{"title":"Numerical Solution of the One-Dimensional Forward Magnetotelluric Sounding Problem Using a Computational Grid Adaptation Approach","authors":"S. N. Sklyar, O. B. Zabinyakova","doi":"10.1134/s1995423924030078","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper considers an implementation of an adaptive computational grid constructing algorithm in a numerical solution of the one-dimensional forward magnetotelluric sounding problem (the Tikhonov–Cagniard problem). The numerical solution of the problem is realized by a method of local integral equations which was proposed by the authors previously. The adaptive computational grid construction is based on geometrical principles of optimizing a piecewise constant interpolant of the electrical conductivity function to be approximated. Numerical experiments are carried out to study and illustrate the effectiveness of the combined method. The algorithm is tested on the Kato–Kikuchi model with a known exact solution.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"29 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995423924030078","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The paper considers an implementation of an adaptive computational grid constructing algorithm in a numerical solution of the one-dimensional forward magnetotelluric sounding problem (the Tikhonov–Cagniard problem). The numerical solution of the problem is realized by a method of local integral equations which was proposed by the authors previously. The adaptive computational grid construction is based on geometrical principles of optimizing a piecewise constant interpolant of the electrical conductivity function to be approximated. Numerical experiments are carried out to study and illustrate the effectiveness of the combined method. The algorithm is tested on the Kato–Kikuchi model with a known exact solution.
期刊介绍：
Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998.
The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields.
The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.
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