A New Way to Make Waves
Abstract
Description
I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other systems described by second differential order hyperbolic equations. The basic ideas should also be applicable to hydrodynamics. It is an especially accurate and efficient way for simulating waves in regions where the characteristics are well behaved. A prime application of the algorithm is to Cauchy-characteristic matching, in which this new approach is matched to a standard Cauchy evolution to obtain a global solution. In a model problem of a nonlinear wave, this proves to be more accurate and efficient than any other present method of assigning Cauchy outer boundary conditions. The approach was developed to compute the gravitational wave signal produced by collisions of two black holes. An application to colliding black holes is presented.
In Proceeding of CIMENICS 2000, The Vth International Congress on Numerical Methods in Engineering and Applied Science (Puerto La Cruz, Venezuela, March 2000)
In Proceeding of CIMENICS 2000, The Vth International Congress on Numerical Methods in Engineering and Applied Science (Puerto La Cruz, Venezuela, March 2000)