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• W3208346350 abstract "Context. Several numerical problems require the interpolation of discretedata that present various types of discontinuities. The radiative transfer is atypical example of such a problem. This calls for high-order well-behavedtechniques to interpolate both smooth and discontinuous data. Aims. The finalaim is to propose new techniques suitable for applications in the context ofnumerical radiative transfer. Methods. We have proposed and tested twodifferent techniques. Essentially non-oscillatory (ENO) techniques generateseveral candidate interpolations based on different substencils. The smoothestcandidate interpolation is determined from a measure for the local smoothness,thereby enabling the essential non-oscillatory property. Weighted ENO (WENO)techniques use a convex combination of all candidate substencils to obtainhigh-order accuracy in smooth regions while keeping the essentiallynon-oscillatory property. In particular, we have outlined and tested a novelwell-performing fourth-order WENO interpolation technique for both uniform andnonuniform grids. Results. Numerical tests prove that the fourth-order WENOinterpolation guarantees fourth-order accuracy in smooth regions of theinterpolated functions. In the presence of discontinuities, the fourth-orderWENO interpolation enables the non-oscillatory property, avoiding oscillations.Unlike B'ezier and monotonic high-order Hermite interpolations, it does notdegenerate to a linear interpolation near smooth extrema of the interpolatedfunction. Conclusions. The novel fourth-order WENO interpolation guaranteeshigh accuracy in smooth regions, while effectively handling discontinuities.This interpolation technique might be particularly suitable for severalproblems, including a number of radiative transfer applications such asmultidimensional problems, multigrid methods, and formal solutions." @default.
• W3208346350 created "2021-11-08" @default.
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• W3208346350 date "2021-10-22" @default.
• W3208346350 modified "2023-09-27" @default.
• W3208346350 title "A novel fourth-order WENO interpolation technique. A possible new tool designed for radiative transfer." @default.
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