Search
Results
-
On the Approximation of Functions with Line Singularities by Ridgelets
(2016)Research reports / Seminar for Applied MathematicsReport -
Ridgelet Methods for Linear Transport Equations
(2014)Research ReportIn 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 ...Report -
FFRT - A Fast Finite Ridgelet Transform for Radiative Transport
(2014)Research ReportThis paper introduces an FFT-based implementation of a fast finite ridgelet transform which we call FFRT. Inspired by recent work where it was shown that ridgelet discretizations of linear transport equations can be easily preconditioned by diagonal preconditioning we use the FFRT for the numerical solution of such equations. Combining this FFRT-based method with a sparse collocation scheme we construct a novel solver for the radiative ...Report -
Optimal Adaptive Ridgelet Schemes for Linear Transport Equations
(2014)Research ReportIn this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. 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. The ...Report