The method of fundamental solutions for pointwise source reconstruction

This work deals with the reconstruction of point sources in the modified Helmholtz equation in two and three dimensions. This problem has critical applications in engineering and medicine, such as the identification of dipoles and monopoles in electroencephalography and magnetoencephalography and lo...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 114; pp. 171 - 179
Main Authors Rocha de Faria, Jairo, Lesnic, Daniel, da Silva Lima, Rômulo, Machado, Thiago José
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 15.05.2022
Elsevier BV
Subjects
Algorithms
Dipoles
Electroencephalography
Helmholtz equations
Inverse problems
Magnetoencephalography
Meshless methods
Method of fundamental solutions
Modified Helmholtz equation
Numerical methods
Pointwise source
Pollution sources
Reconstruction
Sensitivity analysis
Spectral methods
Pointwise source
Modified Helmholtz equation
Inverse problems
Sensitivity analysis
Method of fundamental solutions
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Summary:This work deals with the reconstruction of point sources in the modified Helmholtz equation in two and three dimensions. This problem has critical applications in engineering and medicine, such as the identification of dipoles and monopoles in electroencephalography and magnetoencephalography and locating sources of environmental pollution. From the numerical point of view, we apply the method of fundamental solutions to solve the direct problems arising from the sensitivity analysis. In addition to the recognized advantages of this meshless spectral method over the traditional mesh-based numerical methods, this approach represents the pointwise sources adequately. Our numerical examples show that the algorithm is capable of accurate reconstruction even when noisy data are inverted.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2022.03.041