Search results for " 65M60"

showing 4 items of 4 documents

Fast MATLAB assembly of FEM matrices in 2D and 3D: Edge elements

2014

We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in discretizations of H(div) spaces and Nedelec elements in discretizations of H(curl) spaces. We explain vectorization ideas and comment on a freely available MATLAB code which is fast and scalable with respect to time.

FOS: Computer and information sciencesDiscretizationfinite element method97N80 65M60Matlab codeComputational scienceMathematics::Numerical AnalysisMATLAB code vectorizationmedicineFOS: MathematicsMathematics - Numerical AnalysisMATLABMathematicscomputer.programming_languageCurl (mathematics)ta113Nédélec elementApplied Mathematicsta111StiffnessRaviart–Thomas elementMixed finite element methodNumerical Analysis (math.NA)Finite element methodComputational Mathematicsedge elementScalabilityComputer Science - Mathematical Softwaremedicine.symptomcomputerMathematical Software (cs.MS)
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Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems

2015

This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed

Mathematical optimizationControl and OptimizationMathematicsofComputing_NUMERICALANALYSISFinite element approximations010103 numerical & computational mathematicsType (model theory)01 natural sciencesparabolic time-periodic optimal control problemsError analysisFOS: MathematicsApplied mathematicsMathematics - Numerical AnalysisNumerical testsfunctional a posteriori error estimates0101 mathematicsMathematics - Optimization and Control49N20 35Q61 65M60 65F08Mathematicsta113Time periodicta111Numerical Analysis (math.NA)State (functional analysis)Optimal controlComputer Science Applications010101 applied mathematicsOptimization and Control (math.OC)multiharmonic finite element methodsSignal ProcessingA priori and a posterioriAnalysisNumerical Functional Analysis and Optimization
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Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part II: A linear scheme

2017

This is the second part of our error analysis of the stabilized Lagrange-Galerkin scheme applied to the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's stabilization method for the conforming linear elements, which leads to an efficient computation with a small number of degrees of freedom especially in three space dimensions. In this paper, Part II, we apply a semi-implicit time discretization which yields the linear scheme. We concentrate on the diffusive viscoelastic model, i.e. in the constitutive equation for time evolution of the conformation tensor a diffusive effect is included. Under mild stability condi…

Numerical AnalysisApplied MathematicsComputationNumerical analysisDegrees of freedom (statistics)010103 numerical & computational mathematicsNumerical Analysis (math.NA)01 natural sciences010101 applied mathematicsComputational MathematicsNonlinear systemMethod of characteristicsModeling and SimulationConvergence (routing)FOS: MathematicsApplied mathematicsTensorMathematics - Numerical Analysis65M12 76A05 65M60 65M250101 mathematicsGalerkin methodAnalysisMathematics
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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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