The Fundamentals of Boundary Element Methods

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Olena Sierikova – National University of Civil Defence of Ukraine, Kharkiv, Ukraine

Series: Mathematics Research Developments
BISAC: MAT000000
DOI: https://doi.org/10.52305/KFFP5657

The boundary element method is one of the most popular methods of numerical modeling for various problems in mechanics and physics. A big attraction for scientists is the possibility to consider not the region for which a problem needs to be solved but to consider the region’s border instead. The boundary element method allows for significant simplification of the decision process, increasing the accuracy and reliability of the results.

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Table of Contents

Preface

Chapter 1. Boundary Element Methods for Liquid Hydrocarbon Reservoirs’ Vibration Analysis
Olena Sierikova
Department of Applied Mechanics and Environmental Protection Technologies, National University of Civil Defence of Ukraine, Kharkiv, Ukraine

Chapter 2. Boundary and Finite Element Methods in Nanocomposites Effective Elastic Characteristics Estimation
Olena Sierikova¹, PhD, Elena Strelnikova², DSc, Kyryl Degtyariov², PhD, Artem Karaev³, PhD, and Irina Hariachevska³, PhD
¹Department of Applied Mechanics and Environmental Protection Technologies, National University of Civil Defence of Ukraine, Kharkiv, Ukraine
²Department of Hydroaeromechanics of Power Machines, A. M. Podgorny Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, Kharkiv, Ukraine
³Education and Research Institute of Computer Physics and Energy, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

Chapter
3. Boundary Element Methods in One-Dimensional Singular Integral Equations
Olena Sierikova¹, PhD, Volodymir Doroshenko², DSc, Ivan Osypov³, PhD, and Denys Protektor³, PhD
¹Department of Applied Mechanics and Environmental Protection Technologies, National University of Civil Defence of Ukraine, Kharkiv, Ukraine
²Department of Information, Analytical Technologies and Management, Kharkiv National University of Radio Electronics, Kharkiv, Ukraine
³Education and Research Institute of Computer Physics and Energy, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

Chapter 4. Boundary Element Methods for Hypersingular Integral Equations Over Circular Domains
Denys Kriutchenko¹, Elena Strelnikova¹, DSc, Yuriy Naumenko², and Olga Zaydenvarg³
¹Department of Hydroaeromechanics of Power Machines, A. M. Podgorny Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, Kharkiv, Ukraine
²Education and Research Institute of Computer Physics and Energy, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
³Department of Applied Mathematics, National Aerospace University, Kharkiv Aviation Institute, Kharkiv, Ukraine

Chapter 5. Boundary Element Method Testing for Axially-Symmetrical Problems
Denys Kriutchenko, Elena Strelnikova, DSc, Kyryl Degtyariov, PhD, and Vasyl Gnitko, PhD
Department of Hydroaeromechanics of Power Machines, A. M. Podgorny Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, Kharkiv, Ukraine

Chapter 6. Construction of Fundamental Solution of {1,2}-Approximation Static Equations of Momentless Stress State for Transversely-Isotropic Plates
Elena Strelnikova, DSc, Ihor Bokov, PhD, and Natalia Bondarenko, PhD
Department of Hydroaeromechanics of Power Machines, A. M. Podgorny Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, Kharkiv, Ukraine

Chapter 7.
Boundary Element Method in Hydroelastic Interaction Problems of Structural Elements
Kyryl Degtyariov¹, PhD, Vasyl Gnitko¹, PhD, Ivan Vierushkin¹, and Mykyta Korneichuk²
¹Department of Hydroaeromechanics of Power Machines, A. M. Podgorny Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, Kharkiv, Ukraine
²Education and Research Institute of Computer Physics and Energy, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

Index

 

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