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2018-05-10
Unconditional Stability Analysis of the 3D-Radial Point Interpolation Method and Crank-Nicolson Scheme
By
Progress In Electromagnetics Research M, Vol. 68, 119-131, 2018
Abstract
This paper provides the theoretical validation of the unconditional stability, using the Von Neumann method, for the radial point interpolation method (RPIM) and Crank-Nicolson (CN) scheme, in a three dimensional (3D) problem. Moreover, the matrix inversion process, typical of the CN implicit scheme, is circumvented and approximated by a finite series for a particular stability factor range. To validate numerically the efficiency of the CN-RPIM unconditional stability, the resonant frequency inside a 2D double ridged rectangular cavity is simulated. The numerical results confirm that the CN-RPIM is significantly efficient, since the simulation time is reduced by up to 90%, and the memory requirement is saved up to 81%, with a few loss of accuracy.
Citation
Naamen Hichem Taoufik Aguili , "Unconditional Stability Analysis of the 3D-Radial Point Interpolation Method and Crank-Nicolson Scheme," Progress In Electromagnetics Research M, Vol. 68, 119-131, 2018.
doi:10.2528/PIERM17100201
http://www.jpier.org/PIERM/pier.php?paper=17100201
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