Dr. Dimitris Vartziotis studied Aeronautical and Space Engineering (MSc) and Civil Engineering (MSc). He carried out his PhD Thesis in Computational Mechanics. He worked as a scientific executive in IBM Germany. He founded and manages the companies ΝΙΚΙ ΜΕΠΕ and TWT GmbH. TWT GmbH has been awarded first place for innovation and overall evaluation amongst the top German automotive companies. His research focuses on scientific technology and theoretical Mathematics. He publishes in international scientific journals of publishing houses such as Elsevier and Springer. Moreover, he is a reviewer for the European Mathematical Society (zbMATH) and the American Mathematical Society (AMS).
Dr. Dimitris Vartziotis, CEO and founder of TWT GmbH Science and Innovation has been named as “Best Automotive Innovation CEO 2020 (Germany)”. On-line magazine “CEO monthly” publishes this award. Learn more on Dr. Vartziotis’ accomplishment and how he shapes TWT towards becoming a knowledge society.
As a general manager of TWT GmbH and NIKI he was responsible for the development of the first Greek car “Aletis” for the Greek Vehicles Industry ΕΛΒΟ Α.Ε. in collaboration with Pininfarina (Italy). The first prototype of “Aletis” was presented at the international automotive exhibition IAA 2001 in Frankfurt.
Dimitris Vartziotis, Florian Schneider, Diana Behnke, Grace Tian
The Chameleon transformation in $n$ dimensions Miscellaneous
2023.
@misc{VartziotisEtAl_2023,
title = {The Chameleon transformation in $n$ dimensions},
author = {Dimitris Vartziotis and Florian Schneider and Diana Behnke and Grace Tian},
doi = {10.13140/RG.2.2.34607.92320},
year = {2023},
date = {2023-09-01},
urldate = {2023-09-01},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis, Doris Bohnet
An Angular Transformation of Triangles Miscellaneous
2023.
@misc{VartziotisBohnet_2023,
title = {An Angular Transformation of Triangles},
author = {Dimitris Vartziotis and Doris Bohnet},
doi = {10.48550/ARXIV.2307.14007},
year = {2023},
date = {2023-07-01},
publisher = {arXiv},
abstract = {Triangles are everywhere in the virtual world. The surface of nearly every graphical object is saved as a triangular mesh on a computer. Light effects and movements of virtual objects are computed on the basis of triangulations. Besides computer graphics, triangulated surfaces are used for the simulations of physical processes, like heating or cooling of objects or deformations. The numerical method for these simulations is often the finite element method, whose accuracy depends on the quality of the triangulation. The quality of a triangle is generally determined by computing its proximity to an equilateral triangle. Namely, the triangle's inner angles should neither be too small nor too big in order to obtain reliable numerical results. Therefore, one often improves the mesh quality before any simulation. The fact that we require triangulations for accurate simulations is the main motivation for our occupation with triangle transformations. We need a triangulation method that transforms each triangle into a more regular one. However, the transformation should not regularize a particular triangle too fast as this may inhibit that the regularity a neighboring triangles can achieve. At the same time, we would like to prove the efficacy of the transformation. a property often missed by the heuristic procedures used in practice. Besides the practical motivation, the transformation itself exhibits interesting properties which can nicely be proved by basic mathematics.},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Florian Pausinger, Dimitris Vartziotis
On the symmetry of finite sums of exponentials Journal Article
In: Elemente der Mathematik, vol. 76, no. 2, pp. 62–73, 2021, ISSN: 0013-6018.
@article{PausingerVartziotis_2021,
title = {On the symmetry of finite sums of exponentials},
author = {Florian Pausinger and Dimitris Vartziotis},
doi = {10.4171/EM/446},
issn = {0013-6018},
year = {2021},
date = {2021-04-01},
journal = {Elemente der Mathematik},
volume = {76},
number = {2},
pages = {62–73},
abstract = {In this note we are interested in the rich geometry of the graph of a curve $gamma_a, b : [0, 1] rightarrow mathbbC$ defined as $gamma_a, b(t) = exp(2pi iat) + exp(2pi ibt)$, in which $a$, $b$ are two different positive integers. It turns out that the sum of only two exponentials gives already rise to intriguing graphs. We determine the symmetry group and the points of self intersection of any such graph using only elementary arguments and describe various interesting phenomena that arise in the study of graphs of sums of more than two exponentials.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Doris Bohnet, Benjamin Himpel
Smoothing Game Miscellaneous
2020.
@misc{VartziotisEtAl_2020,
title = {Smoothing Game},
author = {Dimitris Vartziotis and Doris Bohnet and Benjamin Himpel},
url = {https://arxiv.org/abs/2010.04956},
doi = {10.48550/ARXIV.2010.04956},
year = {2020},
date = {2020-01-01},
publisher = {arXiv},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis
Computing Arithmetic Series by Expressing the Summands as a Sum of Ones Miscellaneous
2019.
