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A brief review of some application driven fast algorithms for elliptic partial differential equations

Prabir Daripa (2012)

Open Mathematics

Some application driven fast algorithms developed by the author and his collaborators for elliptic partial differential equations are briefly reviewed here. Subsequent use of the ideas behind development of these algorithms for further development of other algorithms some of which are currently in progress is briefly mentioned. Serial and parallel implementation of these algorithms and their applications to some pure and applied problems are also briefly reviewed.

A Static condensation Reduced Basis Element method : approximation and a posteriori error estimation

Dinh Bao Phuong Huynh, David J. Knezevic, Anthony T. Patera (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose a new reduced basis element-cum-component mode synthesis approach for parametrized elliptic coercive partial differential equations. In the Offline stage we construct a Library of interoperable parametrized reference components relevant to some family of problems; in the Online stage we instantiate and connect reference components (at ports) to rapidly form and query parametric systems. The method is based on static condensation at the interdomain level, a conforming eigenfunction “port”...

An algebraic addition-theorem for Weierstrass' elliptic function and nomograms

Akira Matsuda (1979)

Aplikace matematiky

A dual transformation is discussed, by which a concurrent chart represented by one equation is transformed into an alignment chart or into a tangential contact chart. Using this transformation an alignment chart where three scales coincide and a tangential contact chart consisting of a family of circles, which represent the relation u + v + w = 0 , are constructed. In this case, a form of the addition-theorem for Weierstrass’ function involving no derivative is used.

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