Convexification Numerical Method for a Coefficient Inverse Problem for the Radiative Transport Equation
Michael V. Klibanov, Jingzhi Li, Loc H. Nguyen, Zhipeng Yang
Abstract
.An \((n+1)\) -D coefficient inverse problem for the stationary radiative transport equation is considered for the first time. A globally convergent so-called convexification numerical method is developed and its convergence analysis is provided. The analysis is based on a Carleman estimate. Extensive numerical studies in the two-dimensional case are presented.Keywordscoefficient inverse problemradiative transport equationconvexification methodspecial orthonormal basisglobal convergence analysisnumerical experimentsMSC codes35R3065M32
Topics & Concepts
Radiative transferInverse problemConvergence (economics)MathematicsNumerical analysisInverseApplied mathematicsMathematical analysisConvection–diffusion equationPhysicsGeometryOpticsEconomic growthEconomicsNumerical methods in inverse problemsRadiative Heat Transfer StudiesMicrowave Imaging and Scattering Analysis