@misc{Vartziotis_2019,
title = {Computing Arithmetic Series by Expressing the Summands as a Sum of Ones},
author = {Dimitris Vartziotis},
year = {2019},
date = {2019-12-01},
abstract = {This note considers the computation of arithmetic series. The aim is to derive an alternative approach to finding the formula by expanding the sum into Ones and finding geometric patterns. The general validity of the formula can then be proven by induction.},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis
Anacarbit – Wittgenstein In Antilog Book
2019, ISBN: 9789609745550.
@book{nokey,
title = {Anacarbit - Wittgenstein In Antilog},
author = {Dimitris Vartziotis},
url = {https://www.protoporia.gr/bartziwths-dhmhtrhs-p-anacarbit-9789609745550.html
https://youtu.be/1lIE5880BiA?si=OB6-gov_9rp2ReBj
https://dipetheioannina.gr/parastaseis/dimitri-vartzioti-anacarbit-o-vitgkenstain-s/},
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year = {2019},
date = {2019-11-01},
urldate = {2019-11-01},
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Dimitris Vartziotis, Doris Bohnet, Benjamin Himpel
GETOpt mesh smoothing: Putting GETMe in the framework of global optimization-based schemes Journal Article
In: Finite Elements in Analysis and Design, vol. 147, pp. 10–20, 2018, ISSN: 0168-874X.
@article{VartziotisEtAl_2018,
title = {GETOpt mesh smoothing: Putting GETMe in the framework of global optimization-based schemes},
author = {Dimitris Vartziotis and Doris Bohnet and Benjamin Himpel},
url = {https://www.sciencedirect.com/science/article/pii/S0168874X17308880},
doi = {https://doi.org/10.1016/j.finel.2018.04.010},
issn = {0168-874X},
year = {2018},
date = {2018-08-01},
journal = {Finite Elements in Analysis and Design},
volume = {147},
pages = {10–20},
abstract = {We present a novel approach to mesh smoothing, called GETOpt, by using a variation of the Geometric Element Transformation Method (GETMe) which falls within the framework of global optimization-based schemes and mesh quality improvement methods. We introduce a global mesh quality measure, which is inspired by rigorous convergence results concerning the size of the geometric elements (non-degeneracy and comparable sizing) and whose gradient flow yields a combination of GETMe and Laplace smoothing. Under this scheme, it can be shown rigorously that the tetrahedral mesh never degenerates. Furthermore, numerical tests show that the sizing of the mesh elements become more comparable and that the FEM gives better approximations in case the PDE problem being solved demonstrates isotropic physical behavior. More specifically, we present in this article an example where the mesh is used to solve Poisson's equation using the standard Galerkin finite element method with piecewise linear and order 2 functions on the low-order mesh.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Juri Merger
GETMe.anis: On geometric polygon transformations leading to anisotropy Miscellaneous
2018.
@misc{VartziotisMerger_2018a,
title = {GETMe.anis: On geometric polygon transformations leading to anisotropy},
author = {Dimitris Vartziotis and Juri Merger},
url = {https://arxiv.org/abs/1805.01767},
doi = {10.48550/ARXIV.1805.01767},
year = {2018},
date = {2018-05-01},
publisher = {arXiv},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis, Juri Merger
Contributions to the study of the non-trivial roots of the Riemann zeta-function Miscellaneous
2018.
@misc{VartziotisMerger_2018,
title = {Contributions to the study of the non-trivial roots of the Riemann zeta-function},
author = {Dimitris Vartziotis and Juri Merger},
url = {https://arxiv.org/abs/1804.00913},
doi = {10.48550/ARXIV.1804.00913},
year = {2018},
date = {2018-04-01},
publisher = {arXiv},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis, Joachim Wipper
The GETMe Mesh Smoothing Framework: A Geometric Way to Quality Finite Element Meshes Book
CRC Press, 2018, ISBN: 978-0-3670-2342-3.
@book{VartziotisWipper_2018,
title = {The GETMe Mesh Smoothing Framework: A Geometric Way to Quality Finite Element Meshes},
author = {Dimitris Vartziotis and Joachim Wipper},
url = {https://www.crcpress.com/The-GETMe-Mesh-Smoothing-Framework-A-Geometric-Way-to-Quality-Finite-Element/Vartziotis-Wipper/p/book/9780367023423},
doi = {10.1201/9780429399626},
isbn = {978-0-3670-2342-3},
year = {2018},
date = {2018-01-01},
publisher = {CRC Press},
keywords = {},
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}
Dimitris Vartziotis, Doris Bohnet
Fractal Curves from Prime Trigonometric Series Journal Article
In: Fractal and Fractional, vol. 2, no. 1, 2018, ISSN: 2504-3110.
