Accession Number : AD1001342


Title :   Fast Implicit Methods For Elliptic Moving Interface Problems


Descriptive Note : Technical Report,30 Sep 2013,30 Sep 2015


Corporate Author : Regents of the University of California Berkeley United States


Personal Author(s) : Strain,John


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/1001342.pdf


Report Date : 11 Dec 2015


Pagination or Media Count : 66


Abstract : Two notable advances in numerical methods were supported by this grant. First, a fast algorithm was derived, analyzed, and tested for the Fourier transform of piecewise polynomials given on d-dimensional simplices in D-dimensional Euclidean space. These transforms play a key role in computational problems ranging from medical imaging to partial differential equations, and existing algorithms are inaccurate and/or prohibitively slow for d 0. The algorithm employs low-rank approximation by Taylor series organized in a butterfly scheme, with moments evaluated by a new dimensional recurrence and simplex quadrature rules. For moderate accuracy and problem size it runs orders of magnitude faster than direct evaluation, and one to three orders of magnitude slower than the classical uniform Fast Fourier Transform. Second, bilinear quadratures ---which numerically evaluate continuous bilinear maps, such as the L2 inner product, on continuous f and g belonging to known finite-dimensional function spaces---were analyzed and developed.


Descriptors :   algorithms , fast fourier transforms , polynomials , computational science , equations , Fourier series


Distribution Statement : APPROVED FOR PUBLIC RELEASE