Title:
DETERMINING FIELD-DEPENDENT CHARACTERISTICS BY EMPLOYING HIGH-ORDER QUADRATURES IN THE PRESENCE OF GEOMETRIC SINGULARITIES
Document Type and Number:
WIPO Patent Application WO2004023352
Kind Code:
A3
Abstract:
A machine for determining field-dependent physical characteristics contains tables of precomputed quadratures and employs them to integrate numerically over a problem boundary. The quadratures are based on products of a kernel function and a basis s that spans a wide range of density functions. The kernel function is dependent on a target node's position, and different quadratures are precomputed for different target-node positions or ranges thereof. In the case of at least some of the quadratures, some the basis functions include integrable singularities. The solver divides the problem boundary into a plurality of problem intervals, to which it maps the canonical interval. To integrate a problem interval for a target point, the solver employs a precomputed quadrature that is associated with the target point's relative position and that was generated by using a basis in which a singularity occurs at each canonical-interval location that was mapped to a geometrical singularity on the problem interval. The quadrature results in high-order accuracy even if no individual basis function includes a singularity whose shape is the same as one induced by the geometric singularity. These quadratures can be coupled with a Fast Multipole Method ("FMM") to evaluate layer potentials rapidly and with high accuracy.
Inventors:
CRUTCHFIELD WILLIAM Y (US)
ETHRIDGE JOSEPH FRANKLIN (US)
GIMBUTAS ZYDRUNAS (US)
GREENGARD LESLIE F (US)
ROKHLIN VLADIMIR (US)
ETHRIDGE JOSEPH FRANKLIN (US)
GIMBUTAS ZYDRUNAS (US)
GREENGARD LESLIE F (US)
ROKHLIN VLADIMIR (US)
Application Number:
PCT/US2003/028229
Publication Date:
August 05, 2004
Filing Date:
September 08, 2003
Export Citation:
Assignee:
MAD MAX OPTICS INC (US)
CRUTCHFIELD WILLIAM Y (US)
ETHRIDGE JOSEPH FRANKLIN (US)
GIMBUTAS ZYDRUNAS (US)
GREENGARD LESLIE F (US)
ROKHLIN VLADIMIR (US)
CRUTCHFIELD WILLIAM Y (US)
ETHRIDGE JOSEPH FRANKLIN (US)
GIMBUTAS ZYDRUNAS (US)
GREENGARD LESLIE F (US)
ROKHLIN VLADIMIR (US)
International Classes:
G06F17/13; G06F17/50; (IPC1-7): G06F17/50
Other References:
KOLM P ET AL: "Numerical quadratures for singular and hypersingular integrals", COMPUT. MATH. APPL. (UK), COMPUTERS & MATHEMATICS WITH APPLICATIONS, FEB. 2001, ELSEVIER, UK, vol. 41, no. 3-4, February 2001 (2001-02-01), pages 327 - 352, XP002280179, ISSN: 0898-1221
YARVIN N ET AL: "An improved fast multipole algorithm for potential fields on the line", SIAM J. NUMER. ANAL. (USA), SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, SIAM, USA, vol. 36, no. 2, 1999, pages 629 - 666, XP008030571, ISSN: 0036-1429
PLACE J ET AL: "Efficient numerical integration using Gaussian quadrature", SIMULATION (USA), SIMULATION, OCT. 1999, SIMULATION COUNCILS, USA, vol. 73, no. 4, October 1999 (1999-10-01), pages 232 - 238, XP008030556, ISSN: 0037-5497
YARVIN N ET AL: "An improved fast multipole algorithm for potential fields on the line", SIAM J. NUMER. ANAL. (USA), SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, SIAM, USA, vol. 36, no. 2, 1999, pages 629 - 666, XP008030571, ISSN: 0036-1429
PLACE J ET AL: "Efficient numerical integration using Gaussian quadrature", SIMULATION (USA), SIMULATION, OCT. 1999, SIMULATION COUNCILS, USA, vol. 73, no. 4, October 1999 (1999-10-01), pages 232 - 238, XP008030556, ISSN: 0037-5497
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