Search results for "Gravitational singularity"

showing 3 items of 163 documents

Up-wind difference approximation and singularity formation for a slow erosion model

2020

We consider a model for a granular flow in the slow erosion limit introduced in [31]. We propose an up-wind numerical scheme for this problem and show that the approximate solutions generated by the scheme converge to the unique entropy solution. Numerical examples are also presented showing the reliability of the scheme. We study also the finite time singularity formation for the model with the singularity tracking method, and we characterize the singularities as shocks in the solution.

granular flowsNumerical AnalysisEntropy solutionsup-wind schemeApplied MathematicsMathematical analysisEngquist–Osher schemeEntropy solutions up-wind scheme Engquist–Osher scheme spectral analysis complex singularities granular flowsspectral analysiscomplex singularitiesComputational MathematicsSingularityEntropy solutions / up-wind scheme / Engquist–Osher scheme / spectral analysis / complex singularities / granular flowsModeling and SimulationSpectral analysisGravitational singularityFinite timeSettore MAT/07 - Fisica MatematicaAnalysisMathematics
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A Complete, Exact and Efficient Implementation for Computing the Edge-Adjacency Graph of an Arrangement of Quadrics

2011

International audience; We present a complete, exact and efficient implementation to compute the edge-adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the edge-adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always comp…

pencils of quadricsIntersection curveComputation010103 numerical & computational mathematics02 engineering and technology[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]01 natural sciencesInterval arithmeticCombinatorics0202 electrical engineering electronic engineering information engineering0101 mathematicsAlgebraic numberMathematicsDiscrete mathematics[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]Algebra and Number TheoryImplicit functionDegenerate energy levels020207 software engineeringComputational Mathematicsintersection of surfacesAdjacency listcurve parameterizationGravitational singularityArrangementquadricsMathematicsofComputing_DISCRETEMATHEMATICS
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Numerical Recovery of Source Singularities via the Radiative Transfer Equation with Partial Data

2013

The inverse source problem for the radiative transfer equation is considered, with partial data. Here we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$ where $X_{V}$ is the partial data solution operator to the radiative transfer equation. The numerical scheme is based in part on a forward solver designed by F. Monard and G. Bal. We will see that one can detect quite well the visible singularities of an internal optical source $f$ for generic anisotropic $k$ and $\sigma$, with or without noise added to the accessible data $X_{V}f$. In particular, we use a truncated Neumann series to estimate $X_{V}$ and $X_{V}^{*}$, which provides a good approximation of $X_{V}^{*…

ta113Applied MathematicsGeneral MathematicsOperator (physics)ta111010102 general mathematicsMathematical analysisMicrolocal analysisNumerical Analysis (math.NA)Inverse problem01 natural sciences35R30 (Primary) 35S05 35R09 35Q20 92C55Neumann series010101 applied mathematicsSobolev spaceMathematics - Analysis of PDEsRadiative transferFOS: MathematicsGravitational singularityMathematics - Numerical Analysis0101 mathematicsAnisotropyMathematicsAnalysis of PDEs (math.AP)
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