This research project deals with a development of highly accurate approximate solution techniques for wave-type phenomena characterized by linear hyperbolic equations. Potential applications include, but are not limited to numerical simulation of propagation of acoustic, elastic, and electromagnetic waves, as well as to analysis of various coupled systems. Several features of this research are significant. For example, high-order radiating boundary conditions are critical for treating unbounded domain problems, and split boundary operators promise high accuracy while providing a posteriori indicator of the error introduce by domain truncation. High-Order Temporal Approximations including new, implicit, unconditionally stable TG (Taylor-Galerkin) schemes promise high accuracy while balancing in an optimal way the variable high-order spatial approximations. Also, hp-data structures and adaptive methods involve date structure in which the mesh size h and the spectral order p of a finite element approximation of a spatial variation of the dependent variables can be varied throughout the (spatial) mesh. If these parameters can be orchestrated in an optimal way, exponential convergence can be attained, meaning that highly accurate results are possible with few degrees of freedom. Smart algorithms are developed in that by monitoring errors in the hp-TG schemes and in radiating boundary operators, automatic changes in solution algorithms can be introduced. The research yields highly accurate computational methods having a potential of reliably resolving the fine-scale and large-scale features of scattering and radiation phenomena needed in advanced designs.

Project Start
Project End
Budget Start
1998-01-01
Budget End
2001-09-30
Support Year
Fiscal Year
1997
Total Cost
$191,211
Indirect Cost
Name
University of Nebraska-Lincoln
Department
Type
DUNS #
City
Lincoln
State
NE
Country
United States
Zip Code
68588