A SOFTWARE PACKAGE FOR SOLVING LARGE SYSTEMS OF NONLINEAR EQUATIONS

Award Information
Agency: National Aeronautics and Space Administration
Branch: N/A
Contract: N/A
Agency Tracking Number: 6764
Amount: $49,000.00
Phase: Phase I
Program: SBIR
Awards Year: 1988
Solicitation Year: N/A
Solicitation Topic Code: N/A
Solicitation Number: N/A
Small Business Information
Kuck & Assoc
1808 Woodfield Dr, Savory, IL, 61820
DUNS: N/A
HUBZone Owned: N
Woman Owned: N
Socially and Economically Disadvantaged: N
Principal Investigator
 DANIEL R WELLS
 () -
Business Contact
Phone: () -
Research Institution
N/A
Abstract
WE PROPOSE TO BUILD A SOFTWARE PACKAGE FOR SOLVING GENERAL LARGE SYSTEMS OF NONLINEAR EQUATIONS SUCH AS THOSE ARISING FROM NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS. PHASE I WILL FOCUS ON TESTING A RANGE OF METHODS BASED ON EFFICIENT VARIANTS OF NEWTON'S METHOD AND PRECONDITIONED CONJUGATE GRADIENT TYPE TECHNIQUES AS WELL AS ON A CLASS OF JACOBIAN-FREE ITERATIVE METHODS. THESE METHODS HAVE ATTRACTED MUCH INTEREST RECENTLY IN PARTICULAR AMONG THE COMPUTATIONAL FLUID DYNAMICS COMMUNITY, BECAUSE OF THEIR SIMPLICITY OF USAGE AND THEIR GENERALITY. THE PACKAGE WILL CONSIST OF TWO PARTS. ITS FIRST PART WILL USE EXPLICIT JACOBIANS AND WILL INTERFACE NEWTON'S METHOD WITH PRECONDITIONED CONJUGATE GRADIENT TYPE TECHNIQUES. ITS SECOND PART WILL BE BASED ON JACOBIAN-FREE METHODS WHICH AREPARTICULARLY DESIRABLE FOR ACCELERATING STANDARD NONLINEAR ITERATIONS OF THE FORM UN+1=M(UN) THAT ARISE IN MANY SPECIALIZED INDUSTRIAL CODES. THUS, THE PACKAGE WILL BE FLEXIBLE ENOUGH TO ALLOW USERS TO TAKE ADVANTAGE OF THEIR OWN AVAILABLE SOFTWARE, IF ANY. THE CODE WILL EMBODY THE BEST KNOWN METHODS TO HANDLE STRONG NONLINEARITIES BY TRUST REGION AND POSSIBLY HOMOTOPY TECHNIQUES AND TO TAKE ADVANTAGE OF SPARSITY. THE AIM OF THE PACKAGE IS TO COMBINE EFFICIENCY, FLEXIBILITY, ROBUSTNESS AND WIDE RANGE OF APPLICABILITY.

* information listed above is at the time of submission.

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