The Construction of Initial Data for Hyperbolic Systems from Nonstandard Data.
STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE
Pagination or Media Count:
We study first order systems of hyperbolic partial differential equations with periodic boundary conditions in the space variables for which complete initial data are not available. We suppose that we can measure UI, the first j components of a solution u of the system, perhaps with its time derivatives, but cannot measure uII, the rest of the components of u, completely and accurately at any time level. Such problems arise in geophysical applications where satellites are used to collect data. We consider two questions how much information is needed to determine the solution uniquely in a way which depends continuously on the data and how are these data computationally used to obtain complete initial data at some time level. One application we examine is the effect of the Coriolis term in the linearized shallow water equations on the possibility of recovering the wind fields from the geopotential height. We present algorithms and computational results for these approaches for a model two-by-two system, and examine the method of intermittent updating currently being used in numerical weather prediction as a method for the assimilation of data. Our results suggest that the use of different frequencies of updating is important to avoid slow convergence.
- Numerical Mathematics
- Computer Programming and Software