We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining,accessible and known pa...We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining,accessible and known part of the boundary of a two-dimensional domain,for problems governed by Helmholtz-type equations.This inverse geometric problem is solved using the plane wavesmethod(PWM)in conjunction with the Tikhonov regularizationmethod.The value for the regularization parameter is chosen according toHansen’s L-curve criterion.The stability,convergence,accuracy and efficiency of the proposedmethod are investigated by considering several examples.展开更多
文摘We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining,accessible and known part of the boundary of a two-dimensional domain,for problems governed by Helmholtz-type equations.This inverse geometric problem is solved using the plane wavesmethod(PWM)in conjunction with the Tikhonov regularizationmethod.The value for the regularization parameter is chosen according toHansen’s L-curve criterion.The stability,convergence,accuracy and efficiency of the proposedmethod are investigated by considering several examples.
