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Accuracy Controlled Schemes for the Neutron Transport Equation

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FKTW05 - Frontiers in numerical analysis of kinetic equations

In this talk we discuss concepts for the numerical solution of the neutron transport equation with the following key feature: for a  given target accuracy an approximate solution is generated that is guaranteed to meet this tolerance with respect to an $L_2$ norm over the spatial and velocity domain. Key ingredients are: formulating an idealized convergent iteration in function space; stable variational formulations of transport equations, in particular, Discontinuous Petrov Galerkin methods and corresponding tight residual a-posteriori error bounds, that allow one to approximately realize the iterates within judiciously chosen dynamic target accuracies; wavelet compression and low-rank approximation of scattering kernels that warrant their efficient application. Thus, rather than solving a fixed discrete problem, discretizations are perpetually updated in an accuracy controlled  nested-refinement spirit. If time permits we indicate how these concepts for solving source problems are used in ongoing work to deal with the criticality problem.  Wolfgang Dahmen Mathematics Department, University of South Carolina, Columbia, SC 292018 , USA                    (joint work with F. Gruber, O. Mula, R. Stevenson)

This talk is part of the Isaac Newton Institute Seminar Series series.

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