@article{VartziotisBohnet_2018,
title = {Fractal Curves from Prime Trigonometric Series},
author = {Dimitris Vartziotis and Doris Bohnet},
url = {https://www.mdpi.com/2504-3110/2/1/2},
doi = {10.3390/fractalfract2010002},
issn = {2504-3110},
year = {2018},
date = {2018-01-01},
journal = {Fractal and Fractional},
volume = {2},
number = {1},
abstract = {We study the convergence of the parameter family of series: $V_alpha, beta ( t ) = sum_p p^-alpha exp (2pi i p^beta t )$, $alpha ,beta ın mathbbR_ >0$, $t ın [ 0 , 1 )$ defined over prime numbers $p$ and, subsequently, their differentiability properties. The visible fractal nature of the graphs as a function of α , β is analyzed in terms of Hölder continuity, self-similarity and fractal dimension, backed with numerical results. Although this series is not a lacunary series, it has properties in common, such that we also discuss the link of this series with random walks and, consequently, explore its random properties numerically.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Benjamin Himpel, Markus Pfeil
Creation of higher-energy superposition quantum states motivated by geometric transformations Miscellaneous
2017.
@misc{VartziotisEtAl_2017,
title = {Creation of higher-energy superposition quantum states motivated by geometric transformations},
author = {Dimitris Vartziotis and Benjamin Himpel and Markus Pfeil},
url = {https://arxiv.org/abs/1712.07963},
doi = {https://doi.org/10.48550/arXiv.1712.07963},
year = {2017},
date = {2017-12-01},
publisher = {arXiv},
abstract = {We suggest a way to produce higher-energy superposition states in a circular system of quantum wells. This is inspired by a link to convergence results for geometric transformations of polygons using circulant Hermitian matrices.},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis, Doris Bohnet
A geometric mesh smoothing algorithm related to damped oscillations Journal Article
In: Computer Methods in Applied Mechanics and Engineering, vol. 326, pp. 102–121, 2017, ISSN: 0045-7825.
@article{VartziotisBohnet_2017,
title = {A geometric mesh smoothing algorithm related to damped oscillations},
author = {Dimitris Vartziotis and Doris Bohnet},
url = {https://www.sciencedirect.com/science/article/pii/S0045782517301676},
doi = {10.1016/j.cma.2017.07.019},
issn = {0045-7825},
year = {2017},
date = {2017-11-01},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {326},
pages = {102–121},
publisher = {Elsevier BV},
abstract = {We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element transformation. In particular, the transformation gives rise directly to a continuous model given by a system of coupled damped oscillations. Derived from this physical model, adaptive parameters are introduced and their benefits presented. The second part discusses the mesh smoothing algorithm based on the element transformation and its numerical performance on example meshes.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Joachim Wipper
The Fractal Nature of an Approximate Prime Counting Function Journal Article
In: Fractal and Fractional, vol. 1, no. 1, pp. 10, 2017, ISSN: 2504-3110.
@article{VartziotisWipper_2017,
title = {The Fractal Nature of an Approximate Prime Counting Function},
author = {Dimitris Vartziotis and Joachim Wipper},
url = {https://www.mdpi.com/2504-3110/1/1/10},
doi = {10.3390/fractalfract1010010},
issn = {2504-3110},
year = {2017},
date = {2017-11-01},
journal = {Fractal and Fractional},
volume = {1},
number = {1},
pages = {10},
publisher = {MDPI AG},
abstract = {Prime number related fractal polygons and curves are derived by combining two different
aspects. One is an approximation of the prime counting function build on an additive function.
The other is prime number indexed basis entities taken from the discrete or continuous Fourier basis.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis
Kommentare zu Wittgensteins Zitaten Book
utzverlag GmbH, 2017, ISBN: 978-3-8316-2031-9.
@book{Vartziotis_2017,
title = {Kommentare zu Wittgensteins Zitaten},
author = {Dimitris Vartziotis},
url = {https://www.literareon.de/index.php/catalog/book/42031},
isbn = {978-3-8316-2031-9},
year = {2017},
date = {2017-10-01},
publisher = {utzverlag GmbH},
keywords = {},
pubstate = {published},
tppubtype = {book}
}
Dimitris Vartziotis, Doris Bohnet
Existence of an attractor for a geometric tetrahedron transformation Journal Article
In: Differential Geometry and its Applications, vol. 49, pp. 197–207, 2016, ISSN: 0926-2245.
