Ridgelet Methods for Linear Transport Equations

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9213)

Abstract

In this paper we present an overview of a novel method for the numerical solution of linear transport equations, which is based on ridgelets and has been introduced in [12, 16]. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that ridgelet systems are well adapted to the structure of linear transport operators, it can be shown that our scheme operates in optimal complexity, even if line singularities are present in the solution. After presenting the basic algorithm, we prove that certain operators are compressible, which is the key to obtain unconditional convergence results. Finally, we show some applications in radiative transport.

Notes

Acknowledgements

The second author gratefully acknowledges support for this work by the Swiss National Science Foundation, Project 146356.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Seminar for Applied Mathematics, Mathematics DepartmentSwiss Federal Institute of TechnologyZürichSwitzerland

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