Inverse Problems · 2006 · 100 citations · 7 references
Natural SciencesMathematicsComputational MechanicsComputational PhysicsDifferential EquationsConvergence AnalysisMaxwell's EquationsNumerical Methods For Differential EquationsPartial Differential EquationsAcoustic Radiation ProblemsCauchy ProblemHelmholtz EquationIll-posed Problem RegularizationNumerical ModelingRadiation ProblemsRegularizationRegularization Techniques
A problem of reconstruction of the radiation field in a domain from experimental data given on a part of boundary is considered. For the model problem described by a Cauchy problem for the Helmholtz equation, an approximate method based on regularization in the frequency space is analysed. Convergence and stability are proved under a suitable choice of regularization parameter. Numerical implementation of the method is discussed.
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