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 :

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