Iterative Substructuring Methods for Elliptic Problems      and Related Algorithms
{'Code': '05010200', 'Directorate': {'Abbreviation': 'CSE', 'LongName': 'Direct For Computer & Info Scie & Enginr'}, 'Division': {'Abbreviation': 'CCF', 'LongName': 'Division of Computing and Communication Foundations'}}
{'SignBlockName': 'S. Kamal Abdali', 'PO_EMAI': None, 'PO_PHON': None}
This project continues to work on iterative substructuring methods.             These are iterative methods for large linear systems of algebraic               equations which arise when elliptic problems are discretized by finite          elements or finite differences.  The region of the problem is divided           into subregions (substructures) and the problems on the subregions are          solved repeatedly while using a preconditioned conjugate gradient               algorithm to satisfy the continuity requirements across the curves or           surfaces that divide the region.  Main current research issues are the          extension of these algorithms to nonconforming finite elements, mixed           methods, etc., and the development of new algorithms, particularly in           three dimensions.  This program will combine theoretical work with              systematic numerical experiments using both model problems and industrial       finite element codes.  The best of these algorithms often represent an          improvement over previously known methods on the uni processors and they        hold considerable promise for multi processor systems.                                                                                                          In addition, new algorithms for certain queuing network problems will be        developed.  Kolmogorov's balance equations are generated and the goal is        to compute the steady state probability distribution in terms of the null       element of the corresponding very large, sparse, nonsymmetric matrix.           The basic idea, which has proven quite successful in a number of cases,         is to use suitably chosen nearby decomposable problems as                       preconditioners.  These algorithms will be further developed, the theory        will be refined to try to explain the interesting distribution of the           singular values of the iteration matrices and an attempt will be made to        extend the applicability of methods to new classes of problems.                                                                                                 This research addresses new and faster methods for solving large systems        of linear equations, a computational task that is fundamental to many           scientific and engineering problems.
{'FirstName': 'Olof', 'LastName': 'Widlund', 'PI_MID_INIT': 'B', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Olof B Widlund', 'EmailAddress': 'widlund@cs.nyu.edu', 'PI_PHON': '2129983110', 'NSF_ID': '000456514', 'StartDate': '07/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'New York University', 'CityName': 'NEW YORK', 'ZipCode': '100121019', 'PhoneNumber': '2129982121', 'StreetAddress': '70 WASHINGTON SQ S', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '10', 'CONGRESS_DISTRICT_ORG': 'NY10', 'ORG_UEI_NUM': 'NX9PXMKW5KW8', 'ORG_LGL_BUS_NAME': 'NEW YORK UNIVERSITY', 'ORG_PRNT_UEI_NUM': 'NX9PXMKW5KW8'}
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[{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '2865', 'Text': 'NUMERIC, SYMBOLIC & GEO COMPUT'}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8703768.xml'}