Asymptotically Optimal High-Order Accurate Algorithms for the Solution of Certain Elliptic PDEs

Kunyansky, Leonid

University of Arizona

关键词: Acoustics;    Wave Equations;    Algorithms;    Tomography;    97 Mathematics And Computing;   

DOI  :  10.2172/953765
RP-ID  :  DOE-ER25577
RP-ID  :  FG02-03ER25577
RP-ID  :  953765

美国|英语

来源: UNT Digital Library

【 摘 要 】

The main goal of the project, "Asymptotically Optimal, High-Order Accurate Algorithms for the Solution of Certain Elliptic PDE's" (DE-FG02-03ER25577) was to develop fast, high-order algorithms for the solution of scattering problems and spectral problems of photonic crystals theory. The results we obtained lie in three areas: (1) asymptotically fast, high-order algorithms for the solution of eigenvalue problems of photonics, (2) fast, high-order algorithms for the solution of acoustic and electromagnetic scattering problems in the inhomogeneous media, and (3) inversion formulas and fast algorithms for the inverse source problem for the acoustic wave equation, with applications to thermo- and opto- acoustic tomography.