, NY.
12. Chinchapatnam, P. P.; Djidjeli, K.; Nair, P. (2006): Unsymmetric and symmetric meshless schemes for the unsteady convection-diffusion equation. CMAME, vol. 195, pp. 2432-2453.
13. Davidson, P. A. (2001): An Introduction to Magnetohydrodynamics. Cambridge University Press.
14. Diltz, G. A. (1999): Moving-Least-SquaresParticle Hydrodynamics -1. Consistency and Stability. International Journal for Numerical Methods in Engineering, vol. 44, pp. 1115-1155.
15. Gruneisen, E. (1933): Ann. Physik, vol. 16, pp. 530.
16. Hwang, D. Q.; Horton, R. D.; Howard, S.; Evans, R. W.; Brockington, S. E. (2006): Advances in CTIX Accelerator Study. Journal of Fusion Energy, vol. 1, no. 1-2, pp. 81-84.
17. Hyman, J.; Shashkov, M. (2001): Mimetic finite difference methods for maxwell's equations and the equations of magnetic diffusion, 2001.
18. Jackson, J. D. (1999) : Classical Electrodynamics. John Wiley and Sons, Inc., New York, NY.
19. Lin, H.; Atluri, S. N. (2000): Meshless Local Petrov-Galerkin (MLPG) Method for ConvectionDiffusion Problems. CMES: Computer Modeling in Engineering and Sciences, vol. 1, pp. 45-60.
20. Lin, H.; Atluri, S. N. (2001): The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations. CMES: Computer Modeling in Engineering and Sciences, vol. 2, pp. 117-142.
21. Maron, J. L.; Howes, G. G. (2003): Gradient Particle Magnetohydrodynamics: A Lagrangian particle code for astrophysical magnetohydrodynamics. ApJ, vol. 595, pp. 564-572.
22. Monaghan, J. J. (1992): Mon. Not. R. Astron. Soc., vol. 30, pp. 543.
23. Nayroles, B.; Touzot, G.; Villon, P. (1992): Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Elements. Comput. Mech., vol. 10, pp. 307-318.
24. Price, D. J.; Monaghan, J. J. (2004): Smoothed Particle Magnetohydrodynamics - I. Algorithm and tests in one dimension. Mon. Not. R. Astron. Soc., vol. 348, pp. 128-138.
25. Rieben, R.; White, D. (2006): Verification of high-order mixed finite element solution of transient magnetic diffusion problems. IEEE Trans. Magnetics, vol. 42, pp. 25-39.
26. Roache, P. J. (2002): Code Verification by the Method of Manufactured Solutions. ASME Journal of Fluids Engineering, vol. 124, no. 1, pp, 4-10.
27. Sterk, M.; Robic, B.; Trobec, R. (2005): Meshfree Method Applied to the Diffusion Equation. In Vajtersic, M.; Trobec, R.; P., Z.; Uhl, A.(Eds): Parallel Numerics '05, volume 1.
28. Stoer, J.; Bulirsch, R. (1991): Introduction to Numerical Analysis. Springer, New York, NY.
29. Van Leer, B. (1974): Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme. J. Comp. Phys., vol. 14, pp. 361-370.
30. Zhu, T.; Atluri, S. N. (1998): A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Comput. Mech., vol. 21, pp. 211-222.
31. Zienkiewicz, O. C.; Taylor, R. L. (1989): The Finite Element Method, Volume 1: Basic Formulations and Linear Problems. McGraw-Hill.