Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Engineering with Computers
Erschienen in: Engineering with Computers 4/2017

25.03.2017 | Original Article

The local radial point interpolation meshless method for solving Maxwell equations

verfasst von: Mehdi Dehghan, Mina Haghjoo-Saniji

Erschienen in: Engineering with Computers | Ausgabe 4/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The Maxwell equations are basic equations of electromagnetic. In this paper we employed ADI–LRPIM (alternative direction implicit method is applied for approximating the time variable and the local radial point interpolation meshless method is used for space variable) to solve the two-dimensional time dependent Maxwell equations. This method consists of two stages for each time step implemented in alternative directions which are simple in computations. Local radial point interpolation method is a type of meshless method which uses a set of nodes scattered within the domain of the problem as well as a set of nodes scattered on the boundaries of the domain instead of using a predefined mesh to represent the problem domain and its boundaries, this feature makes, LRPIM to be flexible. Also it produces acceptable results for solving many partial differential equations. The proposed method is accurate and efficient, these features are illustrated by solving numerical examples in transverse magnetic and transverse electric fields. We used a kind of finite difference scheme for approximation of derivative terms in main relations to reduce errors and computational cost and eliminate integrals of weak form on internal boundaries by suitable selection of test function.
Vorheriger Artikel A 2D mechanical–thermal coupled model to simulate material mixing observed in friction stir welding process
Nächster Artikel GPUs in subsurface simulation: an investigation