@article{VartziotisBohnet_2016,
title = {Existence of an attractor for a geometric tetrahedron transformation},
author = {Dimitris Vartziotis and Doris Bohnet},
url = {https://www.sciencedirect.com/science/article/pii/S0926224516300808},
doi = {10.1016/j.difgeo.2016.08.002},
issn = {0926-2245},
year = {2016},
date = {2016-12-01},
journal = {Differential Geometry and its Applications},
volume = {49},
pages = {197–207},
publisher = {Elsevier BV},
abstract = {We analyze the dynamical properties of a tetrahedron transformation on the space of non-degenerate tetrahedra which can be identified with the non-compact globally symmetric 8-dimensional space SL(3,R)/SO(3,R). We establish the existence of a local attractor which coincides with the set of regular tetrahedra and identify conditions which imply that the basin of attraction is the entire space. In numerical tests, these conditions are fulfilled for a large set of random tetrahedra.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis
Curvature transformation Miscellaneous
2016.
@misc{Vartziotis_2016,
title = {Curvature transformation},
author = {Dimitris Vartziotis},
url = {https://arxiv.org/abs/1608.03898},
doi = {10.48550/arXiv.1608.03898},
year = {2016},
date = {2016-07-01},
publisher = {arXiv},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis, Aristos Tzavellas
On sums of prime factors Miscellaneous
2016.
@misc{VartziotisTzavellas_2016,
title = {On sums of prime factors},
author = {Dimitris Vartziotis and Aristos Tzavellas},
url = {https://arxiv.org/abs/1607.08521},
doi = {10.48550/arXiv.1607.08521},
year = {2016},
date = {2016-07-01},
publisher = {arXiv},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis, Doris Bohnet
Convergence properties of a geometric mesh smoothing algorithm Miscellaneous
2014.
@misc{VartziotisBohnet_2014a,
title = {Convergence properties of a geometric mesh smoothing algorithm},
author = {Dimitris Vartziotis and Doris Bohnet},
doi = {https://doi.org/10.48550/arXiv.1411.3869},
year = {2014},
date = {2014-11-01},
publisher = {arXiv},
abstract = {We describe a simple geometric transformation of triangles which leads to an efficient and effective algorithm to smooth triangle and tetrahedral meshes. Our focus lies on the convergence properties of this algorithm: we prove the effectivity for some planar triangle meshes and further introduce dynamical methods to study the dynamics of the algorithm which may be used for any kind of algorithm based on a geometric transformation.},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis, Benjamin Himpel
Laplacian smoothing revisited Miscellaneous
2014.
@misc{VartziotisHimpel_2014,
title = {Laplacian smoothing revisited},
author = {Dimitris Vartziotis and Benjamin Himpel},
doi = {https://doi.org/10.48550/arXiv.1406.4333},
year = {2014},
date = {2014-06-01},
publisher = {arXiv},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis, Benjamin Himpel
Efficient and Global Optimization-Based Smoothing Methods for Mixed-Volume Meshes Proceedings Article
In: Proceedings of the 22nd International Meshing Roundtable, pp. 293–311, Springer International Publishing, 2014.
@inproceedings{VartziotisHimpel_2014b,
title = {Efficient and Global Optimization-Based Smoothing Methods for Mixed-Volume Meshes},
author = {Dimitris Vartziotis and Benjamin Himpel},
doi = {10.1007/978-3-319-02335-9_17},
year = {2014},
date = {2014-01-01},
booktitle = {Proceedings of the 22nd International Meshing Roundtable},
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Dimitris Vartziotis, Benjamin Himpel
Efficient and Global Optimization-Based Smoothing Methods for Mixed-Volume Meshes Proceedings Article
In: Sarrate, Josep, Staten, Matthew (Ed.): Proceedings of the 22nd International Meshing Roundtable, pp. 293–311, Springer International Publishing, Cham, 2014, ISBN: 978-3-319-02335-9.
@inproceedings{VartziotisHimpel_2014c,
title = {Efficient and Global Optimization-Based Smoothing Methods for Mixed-Volume Meshes},
author = {Dimitris Vartziotis and Benjamin Himpel},
editor = {Josep Sarrate and Matthew Staten},
url = {https://link.springer.com/chapter/10.1007/978-3-319-02335-9_17},
isbn = {978-3-319-02335-9},
year = {2014},
date = {2014-01-01},
booktitle = {Proceedings of the 22nd International Meshing Roundtable},
pages = {293–311},
publisher = {Springer International Publishing},
address = {Cham},
abstract = {Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a systematic approach to global optimization-based versions of such methods for mixed volume meshes, which generalizes to arbitrary dimensions. We also identify some algorithms based on simple regularizing geometric element transformation optimizing certain global algebraic mesh quality measures.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Dimitris Vartziotis, Benjamin Himpel
Efficient Mesh Optimization Using the Gradient Flow of the Mean Volume Journal Article
In: SIAM Journal on Numerical Analysis, vol. 52, no. 2, pp. 1050–1075, 2014.
