Solving potential problems in two dimensions in semi-infinite media using the Boundary Element Method // Resolver problemas potenciales en dos dimensiones en medios semi-infinitos usando el Método de Elemento de Límite

Authors

  • Carlos Friedrich Loeffler Programa de Pós-Graduação em Engenharia Mecânica, Universidade Federal do Espírito Santo. Vitória, ES, Brasil
  • Filipe Cestari Coutinho Research and Development Engineer na Prysmian Group. Vila Velha, ES, Brasil
  • Luciano de Oliveira Castro Lara Programa de Pós-Graduação em Engenharia Mecânica, Universidade Federal do Espírito Santo. Vitória, ES, Brasil

Abstract

Se ha demostrado que el conocimiento adecuado de los fenómenos físicos es esencial para el desarrollo de nuevas tecnologías. Este conocimiento permite estudiar varios problemas de ingeniería y encontrar soluciones. Se han estudiado y resuelto problemas cada vez más complejos, especialmente en los últimos siglos. Los espacios infinitos y semi-infinitos presentaron gran dificultad de discretización debido a la escasez de recursos para ello. Con la aparición de los métodos numéricos, estos problemas tuvieron su solución más cercana posible a ser encontrados. El presente trabajo presenta la formulación y los principios matemáticos que componen el modelo del Método del Elemento de límite para abordar problemas bidimensionales con dominios infinitos y semi-infinitos. Se discuten los detalles sobre la definición de las variables relevantes, las características de las soluciones fundamentales en estos casos y el comportamiento de las variables primarias en puntos infinitamente distantes. Los aspectos relacionados con la discretización y las cuestiones numéricas también se abordan mediante la resolución de dos problemas de semiplano particulares. Los resultados numéricos obtenidos mostraron una precisión satisfactoria, lo que confirma que el Método del Elemento de límite es la técnica más adecuada aún hoy para resolver este tipo de problemas.

Palabras claves: Método de elemento de límite; dominios semi-infinitos; Método de imágenes.

Abstract

Adequate knowledge of physical phenomena has been shown to be essential for the development of new technologies. Such knowledge allows several engineering problems to be studied and solutions to be found. More and more complex problems have been studied and solved, especially in recent centuries. Infinite and semi-infinite spaces presented great discretization difficulty due to the scarcity of resources for this. With the emergence of numerical methods, these problems had their closest possible solution to being found. The present work presents the formulation and mathematical principles that comprise the Boundary Element Method model to approach two-dimensional problems with infinite and semi-infinite domains. The particulars regarding the definition of the relevant variables, the characteristics of the fundamental solutions in these cases, and the behavior of primal variables at infinitely distant points are discussed. Aspects related to the discretization and numerical issues are also addressed by solving two particular semi-plane problems. The numerical results obtained showed satisfactory accuracy, confirming that the Boundary Element Method is the most adequate technique even today to solve such problems..

Key words: Boundary Element Method; semi-Infinite domains; Method of Images.

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Published

2022-09-01 — Updated on 2022-12-08

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How to Cite

1.
Friedrich Loeffler C, Cestari Coutinho F, Castro Lara L de O. Solving potential problems in two dimensions in semi-infinite media using the Boundary Element Method // Resolver problemas potenciales en dos dimensiones en medios semi-infinitos usando el Método de Elemento de Límite. Ing. Mec. [Internet]. 2022 Dec. 8 [cited 2025 Sep. 13];25(3):e655. Available from: https://ingenieriamecanica.cujae.edu.cu/index.php/revistaim/article/view/708

Issue

Vol. 25 No. 3 (2022): septiembre-diciembre

Section

Original article

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