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Abbasbandy S, Naz R, Hayat T, Alsaedi A (2014) Numerical and analytical solutions for Falkner–Skan flow of MHD Maxwell fluid. Appl Math Comput 242(1):569–575MathSciNetMATH
2.
Abbaszadeh M, Dehghan M (2015) A meshless numerical procedure for solving fractional reaction subdiffusion model via a new combination of alternating direction implicit (ADI) approach and interpolating element free Galerkin (EFG) method. Comput Math Appl 70:2493–2512MathSciNetCrossRef
3.
Ala G, Francomano E (2015) Numerical investigations of an implicit leapfrog time-domain meshless method. J Sci Comput 62:898–912MathSciNetCrossRefMATH
4.
Ala G, Francomano E (2012) An improved smoothed particle electromagnetics method in 3D time domain simulations. Int J Numer Modell Electron Netw Dev Fields 25:325–337CrossRef
5.
Ala G, Francomano E, Ganci S (2015) Unconditionally stable meshless integration of time-domain Maxwell’s curl equations. Appl Math Comput 255:157–164MathSciNetMATH
6.
Binns KJ, Lawrenson PJ, Trowbridge CW (1993) The analytical and numerical solution of electric and magnetic fields. Wiley, USA
7.
Buhmann MD (2003) Radial basis functions: theory and implementations. Cambridge University Press, CambridgeCrossRefMATH
8.
Burden RL, Faires JD (2010) Numerical analysis. Cengage Learn
9.
Chari MVK, Silvester PP (1980) Finite element in electrical and magnetic field problems. Wiley, USA
10.
Chatterjee R (2003) Antenna theory and practice, vol 1996(19). New Age International, India
11.
Dehghan M (2002) A new ADI technique for two-dimensional parabolic equation with an integral condition. Comput Math Appl 43:1477–1488MathSciNetCrossRefMATH
12.
Dehghan M, Abbaszadeh M, Mohebbi A (2015) A meshless technique based on the local radial basis functions collocation method for solving parabolic–parabolic Patlak–Keller–Segel chemotaxis model. Eng Anal Bound Elem 56:129–144MathSciNetCrossRef
13.
Dehghan M, Ghesmati A (2010) Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM). Comput Phys Commun 181:772–786MathSciNetCrossRefMATH
14.
Dehghan M, Ghesmati A (2010) Combination of meshless local weak and strong (MLWS) forms to solve the two dimensional hyperbolic telegraph equation. Eng Anal Bound Elem 34:324–336MathSciNetCrossRefMATH
15.
Dehghan M, Salehi R (2014) A meshless local Petrov–Galerkin method for the time-dependent Maxwell equations. J Comput Appl Math 268:93–110MathSciNetCrossRefMATH
16.
Dehghan M (2006) Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices. Math Comput Simul 71:16–30MathSciNetCrossRefMATH
17.
Fasshauer G (2007) Meshfree approximation methods with Matlab. World Scientific, DaverseCrossRefMATH
18.
19.
Forsythe GE, Wasow WR (1960) Finite difference method for partial differential equations. Wiley, USAMATH
20.
Gao L, Zhang B, Liang D (2007) The splitting finite-difference time-domain methods for Maxwell equations in two dimensions. J Comput Appl Math 205:207–230MathSciNetCrossRefMATH
21.
22.
Harrington RF (1993) Field computation by moment method. Oxford University Press, USACrossRef
23.
Hayat T, Abbas Z, Sajid M (2006) Series solution for the upper-convected Maxwell fluid over a porous stretching plate. Phys Lett A 358(56):396–403CrossRefMATH
24.
Hosseinzadeh H, Dehghan M, Mirzaei D (2013) The boundary elements method for magneto-hydrodynamic (MHD) channel flows at high Hartmann number. Appl Math Modell 37:2337–2351MathSciNetCrossRefMATH
25.
Ilati M, Dehghan M (2016) Remediation of contaminated groundwater by meshless local weak forms. Comput Math Appl 72:2408–2416MathSciNetCrossRefMATH
26.
27.
Kaufmann T, Fumeaux C, Vahldieck R (2008) The meshless radial point interpolation method for time-domain electromagnetics. Dig IEEE MTT-S Int Microw Symp 61:15–20
28.
Kaufmann T, Yu Y, Engström C, Chen Z, Fumeaux C (2012) Recent developments of the meshless radial point interpolation method for time-domain electromagnetics. Int J Numer Modell Electron Netw Dev Fields 25:468–489CrossRef
29.
Kopriva DA (2009) Implementing Spectral methods for partial differential equations: algorithms for scientists and engineers. Springer, The NetherlandsCrossRefMATH
30.
Lebedev AS, Fedoruk MP, Shtyrina OV (2006) Finite-volume algorithm for solving the time-dependent Maxwell equations on unstructured meshes. Comput Math Math Phys 46:1219–1233MathSciNetCrossRef
31.
Lee J, Fornberg B (2004) Some unconditionally stable time stepping methods for the 3D Maxwell’s equa tions. J Comput Appl Math 166:497–523MathSciNetCrossRefMATH
32.
Liu GR, Gu YT (2005) An introduction to meshfree methods and their programming. Springer, The Netherlands
33.
Liu GR, Zhang GY, Gu YT, Wang YY (2005) A meshfree radial point interpolation method (RPIM) for three-dimensional solids. Comput Mech 36:421–430MathSciNetCrossRefMATH
34.
Li X (2016) Error estimates for the moving least-square approximation and the element-free Galerkin method in n-dimensional spaces. Appl Numer Math 99:77–97MathSciNetCrossRefMATH
35.
Liu GR (2009) Meshfree methods: moving beyond the finite element method, vol 2. CRC Press, SingaporeCrossRef
36.
Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, SingaporeCrossRefMATH
37.
Mastryukov AF, Mikhailenko BG (2010) Solving the 2D Maxwell equations by a Laguerre spectral method. Numer Anal Appl 3:118–132CrossRef
38.
Maxwell JC (1952) A dynamical theory of the electromagnetic field. Sci Pap James Clerk Maxwell 1:528–567
39.
40.
Movahhedi M, Abdipour A, Nentchev A, Dehghan M, Selberherr S (2007) Alternating-direction implicit formulation of the finite-element time-domain method. IEEE Microw Theory Tech 55:1322–1331CrossRef
41.
42.
Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech 10:307–318CrossRefMATH
43.
Onate E, Perazzo F, Miquel J (2001) A finite point method for elasticity problems. Comput Struct 79:2151–2163CrossRef
44.
Peaceman D, Rachford H (1955) The numerical solution of elliptic and parabolic differential equations. J SIAM 3:28–41MATH
45.
Sabouri M, Dehghan M (2015) An efficient implicit spectral element method for time-dependent nonlinear diffusion equations by evaluating integrals at one quadrature point. Comput Math Appl 70:2513–2541MathSciNetCrossRef
46.
Sarabadan S, Shahrezaee M, Rad JA, Parand K (2014) Numerical solution of Maxwell equations using local weak form meshless techniques. J Math Comput Sci 13:168–185
47.
Sengupta DL, Sarkar TK (2003) Maxwell, Hertz, the Maxwellians, and the early history of electromagnetic waves. IEEE Antennas Propag Mag 45:13–19CrossRef
48.
Shakeri F, Dehghan M (2013) A high order finite volume element method for solving elliptic partial integro-differential equations. Appl Numer Math 65:105–118MathSciNetCrossRefMATH
49.
Shakeri F, Dehghan M (2008) The method of lines for solution of the one-dimensional wave equation subject to an integral conservation condition. Comput Math Appl 56:2175–2188MathSciNetCrossRefMATH
50.
Shashkov M (1995) Conservative Finite-difference methods on general grids. CRC Press, USA
51.
Stuben K, Trottenberg U (1982) Multigrid methods: fundamental algorithms, model problem analysis and applications. Springer, BerlinMATH
52.
Xu J, Belytschko T Discontinuous radial basis function approximations for meshfree methods. Meshfree methods for partial differential equations II, volume 43 of the series lecture notes in computational science and engineering, pp 231–253
53.
Yee K (1966) Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. Antennas Propag 14:302–307CrossRefMATH
54.
Yu Y, Chen Z (2009) A 3-D radial point interpolation method for meshless time-domain modeling. Microw Theory Tech 57:2015–2020CrossRef
55.
Yu Y, Chen Z (2009) Towards the development of unconditionally stable time-domain meshless numerical methods. Microw Symp Dig, pp 7–12
56.
Yu Y, Chen Z (2010) Towards the development of an unconditionally stable time-domain meshless method. Microw Theory Tech 58:578–586CrossRef
57.
Zeng F, Ma H, Liang D (2014) Energy-conserved splitting spectral method for two-dimensional Maxwell’s equations. J Comput Appl Math 265:301–321MathSciNetCrossRefMATH
Metadaten
Titel
The local radial point interpolation meshless method for solving Maxwell equations
verfasst von
Mehdi Dehghan
Mina Haghjoo-Saniji
Publikationsdatum
25.03.2017
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 4/2017
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-017-0505-2

Weitere Artikel der Ausgabe 4/2017

Engineering with Computers 4/2017 Zur Ausgabe

Original Article

Edge-based anisotropic mesh adaptation of unstructured meshes with applications to compressible flows

Original Article

A 2D mechanical–thermal coupled model to simulate material mixing observed in friction stir welding process

Original Article

Estimation of blast-induced ground vibration through a soft computing framework

Original Article

Investigation of transport property of fibrous media: 3D virtual modeling and permeability calculation

Original Article

A local meshless method for solving multi-dimensional Vlasov–Poisson and Vlasov–Poisson–Fokker–Planck systems arising in plasma physics

Original Article

A Monte Carlo technique in safety assessment of slope under seismic condition

Neuer Inhalt

    Bildnachweise