@article{VartziotisHimpel_2014a,
title = {Efficient Mesh Optimization Using the Gradient Flow of the Mean Volume},
author = {Dimitris Vartziotis and Benjamin Himpel},
url = {https://doi.org/10.1137/130914000},
doi = {10.1137/130914000},
year = {2014},
date = {2014-01-01},
journal = {SIAM Journal on Numerical Analysis},
volume = {52},
number = {2},
pages = {1050–1075},
publisher = {Society for Industrial & Applied Mathematics (SIAM)},
abstract = {The signed volume function for polyhedra can be generalized to a mean volume function for volume elements by averaging over the triangulations of the underlying polyhedron. If we consider these up to translation and scaling, the resulting quotient space is diffeomorphic to a sphere. The mean volume function restricted to this sphere is a quality measure for volume elements. We show that the gradient ascent of this map regularizes the building blocks of hybrid meshes consisting of tetrahedra, hexahedra, prisms, pyramids, and octahedra, that is, the optimization process converges to regular polyhedra. We show that the (normalized) gradient flow of the mean volume yields a fast and efficient optimization scheme for the finite element method known as the geometric element transformation method. Furthermore, we shed some light on the dynamics of this method and the resulting smoothing procedure both theoretically and experimentally.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Doris Bohnet
Regularizations of non-euclidean polygons Miscellaneous
2013.
@misc{VartziotisBohnet_2013,
title = {Regularizations of non-euclidean polygons},
author = {Dimitris Vartziotis and Doris Bohnet},
doi = {https://doi.org/10.48550/arXiv.1312.2500},
year = {2013},
date = {2013-11-01},
publisher = {arXiv},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis, Benjamin Himpel
Efficient and Global Optimization-Based Smoothing Methods for Mixed-Volume Meshes Miscellaneous
2013.
@misc{VartziotisHimpel_2013,
title = {Efficient and Global Optimization-Based Smoothing Methods for Mixed-Volume Meshes},
author = {Dimitris Vartziotis and Benjamin Himpel},
doi = {10.48550/arXiv.1306.2260},
year = {2013},
date = {2013-06-01},
publisher = {arXiv},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Dimitris Vartziotis, Joachimand Wipper, Manolis Papadrakakis
Improving mesh quality and finite element solution accuracy by GETMe smoothing in solving the Poisson equation Journal Article
In: Finite Elements in Analysis and Design, vol. 66, pp. 36–52, 2013, ISSN: 0168-874X.
@article{VartziotisEtAl_2013,
title = {Improving mesh quality and finite element solution accuracy by GETMe smoothing in solving the Poisson equation},
author = {Dimitris Vartziotis and Joachimand Wipper and Manolis Papadrakakis},
url = {https://www.sciencedirect.com/science/article/pii/S0168874X12002077},
doi = {10.1016/j.finel.2012.11.004},
issn = {0168-874X},
year = {2013},
date = {2013-04-01},
journal = {Finite Elements in Analysis and Design},
volume = {66},
pages = {36–52},
publisher = {Elsevier BV},
abstract = {Mesh quality plays an essential role in finite element applications, since it affects the efficiency of the simulation with respect to solution accuracy and computational effort. Therefore, mesh smoothing techniques are often applied for improving mesh quality while preserving mesh topology. One of these methods is the recently proposed geometric element transformation method (GETMe), which is based on regularizing element transformations. It will be shown numerically that this smoothing method is particularly suitable, from an applicational point of view, since it leads to a significant reduction of discretization errors within the first few smoothing steps requiring only little computational effort. Furthermore, due to reduced condition numbers of the stiffness matrices the performance of iterative solvers of the resulting finite element equations is improved. This is demonstrated for the Poisson equation with a number of meshes of different complexity and type as well as for piecewise linear and quadratic finite element basis functions. Results are compared to those obtained by two variants of Laplacian smoothing and a state of the art global optimization-based approach.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Manolis Papadrakakis
Improved GETMe by adaptive mesh smoothing Journal Article
In: Computer Assisted Methods in Engineering and Science, vol. 20, no. 1, pp. 55–71, 2013, ISSN: 2956-5839.
@article{VartziotisPapadrakakis_2013,
title = {Improved GETMe by adaptive mesh smoothing},
author = {Dimitris Vartziotis and Manolis Papadrakakis},
url = {https://cames.ippt.pan.pl/index.php/cames/article/view/80},
issn = {2956-5839},
year = {2013},
date = {2013-01-01},
journal = {Computer Assisted Methods in Engineering and Science},
volume = {20},
number = {1},
pages = {55–71},
abstract = {Mesh smoothing improves mesh quality by node relocation without altering mesh topology. Such methods play a vital role in finite element mesh improvement with a direct consequence on the quality of the discretized solution. In this work, an improved version of the recently proposed geometric element transformation method (GETMe) for mesh smoothing is presented. Key feature is the introduction of adaptive concepts, which improve the resulting mesh quality, reduce the number of parameters, and enhance the parallelization capabilities. Implementational aspects are discussed and results of a more efficient version are presented, which demonstrate that GETMe adaptive smoothing yields high quality meshes, is particularly fast, and has a comparably low memory profile. Furthermore, results are compared to those of other state-of-the-art smoothing methods.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Joachim Wipper
Fast smoothing of mixed volume meshes based on the effective geometric element transformation method Journal Article
In: Computer Methods in Applied Mechanics and Engineering, vol. 201-204, pp. 65–81, 2012.
