Fast Implicit Methods For Elliptic Moving Interface Problems
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 11, 2015
- Accession Number
- AD1001342
Entities
People
- John Strain
Organizations
- University of California Regents