Search results for " 65M70"

showing 2 items of 2 documents

Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems

2019

In this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together with previous results on upper bounds (majorants) for one of the cost functionals, both minorants and majorants lead to two-sided estimates of functional type for the optimal control problem. Both upper and lower bounds are derived for the second new cost functional subject to the same parabolic PDE-constraints, but where the target is a desired gradient. The time-periodic optimal control problems are discretized by the multiharmonic finite element method leading to lar…

Optimization problemtime-periodic conditionmultiharmonic finite element methodDiscretizationtwo-sided boundsSystems and Control (eess.SY)010103 numerical & computational mathematicsSystem of linear equationsElectrical Engineering and Systems Science - Systems and Control01 natural sciencesUpper and lower boundsSaddle pointFOS: MathematicsFOS: Electrical engineering electronic engineering information engineeringApplied mathematicsMathematics - Numerical AnalysisBoundary value problem0101 mathematicsMathematics - Optimization and ControlMathematicsosittaisdifferentiaaliyhtälöt35Kxx 65M60 65M70 65M15 65K10parabolic optimal control problemsNumerical Analysis (math.NA)matemaattinen optimointiOptimal controlFinite element method010101 applied mathematicsComputational MathematicsComputational Theory and MathematicsOptimization and Control (math.OC)Modeling and Simulationa posteriori error analysisnumeerinen analyysiguaranteed lower boundsComputers & Mathematics with Applications
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On a nonlinear Schrödinger equation for nucleons in one space dimension

2021

We study a 1D nonlinear Schrödinger equation appearing in the description of a particle inside an atomic nucleus. For various nonlinearities, the ground states are discussed and given in explicit form. Their stability is studied numerically via the time evolution of perturbed ground states. In the time evolution of general localized initial data, they are shown to appear in the long time behaviour of certain cases.

numerical studySpace dimensionNonlinear Schrö010103 numerical & computational mathematicsNonlinear Schrödinger equations01 natural sciencesStability (probability)symbols.namesakeMathematics - Analysis of PDEs[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Mathematics - Numerical Analysis0101 mathematics[MATH]Mathematics [math]dinger equationsNonlinear Schrödinger equationMathematicsMSC 35Q55 35C08 65M70Numerical AnalysisApplied Mathematics010102 general mathematicsTime evolutionground statesComputational MathematicsClassical mechanicsModeling and SimulationAtomic nucleussymbolsParticleNucleonAnalysis[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
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