@article{VartziotisWipper_2012,
title = {Fast smoothing of mixed volume meshes based on the effective geometric element transformation method},
author = {Dimitris Vartziotis and Joachim Wipper},
doi = {10.1016/j.cma.2011.09.008},
year = {2012},
date = {2012-01-01},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {201-204},
pages = {65–81},
publisher = {Elsevier BV},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Simon Huggenberger
Iterative geometric triangle transformations Journal Article
In: Elemente der Mathematik, vol. 67, no. 2, pp. 68–83, 2012.
@article{VartziotisHuggenberger_2012,
title = {Iterative geometric triangle transformations},
author = {Dimitris Vartziotis and Simon Huggenberger},
url = {https://ems.press/journals/em/articles/11208},
doi = {10.4171/em/196},
year = {2012},
date = {2012-01-01},
journal = {Elemente der Mathematik},
volume = {67},
number = {2},
pages = {68–83},
publisher = {European Mathematical Society - EMS - Publishing House GmbH},
abstract = {Seit über einem Jahrhundert sind geometrische Transformationen von Dreiecken Gegenstand mathematischer Untersuchungen. In dem vorliegenden Artikel wird ein Ausgangsdreieck in ein neues Dreieck transformiert, indem auf jeder der Dreiecksseiten ein gleichschenkliges, nach aussen gerichtetes Aufsatzdreieck errichtet wird. Die Scheitelpunkte der Aufsatzdreiecke bilden die Eckpunkte des neuen Dreiecks. Durch wiederholtes Anwenden dieser Transformation erhält man eine Folge von Dreiecken. Die Form der Dreiecke dieser Folge konvergiert gegen eine charakteristische Dreiecksform, von der nachgewiesen wird, dass sie mit jedem Transformationsschritt echt angenähert wird.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Iraklis Goudas, Spyros Savvas, Athanasios Batagiannis, Florian Dittmann, Francesca Zanier
Roadscanner: Feasibility Study and Development of a GNSS-Probe for Creating Digital Maps of High Accuracy and Integrity Journal Article
In: Procedia – Social and Behavioral Sciences, vol. 48, pp. 2473–2481, 2012, ISSN: 1877-0428, (Transport Research Arena 2012).
@article{VartziotisEtAl_2012,
title = {Roadscanner: Feasibility Study and Development of a GNSS-Probe for Creating Digital Maps of High Accuracy and Integrity},
author = {Dimitris Vartziotis and Iraklis Goudas and Spyros Savvas and Athanasios Batagiannis and Florian Dittmann and Francesca Zanier},
url = {https://www.sciencedirect.com/science/article/pii/S1877042812029618},
doi = {10.1016/j.sbspro.2012.06.1218},
issn = {1877-0428},
year = {2012},
date = {2012-01-01},
journal = {Procedia - Social and Behavioral Sciences},
volume = {48},
pages = {2473–2481},
publisher = {Elsevier BV},
abstract = {This paper describes the main outcome of the Roadscanner project, in developing a Vehicle Probe prototype equipped with a Global Navigation Satellite System (GNSS) receiver, an Inertial Navigation System (INS) and a Laser Scanner (LS) unit to create digital maps of high accuracy and integrity. GNSS have become an important factor in transport with limitless possibilities. The GNSS concept is based on a constellation of satellites that provides autonomous geo-spatial positioning with global coverage. This enables GNSS receivers to calculate a Position Velocity Time (PVT) solution using the signals transmitted from satellites along the line-of-sight to the receiver. Following the obvious application of navigation and guidance for various types of vehicles, the advances in accuracy and integrity of PVT have enabled other uses, such as Advanced Driver Assistance Systems (ADAS) and digital automotive simulations. However, GNSS also has intrinsic limitations (subject for example to radio-frequency interference, signal availability and vehicle dynamics), which can be a serious hindrance for demanding applications, where accuracy and integrity are critical. In order to remedy GNSS drawbacks, the satellite receiver data can be integrated with additional sensors, such as an INS. The sensor fusion provides a solution of enhanced accuracy, robustness and integrity and also yields attitude information. Furthermore, adding a laser scanner (LS) provides road surface measurements, which are important for simulation, or road surface quality inspection.},
note = {Transport Research Arena 2012},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Joachim Wipper
A dual element based geometric element transformation method for all-hexahedral mesh smoothing Journal Article
In: Computer Methods in Applied Mechanics and Engineering, vol. 200, no. 9-12, pp. 1186–1203, 2011.
