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Eulerian path

About: Eulerian path is a research topic. Over the lifetime, 4917 publications have been published within this topic receiving 132148 citations. The topic is also known as: Eulerian trail.


Papers
More filters
Journal ArticleDOI
TL;DR: The algorithm can be used as a building block for solving other distributed graph problems, and can be slightly modified to run on a strongly-connected diagraph for generating the existent Euler trail or to report that no Euler trails exist.

13,828 citations

Journal ArticleDOI
TL;DR: This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics.
Abstract: This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics. The IB formulation of such problems, derived here from the principle of least action, involves both Eulerian and Lagrangian variables, linked by the Dirac delta function. Spatial discretization of the IB equations is based on a fixed Cartesian mesh for the Eulerian variables, and a moving curvilinear mesh for the Lagrangian variables. The two types of variables are linked by interaction equations that involve a smoothed approximation to the Dirac delta function. Eulerian/Lagrangian identities govern the transfer of data from one mesh to the other. Temporal discretization is by a second-order Runge–Kutta method. Current and future research directions are pointed out, and applications of the IB method are briefly discussed. Introduction The immersed boundary (IB) method was introduced to study flow patterns around heart valves and has evolved into a generally useful method for problems of fluid–structure interaction. The IB method is both a mathematical formulation and a numerical scheme. The mathematical formulation employs a mixture of Eulerian and Lagrangian variables. These are related by interaction equations in which the Dirac delta function plays a prominent role. In the numerical scheme motivated by the IB formulation, the Eulerian variables are defined on a fixed Cartesian mesh, and the Lagrangian variables are defined on a curvilinear mesh that moves freely through the fixed Cartesian mesh without being constrained to adapt to it in any way at all.

4,164 citations

Book
12 Sep 2000
TL;DR: In this paper, the authors present a list of boxes for Lagrangian and Eulerian Finite Elements in One Dimension (LDF) in one dimension, including Beams and Shells.
Abstract: Preface. List of Boxes. Introduction. Lagrangian and Eulerian Finite Elements in One Dimension. Continuum Mechanics. Lagrangian Meshes. Constitutive Models Solution Methods and Stability. Arbitrary Lagrangian Eulerian Formulations. Element Technology. Beams and Shells. Contact--Impact. Appendix 1: Voigt Notation. Appendix 2: Norms. Appendix 3: Element Shape Functions. Glossary. References. Index.

3,928 citations

Journal ArticleDOI
TL;DR: In this article, a new numerical technique is presented that has many advantages for obtaining solutions to a wide variety of time-dependent multidimensional fluid dynamics problems, including stability, accuracy, and zoning.

2,226 citations

Journal ArticleDOI
TL;DR: A new numerical method based on a combination of the classical shape derivative and of the level-set method for front propagation, which can easily handle topology changes and is strongly dependent on the initial guess.

2,176 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
2023296
2022544
2021219
2020236
2019227