Speaker
Description
The injection and absorption of waves entering or escaping open boundaries in EM-PIC simulations is of interest provided the numerical reflections are low, and the boundary is stable. The Higdon [1] operator method provides the basis of a multi-phase velocity matching algorithm. The potential for high order implementation provides for (a) injection of low reflection incident waves into the interior of the simulation environment, (b) near perfect absorption of scattered outgoing waves, and (c) is insensitive in EM-PIC to particles traversing the boundary edge. This method has been applied with substantial success in several wave equation environments. These include dispersive electromagnetic wave modeling, as well as the shallow water equations and acoustic phenomena.
The general Higdon operator of order J may be described as follows for wave propagation along the x axis, as the product of multiple uni-directional wave equations, each product uses a potentially unique value of phase velocity. For J=1, this reduces to the standard 1-dimensional wave equation in which the sign of the phase velocity indicate either a forward or backward traveling wave. As J, the number of product terms, increases it is necessary to capture information that is more remote spatially and temporally from the boundary edge. Givoli and Neta [1] suggested the method of recasting the solution in terms of auxiliary functions of arbitrarily high order. We will report on our implementation of this method for 1st and 2nd order FD approximations and the effectiveness on broadband transmission.
1. Dan Givoli and Ben Neta, “High-Order Higdon Non-Reflecting Boundary Conditions for the Shallow Water Equations”, NAVAL POSTGRADUATE SCHOOL, Monterey, CA, NPS-MA-02-001, April 2002.
