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Stable Identification of Sources Located on Interface of Nonhomogeneous Media

Author

Listed:
  • 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
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

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.

Suggested Citation

  • José Julio Conde Mones & Emmanuel Roberto Estrada Aguayo & José Jacobo Oliveros Oliveros & Carlos Arturo Hernández Gracidas & María Monserrat Morín Castillo, 2021. "Stable Identification of Sources Located on Interface of Nonhomogeneous Media," Mathematics, MDPI, vol. 9(16), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1932-:d:613928
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    Citations

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    Cited by:

    1. María Monserrat Morín-Castillo & Jesús Arriaga-Hernández & Bolivia Cuevas-Otahola & José Jacobo Oliveros-Oliveros, 2022. "Analysis of Dipolar Sources in the Solution of the Electroencephalographic Inverse Problem," Mathematics, MDPI, vol. 10(11), pages 1-22, June.
    2. José Julio Conde Mones & Carlos Arturo Hernández Gracidas & María Monserrat Morín Castillo & José Jacobo Oliveros Oliveros & Lorenzo Héctor Juárez Valencia, 2022. "Stable Numerical Identification of Sources in Non-Homogeneous Media," Mathematics, MDPI, vol. 10(15), pages 1-31, August.

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