MATRIX-FREE SOLUTION ALGORITHMS IN A FINITE ELEMENT CONTEXT

Award Information
Agency:
National Science Foundation
Branch
n/a
Amount:
$49,000.00
Award Year:
1988
Program:
SBIR
Phase:
Phase I
Contract:
n/a
Award Id:
7506
Agency Tracking Number:
7506
Solicitation Year:
n/a
Solicitation Topic Code:
n/a
Solicitation Number:
n/a
Small Business Information
1600 Orrington Avenue, Suite 400, Evanston, IL, 60201
Hubzone Owned:
N
Minority Owned:
N
Woman Owned:
N
Duns:
n/a
Principal Investigator:
MICHAEL S ENGELMAN PHD
() -
Business Contact:
() -
Research Institution:
n/a
Abstract
FINITE ELEMENT METHODS (FEM) APPLIED TO COMPUTATIONAL FLUID DYNAMICS OPEN UP THE POSSIBILITY OF NUMERICAL SIMULATION OF HIGHLY COMPLEX FLUID FLOWS OCCURRING IN INDUSTRIAL SITUATIONS. THE STATE-OF-THE-ART LIMITATION ON THE USE OF FEM IS COMPUTER RESOURCES: THE METHOD REQUIRES THE SOLUTION OF A VERY LARGE SYSTEM OF ALGEBRAIC EQUATIONS, CURRENTLY EFFECTED BY INVERTING THE JACOBIAN MATRIX, A PROCESS INVOLVING VERY HIGH COSTS IN COMPUTER TIME, IO AND PERIPHERAL STORAGE. THIS RESEARCH PROJECT AIMS TO INVESTIGATE AND IMPLEMENT A NEW MATRIX-FREE SOLUTION TECHNIQUE THAT OBVIATES THE COSTLY MATRIX INVERSION; THIS TECHNIQUE IS BASED ON A VARIANT OF THE CONJUGATE GRADIENT METHOD. RECENT RESEARCH AND TESTING ON SIMPLE PROBLEMS HAS INDICATED THE PROSPECT OF A DRAMATIC SAVING IN COSTS. SUCCESSFUL IMPLEMENTATION IN A FEM, FLUID DYNAMICS CONTEXT WILL VASTLY EXPAND THE RANGE OF FLOWS (TURBULENT, NON-NEWTONIAN, THREE-DIMENSIONAL) THAT CAN BE SIMULATED WITHCURRENTLY AVAILABLE HARDWARE.

* information listed above is at the time of submission.

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