International Journal for Numerical Methods in Engineering · 1991 · 60 citations · 22 references
EngineeringComputational EngineeringElectrical EngineeringComputational Heat TransferComputational MechanicsHeat TransferHeat ConductionHeat Transfer AnalysisHeat Transfer ModelingInverse Heat TransferInverse ProblemsNumerical Methods For Differential EquationsIll-posed Problem AnalysisInverse Conduction ProblemInverse Heat ConductionInverse Heat Conduction ProblemsParabolic Partial Differential Equations
Abstract A numerical method for the solution of inverse heat conduction problems in two‐dimensional rectangular domains is established and its performance is demonstrated by computational results. The present method extends Beck's 8 method to two spatial dimensions and also utilizes future times in order to stabilize the ill‐posedness of the underlying problems. The approach relies on a line approximation of the elliptic part of the parabolic differential equation leading to a system of one‐dimensional problems which can be decoupled.
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