@article{VartziotisWipper_2011,
title = {A dual element based geometric element transformation method for all-hexahedral mesh smoothing},
author = {Dimitris Vartziotis and Joachim Wipper},
url = {https://www.sciencedirect.com/science/article/pii/S0045782510002719},
doi = {https://doi.org/10.1016/j.cma.2010.09.012},
year = {2011},
date = {2011-02-01},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {200},
number = {9-12},
pages = {1186–1203},
abstract = {Due to their increased complexity hexahedral elements are more challenging with respect to mesh generation and mesh improvement techniques than tetrahedral elements. In particular, there is a lack of geometry-based all-hexahedral smoothing methods for mesh quality improvement being easy to implement, practicable, and efficient. The recently introduced geometric element transformation method represents a new promising element oriented smoothing concept to resolve this deficiency. By giving a dual octahedron based regularizing transformation this new approach is adapted in order to smooth all-hexahedral meshes. First numerical tests indicate that the resulting smoothing method yields high quality results at least comparable to those of a state of the art global optimization-based approach while being significantly faster.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Kostas Vartziotis, Victor Fäßler, Evaggelos Savvas, Iraklis Goudas, Maria Zavali
An online system for the support of Total Hip Arthroplasty and rapid implant design and manufacturing Proceedings Article
In: Proceedings of the 10th IEEE International Conference on Information Technology and Applications in Biomedicine, pp. 1–4, 2010, ISSN: 2168-2208.
@inproceedings{VartziotisEtAl_2010,
title = {An online system for the support of Total Hip Arthroplasty and rapid implant design and manufacturing},
author = {Dimitris Vartziotis and Kostas Vartziotis and Victor Fäßler and Evaggelos Savvas and Iraklis Goudas and Maria Zavali},
doi = {10.1109/ITAB.2010.5687706},
issn = {2168-2208},
year = {2010},
date = {2010-11-01},
booktitle = {Proceedings of the 10th IEEE International Conference on Information Technology and Applications in Biomedicine},
pages = {1–4},
abstract = {As Information Technology (IT) and Engineering advances are becoming widely available, other scientific disciplines are taking advantage of them. Especially, medicine can benefit greatly from applications of IT or Engineering or their combination. Nevertheless, medical professionals lack the required IT-expertise and training. This fact poses several problems, both in the initial acceptance of novel technologies and their subsequent efficient use. This work presents an IT system, as applied to Total Hip Arthroplasty (THA) preoperative planning. The system is designed to provide insight to the patient's anatomy, as well as assist the operating surgeon with the selection, design and fitting of orthopedic implants. Furthermore, special care has been given to ease of use and hiding the complexities involved when cross discipline expertise is required.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Dimitris Vartziotis, Joachim Wipper
Characteristic parameter sets and limits of circulant Hermitian polygon transformations Journal Article
In: Linear Algebra and its Applications, vol. 433, no. 5, pp. 945–955, 2010, ISSN: 0024-3795.
@article{VartziotisWipper_2010,
title = {Characteristic parameter sets and limits of circulant Hermitian polygon transformations},
author = {Dimitris Vartziotis and Joachim Wipper},
url = {https://www.sciencedirect.com/science/article/pii/S0024379510001990},
doi = {https://doi.org/10.1016/j.laa.2010.04.022},
issn = {0024-3795},
year = {2010},
date = {2010-01-01},
journal = {Linear Algebra and its Applications},
volume = {433},
number = {5},
pages = {945–955},
abstract = {Polygon transformations based on taking the apices of similar triangles constructed on the sides of an initial polygon are analyzed as well as the limit polygons obtained by iteratively applying such transformations. In contrast to other approaches, this is done with respect to two construction parameters representing a base angle and an apex perpendicular subdivision ratio. Furthermore, a combined transformation leading to circulant Hermitian matrices is proposed, which eliminates the rotational effect of the basic transformation. A finite set of characteristic parameter subdomains is derived for which the sequence converges to specific eigenpolygons. Otherwise, limit polygons turn out to be linear combinations of up to three eigenpolygons. This leads to a full classification of circulant Hermitian similar triangles based polygon transformations and their limit polygons. As a byproduct classical results as Napoleon's theorem and the Petr–Douglas–Neumann theorem can be easily deduced.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Joachim Wipper, Bernd Schwald
The geometric element transformation method for tetrahedral mesh smoothing Journal Article
In: Computer Methods in Applied Mechanics and Engineering, vol. 199, no. 1, pp. 169–182, 2009, ISSN: 0045-7825.
