A new Eulerian method for the computation of propagating short acoustic and electromagnetic pulses

A new method is described to compute short acoustic or electromagnetic puls es that propagate according to geometrical optics. The pulses are treated a s zero thickness sheets that can propagate over long distances through inho mogeneous media with multiple reflections. The method has many of the advan tages of Lagrangian ray tracing, but is completely Eulerian, typically usin g a uniform Cartesian grid, Accordingly, it can treat arbitrary configurati ons of pulses that can reflect from surfaces and pass through each other wi thout requiring special computational marker arrays for each pulse, Also, i nformation describing the pulses, which are treated as continuous surfaces, can be available throughout the computational grid, rather than only at is olated individual markers. The method uses a new type of representation, wh ich we call "Dynamic Surface Extension." The basic idea is to propagate or "broadcast" defining fields from each pulse surface through a computational grid. These fields carry information about a nearby pulse surface that is used at each node to compute the location of the pulse surfaces and other a ttributes, such as amplitude. Thus the emphasis is on the dynamics of these propagating defining fields, which obey only local Eulerian equations at e ach node. The Dynamic Surface Extension representation can be thought of as dual to level set representation: The defining fields involve single value d variables which are constant at each time along lines that are normal to the evolving surface, whereas level set techniques involve a function which has constant values on the evolving surface and neighboring surfaces. In t his way the new method overcomes the inability of level set or Eikonal meth ods to treat intersecting pulses that obey a wave equation and can pass thr ough each other, while still using only single-valued variables. Propagatin g thin pulse surfaces in 1-D, 2-D, and 3-D that can reflect from boundaries and pass through each other are computed using the new method. The method was first presented as a new, general representation of surfaces, filaments , and particles by J. Steinhoff and M. Fan (1998, Eulerian computation of e volving surfaces, curves and discontinuous fields, UTSI preprint). (C) 2000 Academic Press.