Open AccessASYMPTOTICALLY OPTIMAL HIGH-ORDER ACCURATE ALGORITHMS FOR THE SOLUTION OF CERTAIN ELLIPTIC PDEs
Author(s) -
Leonid Kunyansky
Publication year - 2008
Language(s) - English
Resource type - Reports
DOI - 10.2172/953765
Subject(s) - eigenvalues and eigenvectors , algorithm , inverse problem , order (exchange) , asymptotically optimal algorithm , inversion (geology) , mathematics , computer science , mathematical analysis , physics , quantum mechanics , paleontology , finance , structural basin , economics , biology
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