@article{VartziotisEtAl_2009,
title = {The geometric element transformation method for tetrahedral mesh smoothing},
author = {Dimitris Vartziotis and Joachim Wipper and Bernd Schwald},
url = {https://www.sciencedirect.com/science/article/pii/S004578250900334X},
doi = {https://doi.org/10.1016/j.cma.2009.09.027},
issn = {0045-7825},
year = {2009},
date = {2009-12-01},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {199},
number = {1},
pages = {169–182},
abstract = {The geometric element transformation method (GETMe) has been introduced as a new element driven approach to mesh smoothing. It is based on simple geometric transformations, which, if applied iteratively, lead to the regularization of mesh elements. Global mesh smoothing can be accomplished by successively improving the worst elements or by averaging node positions obtained by the simultaneous transformation of all elements. GETMe smoothing has been successfully applied in the case of surface meshes. As shown in this paper, this approach also naturally extends to tetrahedral mesh smoothing without major conceptual modifications. A regularizing transformation for tetrahedra is presented and a combined approach of simultaneous and sequential GETMe smoothing is described. First numerical examples yield high quality meshes superior to those obtained by other geometry-based methods. In fact, the presented results are in a majority of cases at least comparable to those obtained by a state of the art global optimization-based method.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Joachim Wipper
The geometric element transformation method for mixed mesh smoothing Journal Article
In: Engineering with Computers, vol. 25, no. 3, pp. 287–301, 2009.
@article{VartziotisWipper_2009b,
title = {The geometric element transformation method for mixed mesh smoothing},
author = {Dimitris Vartziotis and Joachim Wipper},
doi = {10.1007/s00366-009-0125-6},
year = {2009},
date = {2009-06-01},
journal = {Engineering with Computers},
volume = {25},
number = {3},
pages = {287–301},
publisher = {Springer Science and Business Media LLC},
abstract = {The geometric element transformation method (GETMe) is a geometry-based smoothing method for mixed and non-mixed meshes. It is based on a simple geometric transformation applicable to elements bounded by polygons with an arbitrary number of nodes. The transformation, if applied iteratively, leads to a regularization of the polygons. Global mesh smoothing is accomplished by averaging the new node positions obtained by local element transformations. Thereby, the choice of transformation parameters as well as averaging weights can be based on the element quality which leads to high quality results. In this paper, a concept of an enhanced transformation approach is presented and a proof for the regularizing effect of the transformation based on eigenpolygons is given. Numerical examples confirm that the GETMe approach leads to superior mesh quality if compared to other geometry-based methods. In terms of quality it can even compete with optimization-based techniques, despite being conceptually significantly simpler.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Joachim Wipper
On the construction of regular polygons and generalized napoleon vertices Journal Article
In: Forum Geometricorum, vol. 9, pp. 213–223, 2009, ISSN: 1534-1178.
@article{VartziotisWipper_2009a,
title = {On the construction of regular polygons and generalized napoleon vertices},
author = {Dimitris Vartziotis and Joachim Wipper},
url = {https://forumgeom.fau.edu/FG2009volume9/FG200920.pdf},
issn = {1534-1178},
year = {2009},
date = {2009-01-01},
journal = {Forum Geometricorum},
volume = {9},
pages = {213–223},
abstract = {An algebraic foundation for the derivation of geometric construction schemes transforming arbitrary polygons with n vertices into $k$-regular $n$-gons is given. It is based on circulant polygon transformations and the associated eigenpolygon decompositions leading to the definition of generalized Napoleon vertices. Geometric construction schemes are derived exemplarily for different choices of $n$ and $k$.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Dimitris Vartziotis, Joachim Wipper
Classification of symmetry generating polygon-transformations and geometric prime algorithms Journal Article
In: Mathematica Pannonica, vol. 20, no. 2, pp. 167–187, 2009, ISSN: 2786-0752.
@article{VartziotisWipper_2009,
title = {Classification of symmetry generating polygon-transformations and geometric prime algorithms},
author = {Dimitris Vartziotis and Joachim Wipper},
url = {http://mathematica-pannonica.ttk.pte.hu/articles/mp20-2/mp20-2-167-187.pdf},
issn = {2786-0752},
year = {2009},
date = {2009-01-01},
journal = {Mathematica Pannonica},
volume = {20},
number = {2},
pages = {167–187},
abstract = {Infinite polygon transformations by iteratively taking the apices of similar isosceles triangles erected on the sides of a polygon are analyzed. In contrast to other approaches, this is done with respect to the base angle of the isosceles triangles. A finite set of characteristic angles is derived, which only depend on the number of vertices of the polygon. This results in a systematic and complete classification of consecutive base angle intervals and the associated limit polygons. The latter in turn are linear combinations of eigen-polygons obtained by diagonalizing the circulant matrix representation of the transformation. Analyzing the principles of the symmetry of eigenpolygons and thereby of the limit polygons reveals a connection to prime numbers. Based on these results, a geometric sieve as well as a factorization algorithm for prime numbers is presented.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
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