Minimal Surfaces and the Plateau Problem: Numerical Methods and Applications

Sapagovas, Mifodijus; Būda, Vytautas; Maskeliūnas, Saulius; Štikonienė, Olga; Štikonas, Artūras

doi:10.15388/24-INFOR552

Informatica

Minimal Surfaces and the Plateau Problem: Numerical Methods and Applications

Volume 35, Issue 2 (2024), pp. 401–420

Mifodijus Sapagovas

Vytautas Būda Saulius Maskeliūnas

Olga Štikonienė

Artūras Štikonas

https://doi.org/10.15388/24-INFOR552

Pub. online: 9 April 2024 Type: Research Article

Open Access

Received
1 February 2024

Accepted
1 April 2024

Published
9 April 2024

Abstract

This article offers a comprehensive overview of the results obtained through numerical methods in solving the minimal surface equation, along with exploring the applications of minimal surfaces in science, technology, and architecture. The content is enriched with practical examples highlighting the diverse applications of minimal surfaces.

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Biographies

Sapagovas Mifodijus

https://orcid.org/0000-0002-7139-3468

mifodijus.sapagovas@mif.vu.lt

M. Sapagovas graduated from the Vilnius University in 1961. He received the doctoral degree in mathematics (PhD) at the Institute of Mathematics in Kiev in 1965. In 1986, he received the doctor habilitatus degree from the M. Keldysh Institute of Applied Mathematics in Moscow. M. Sapagovas is a professor (1989), a member of the Lithuanian Academy of Sciences (1987), professor-emeritus of the Statistics and Probability Group at the Institute of Data Science and Digital Technologies. The main field of scientific interest is the numerical methods for nonlinear PDE as well as mathematical modelling.

Būda Vytautas

vytautas.buda@ism.lt

V. Būda graduated from the Vilnius University in 1978. He received a Doctor’s degree in mathematics (PhD) at the Institute of Mathematics and Informatics in 1988. He worked as an associate professor at the Vilnius Gediminas Technical University and the University of Management and Economics (ISM, Vilnius) between 1988–2018. After retirement, he takes a position as a part-time lecturer at the ISM.

Maskeliūnas Saulius

https://orcid.org/0000-0002-3587-9655

saulius.maskeliunas@mif.vu.lt

S. Maskeliūnas received a doctoral degree in informatics from the Institute of Mathematics and Informatics in 1996. He is a researcher at the Cyber-Social Systems Engineering Group and deputy director at the Institute of Data Science and Digital Technologies. His general interests include: information systems and knowledge-based systems, in particular, (from most important now to past ones): semantic web, scientometrics, web services, ontological engineering, knowledge management and organisational memories, workflow automation, qualitative reasoning, expert systems.

Štikonienė Olga

https://orcid.org/0000-0002-0302-3449

olga.stikoniene@mif.vu.lt

O. Štikonienė graduated from the Lomonosov Moscow State University. She obtained her PhD in Mathematics at the Institute of Mathematics and Informatics in 1997. Currently, she is a professor at the Institute of Applied Mathematics at Vilnius University. Her research interests include numerical methods for nonlinear partial differential equations, nonlocal differential problems, and mathematical modelling in physics and medicine.

Štikonas Artūras

https://orcid.org/0000-0002-5872-5501

arturas.stikonas@mif.vu.lt

A. Štikonas studied at Vilnius University in 1980–1982 and Lomonosov Moscow State University in 1982–1986. PhD (mathematics and physics), Department of Numerical Mathematics, Academy of Science, USSR in 1990. In 2008, he defended habilitation thesis. Since 2017, he works as a professor and research professor at the Institute of Applied Mathematics, Vilnius University. His research focuses on numerical methods and problems with nonlocal conditions.

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Keywords

Plateau problem minimal surface equation numerical methods applications of minimal surfaces

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