PARALLEL METHODS FOR THE SCHROEDINGER EQUATION

Award Information
Agency:
Department of Commerce
Branch
n/a
Amount:
$46,548.00
Award Year:
1994
Program:
SBIR
Phase:
Phase I
Contract:
n/a
Award Id:
26845
Agency Tracking Number:
26845
Solicitation Year:
n/a
Solicitation Topic Code:
n/a
Solicitation Number:
n/a
Small Business Information
1 Memorial Dr, Cambridge, MA, 02142
Hubzone Owned:
N
Minority Owned:
N
Woman Owned:
N
Duns:
n/a
Principal Investigator:
John Weiss
(617) 577-1700
Business Contact:
() -
Research Institution:
n/a
Abstract
WE WILL DEVELOP WAVELET-BASED DOMAIN DECOMPOSITION PROCEDURES FOR THE SOLUTION OF THE INITIAL VALUE PROBLEM FOR THE SCHROEDINGER EQUATION ON MULTIDIMENSIONAL SPATIAL DOMAINS. ACCURATE AND PRACTICAL NUMERICAL CALCULATIONS WOULD BE OF GREAT USE IN THE IMPLEMENTATION AND EXTENSION OF THE BORN-OPPENHEIMER PROCEDURE. BEING BOTH COMPACTLY SUPPORTED AND ORTHOGONAL, WAVELETS COMBINE THE ADVANTAGES OF FINITE ELEMENT, SPLINE AND FOURIER SPECTRAL METHODS. THE SYMMETRIES OF OPERATORS AND OMAINS ARE PRESERVED BY OUR METHOD. FOR DOMAINS WITH A HIGH LEVEL OF SYMMETRY, THIS ALLOWS THE ACCURATE NUMERICAL RESOLUTION OF DISCRETELY ORTHOGONAL SPACES THAT BLOCK DIAGONALIZE THE OPERATOR IN THESE DOMAINS. THESE RESULTS HAVE INTERESTING APPLICATIONS TO DOMAIN DECOMPOSITION, SINCE THEY ALLOW THE DEFINITION OF HIGHLY ACCURATE WAVELET ELEMENTS THAT SHOULD BE SIMPLE TO MATCH ACROSS ELEMENT BOUNDARIES. THE COUPLING OF SOLUTION AND BOUNDARY CONDITION IMPLIED BY OUR METHOD WILL LEAD TO A SUBSTANTIAL IMPROVEMENT IN SPEED AND ACCURACY THAT WILL SCALE WITH INCREASES IN THE SIZE AND COMPLEXITY OF A PROBLEM.

* information listed above is at the time of submission.

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