Commun. Comput. Phys., 1 (2006), pp. 311-335.


An Accurate Numerical Scheme for Maxwell Equation with CIP-Method of Characteristics

Youichi Ogata 1, Takashi Yabe 1*, Kouichi Odagaki 1

1 Department of Mechanical Sciences and Engineering, Tokyo Institute of Technology, 2-12-1 Meguro-ku, Ookayama 152-8552, Japan.

Received 1 November 2005; Accepted (in revised version) 24 November 2005

Abstract

A new multi-dimensional scheme for the Maxwell equations is established by the CIP method in combination with the method of chracteristics(CIP-MOC). In addition, the CIP-MOC can be extened to arbitrary grid system by the Soroban grid without losing the thrid-order accuracy. With the accuracy fixed, the grid points required for the CIP are 40 times less than the conventional schemes like the FDTD in three dimensions. Numerical solutions obtained by the CIP-MOC are compared with analytical solution and the FDTD in plane-wave scattering by a perfectly-conducting circular cylinder, and the CIP-MOC agrees very well with analytical solutions. The Soroban grid is also applied to the Vlasov equation that describes the kinematics of plasmas that is frequently combined with the Maxwell equation. The adaptively moving points in velocity space are similar to the particle codes but can provide accurate solutions.


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Key words: Maxwell equation; Vlasov equation; CIP method; method of characteristics; Soroban grid.


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Correspondence to: Takashi Yabe , Department of Mechanical Sciences and Engineering, Tokyo Institute of Technology, 2-12-1 Meguro-ku, Ookayama 152-8552, Japan. Email: yabe@mech.titech.ac.jp
 

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