Convexification for an inverse parabolic problem
Michael V. Klibanov, Jingzhi Li, Wenlong Zhang
Abstract
Abstract A convexification-based numerical method for a coefficient inverse problem for a parabolic PDE is presented. The key element of this method is the presence of the so-called Carleman weight function in the numerical scheme. Convergence analysis ensures the global convergence of this method, as opposed to the local convergence of the conventional least squares minimization techniques. Numerical results demonstrate a good performance.
Topics & Concepts
MathematicsConvergence (economics)Inverse problemInverseMinificationApplied mathematicsWeight functionNumerical analysisFinite element methodFunction (biology)Parabolic partial differential equationMathematical analysisMathematical optimizationPartial differential equationGeometryThermodynamicsEconomicsEvolutionary biologyBiologyPhysicsEconomic growthNumerical methods in inverse problemsComposite Material MechanicsAdvanced Mathematical Modeling in Engineering