Search results for "Strang splitting"

showing 3 items of 3 documents

Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well

2014

This paper is a direct offspring of Ref. [J. Math. Phys. 54, 072103, (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of mentions was maid with respect to various inconsistencies and faulty statements omnipresent in the literature devoted to so-called fractional quantum mechanics spectral problems. Presently, we give a decisive computer-assisted proof, for an exemplary finite and ultimately infinite Cauchy well problem, that spectral solutions proposed so far were plainly wrong. As a constructive input, we provide an explicit spectral solution of the finite Cauchy well. The infinite well emerges as a limiting case in a sequence of deep…

Quantum PhysicsStatistical Mechanics (cond-mat.stat-mech)Quantum dynamicsProbability (math.PR)FOS: Physical sciencesCauchy distributionStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Functional Analysis (math.FA)Schrödinger equationMathematics - Functional Analysissymbols.namesakeQuantum nonlocalityStrang splittingFOS: MathematicssymbolsApplied mathematicsQuantum Physics (quant-ph)Fractional quantum mechanicsSchrödinger's catEigenvalues and eigenvectorsMathematical PhysicsCondensed Matter - Statistical MechanicsMathematics - ProbabilityMathematics
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WENO schemes applied to the quasi-relativistic Vlasov-Maxwell model for laser-plasma interaction

2014

Abstract In this paper we focus on WENO-based methods for the simulation of the 1D Quasi-Relativistic Vlasov–Maxwell (QRVM) model used to describe how a laser wave interacts with and heats a plasma by penetrating into it. We propose several non-oscillatory methods based on either Runge–Kutta (explicit) or Time-Splitting (implicit) time discretizations. We then show preliminary numerical experiments.

Strategy and ManagementFOS: Physical sciences010103 numerical & computational mathematics01 natural scienceslaw.inventionMathematics::Numerical Analysislaser-plasma interactionMathematics - Analysis of PDEslawMedia TechnologyFOS: MathematicsVlasov--Maxwell[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]General Materials ScienceMathematics - Numerical Analysis0101 mathematicsMarketingPhysicsPhysics::Computational PhysicsWENOPlasmaNumerical Analysis (math.NA)Computational Physics (physics.comp-ph)LaserRunge--Kutta schemes010101 applied mathematicsClassical mechanicsStrang splittingFocus (optics)Physics - Computational PhysicsAnalysis of PDEs (math.AP)Strang splitting
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A semi-Lagrangian AMR scheme for 2D transport problems in conservation form

2013

In this paper, we construct a semi-Lagrangian (SL) Adaptive-Mesh-Refinement (AMR) solver for 1D and 2D transport problems in conservation form. First, we describe the a-la-Harten AMR framework: the adaptation process selects a hierarchical set of grids with different resolutions depending on the features of the integrand function, using as criteria the point value prediction via interpolation from coarser meshes, and the appearance of large gradients. We integrate in time by reconstructing at the feet of the characteristics through the Point-Value Weighted Essentially Non-Oscillatory (PV-WENO) interpolator. We propose, then, an extension to the 2D setting by making the time integration dime…

Numerical AnalysisMathematical optimizationSpeedupPhysics and Astronomy (miscellaneous)Adaptive mesh refinementApplied MathematicsFunction (mathematics)SolverComputer Science ApplicationsComputational MathematicsStrang splittingModeling and SimulationApplied mathematicsPolygon meshConservation formMathematicsInterpolationJournal of Computational Physics
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