Alternating Implicit Block FDTD Method For Scalar Wave Equation
In this paper, an alternating implicit block method for
solving two dimensional scalar wave equation is presented. The
new method consist of two stages for each time step implemented
in alternating directions which are very simple in computation. To
increase the speed of computation, a group of adjacent points is
computed simultaneously. It is shown that the presented method
increase the maximum time step size and more accurate than the
conventional finite difference time domain (FDTD) method and other
existing method of natural ordering.
[1] K.S.Yee, "Numerical solution of initial boundary value problem involving
Maxwell-s equations in isotropic media", IEEE Trans. Antennas Propagation,
AP-14 (1966) 302-307.
[2] Paul H. Aoyagi, Jin-Fa Lee, and R. Mittra, "A Hybrid Yee
Algorithm/Scalar-Wave Equation Approach", IEEE Trans. Microwave
Theory and Tech., 41(9) (1993) 1593-1600.
[3] D.J.Evans, "Group explicit methods for the numerical solution of partial
differential equations -(Topics in Computer Mathematics)", Gordon and
Breach Science Publishers, 1997.
[4] D.W. Peaceman and H.Rachford, "The numerical solution of parabolic
and ellptic differential equations", J. Soc. Indust. Appl. Math, 3 (1955)
505-512.
[5] V.K.Saul-yev, "Integration of equations of parabolic type equation by the
method of Net", Pergamon Press, New York, 1964.
[6] Rohallah Tavakoli and Parviz Davami, "New stable group explicit finite
difference method for solution of diffusion equation", Applied mathematics
and Computation, 181 (2006) 1379-1386.
[7] Rohallah Tavakoli and Parviz Davami, "2D parallel and stable group
explicit finite difference method for solution of diffusion equation",
Applied mathematics and Computation, 188 (2007) 1184-1192.
[8] N.M.Nusi, M. Othman, M. Suleiman, F. Ismail, and N. Alias, "Numerical
solution of 2D TM wave propagation with 4-point EG-FDTD scheme",
Proc. of the 4th International Conference on Research and Education in
Mathematics (ICREM4), Renaissance Hotel, Kuala Lumpur (2009) 21-23
Oct.
[1] K.S.Yee, "Numerical solution of initial boundary value problem involving
Maxwell-s equations in isotropic media", IEEE Trans. Antennas Propagation,
AP-14 (1966) 302-307.
[2] Paul H. Aoyagi, Jin-Fa Lee, and R. Mittra, "A Hybrid Yee
Algorithm/Scalar-Wave Equation Approach", IEEE Trans. Microwave
Theory and Tech., 41(9) (1993) 1593-1600.
[3] D.J.Evans, "Group explicit methods for the numerical solution of partial
differential equations -(Topics in Computer Mathematics)", Gordon and
Breach Science Publishers, 1997.
[4] D.W. Peaceman and H.Rachford, "The numerical solution of parabolic
and ellptic differential equations", J. Soc. Indust. Appl. Math, 3 (1955)
505-512.
[5] V.K.Saul-yev, "Integration of equations of parabolic type equation by the
method of Net", Pergamon Press, New York, 1964.
[6] Rohallah Tavakoli and Parviz Davami, "New stable group explicit finite
difference method for solution of diffusion equation", Applied mathematics
and Computation, 181 (2006) 1379-1386.
[7] Rohallah Tavakoli and Parviz Davami, "2D parallel and stable group
explicit finite difference method for solution of diffusion equation",
Applied mathematics and Computation, 188 (2007) 1184-1192.
[8] N.M.Nusi, M. Othman, M. Suleiman, F. Ismail, and N. Alias, "Numerical
solution of 2D TM wave propagation with 4-point EG-FDTD scheme",
Proc. of the 4th International Conference on Research and Education in
Mathematics (ICREM4), Renaissance Hotel, Kuala Lumpur (2009) 21-23
Oct.
@article{"International Journal of Electrical, Electronic and Communication Sciences:59996", author = "N. M. Nusi and M. Othman and M. Suleiman and F. Ismail and N. Alias", title = "Alternating Implicit Block FDTD Method For Scalar Wave Equation", abstract = "In this paper, an alternating implicit block method for
solving two dimensional scalar wave equation is presented. The
new method consist of two stages for each time step implemented
in alternating directions which are very simple in computation. To
increase the speed of computation, a group of adjacent points is
computed simultaneously. It is shown that the presented method
increase the maximum time step size and more accurate than the
conventional finite difference time domain (FDTD) method and other
existing method of natural ordering.", keywords = "FDTD, Scalar wave equation, alternating direction
implicit (ADI), alternating group explicit (AGE), asymmetric approximation.", volume = "6", number = "8", pages = "850-3", }