Stable Identification of Sources Located on Interface of Nonhomogeneous Media

José Julio Conde Mones, Emmanuel Roberto Estrada Aguayo, José Jacobo Oliveros Oliveros, Carlos Arturo Hernández Gracidas and María Monserrat Morín Castillo
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José Julio Conde Mones: Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, Colonia San Manuel, Ciudad Universitaria, Puebla C.P. 72570, Mexico
Emmanuel Roberto Estrada Aguayo: Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, Colonia San Manuel, Ciudad Universitaria, Puebla C.P. 72570, Mexico
José Jacobo Oliveros Oliveros: Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, Colonia San Manuel, Ciudad Universitaria, Puebla C.P. 72570, Mexico
Carlos Arturo Hernández Gracidas: CONACYT-BUAP, Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, Colonia San Manuel, Ciudad Universitaria, Puebla C.P. 72570, Mexico
María Monserrat Morín Castillo: Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, Colonia San Manuel, Ciudad Universitaria, Puebla C.P. 72570, Mexico

Mathematics, 2021, vol. 9, issue 16, 1-23

Abstract: This paper presents a stable method for the identification of sources located on the separation interface of two homogeneous media (where one of them is contained by the other one), from measurement yielded by those sources on the exterior boundary of the media. This is an ill-posed problem because numerical instability is presented, i.e., minimal errors in the measurement can result in significant changes in the solution. To obtain the proposed stable method the identification problem is categorized into three subproblems, two of which present numerical instability and regularization methods must be applied to obtain their solution in a stable form. To manage the numerical instability due to the ill-posedness of these subproblems, the Tikhonov regularization and sequential smoothing methods are used. We illustrate this methodology in a circular and irregular region to demonstrate the feasibility of the proposed method, which yields convergent and stable solutions for input data with and without noise.

Keywords: inverse problem; source identification; ill-posed problem; regularization method; sequential smoothing method; conjugate gradient method; finite element method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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