 
Summary: Journal of Computational Physics 180, 270296 (2002)
doi:10.1006/jcph.2002.7093
Nonreflecting Boundary Conditions for the
TimeDependent Wave Equation
Bradley Alpert,,1
Leslie Greengard,,2
and Thomas Hagstrom,3
National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305; Courant Institute
of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 100121110; and
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131
Email: alpert@boulder.nist.gov, greengard@cims.nyu.edu, and hagstrom@math.unm.edu
Received August 1, 2001; revised April 23, 2002
We describe a new, efficient approach to the imposition of exact nonreflecting
boundary conditions for the scalar wave equation. We compare the performance of
our approach with that of existing methods by coupling the boundary conditions to
finitedifference schemes. Numerical experiments demonstrate a significant gain in
accuracy at no additional cost. c 2002 Elsevier Science (USA)
1. INTRODUCTION
The scalar wave equation and Maxwell's equations govern problems in such diverse
application areas as ultrasonics, seismics, underwater acoustics, antenna design, and mi
