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Ridgelet Methods for Linear Transport Equations

by P. Grohs and A. Obermeier

(Report number 2014-35)

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 [GO14,EGO14]. 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.

Keywords: Adaptive Frame Methods, Ridgelets, Optimal Complexity, Radiative Transport

@Techreport{GO14_585,
  author = {P. Grohs and A. Obermeier},
  title = {Ridgelet Methods for Linear Transport Equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2014-35},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2014/2014-35.pdf },
  year = {2014}
}

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