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Sławomir MILEWSKI

DSc PhD (Civil Engineering), Professor of Cracow University of Technology
Cracow University of Technology
Postal address: Cracow University of Technology
Chair for Computational Engineering (L-10)
Civil Engineering Department (WIL)
Warszawska 24
31-155 Kraków
POLAND
Phone:		+ 48 - 12 - 628 25 63
Room:		p.401f/IV floor, WIEiK
E-mail:		slawomir.milewski@pk.edu.pl email to me
Web page :		www.L5.pk.edu.pl/~slawek

EDUCATION

01.10.1999 - 27.10.2004 M.Sc. studies
Cracow University of Technology
Civil Engineering Department
Computational Mechanics
M.S. thesis "Higher Order Finite Difference Method and its applications in 1D boundary value problems of mechanics" (in Polish), October 27,2004
01.10.2004 - 30.09.2008 PhD studies
Cracow University of Technology
Civil Engineering Department
Institute for Computational Engineering
Phd thesis "Higher Order approximation in the meshless finite difference method based on the correction terms - application in mechanics" , March 25, 2009

PROFESSIONAL INTERESTS

computer programming (Pascal, C++, Matlab)
solid mechanics science
numerical and computational methods (especially error analysis and adaptivity in meshless methods, e.g. in Meshless FDM)
physics and applied mathematics
selected probabilistic approaches (Monte Carlo simulation, genetic algorithms, ...)

PUBLICATIONS (according to Scopus)

Cecot W., Milewski S., Orkisz J.
Determination of overhead power line cables configuration by the FEM and meshless FDM International Journal of Computational Methods
International Journal of Computational Methods, 1850004 (2017) [20 pages] DOI: http://dx.doi.org/10.1142/S0219876218500044
ABSTRACT: The paper addresses numerical modeling of overhead power line cables subjected to static loads. Cable extensibility, their large 3D displacements as well as an interaction with strings of insulators and elastic towers are considered. A 2D exact closed solution available for certain type of loading was generalized by us to a 3D displacement case and applied as one of the benchmarks, that were used in convergence, efficiency and accuracy studies of numerical methods to select the most reliable one. Various formulations of the problem (strong and weak in both the Bubnov and local PetrovGalerkin MLPG-5 versions) as well as various solution approximation approaches were examined, namely the finite element method (FEM) with the higher order shape functions as well as for the first time the meshless finite difference method (MFDM). Validation done by comparison of the numerical results with in situ measurements confirmed that the assumed models are reliable.
AUTHOR KEYWORDS: Extensible cable; catenary curve; overhead power lines; FEM; MFDM; numerical modeling, validation
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0219876218500044
Jaskowiec J., Milewski S.
Coupling finite element method with meshless finite difference method in thermomechanical problems
Computers & Mathematics with Applications, 72 (9): 2259-2279 (2016)
ABSTRACT: This paper focuses on coupling two different computational approaches, namely finite element method (FEM) and meshless finite difference method (MFDM), in one domain. The coupled approach is applied in solving thermomechanical initial-boundary value problem where the heat transport in the domain is non-stationary. In this method, the domain is divided into two subdomains for FEM and MFDM, respectively. Contrary to other coupling techniques, the approach presented in this paper is defined in terms of mathematical problem formulation rather than at the approximation level. In the weak form of thermomechanical initial-boundary value problem (variational principle), the appropriate additional coupling integrals are defined a-priori. Subsequently, the FEM and the MFDM approximations, which may differ from each other, are provided to the formulation. It is assumed that there exists a very thin layer of material between the subdomains, which is not spatially discretized. The width of this layer may be considered the coupling parameter and it is the same for both, thermal and mechanical parts. Similar approach is applied to essential boundary conditions (e.g. prescribed temperature and displacements). Consequently, the consistent formulation of the mixed problem for the coupled FEM-MFDM method is derived. The analysis is illustrated with two- and three-dimensional examples of mechanical and thermomechanical problems.
AUTHOR KEYWORDS: Meshless finite difference method, Finite element method, coupling approach, thermomechanics
LINK TO ARTICLE: link
Jaworska I., Milewski S.
ON TWO-SCALE ANALYSIS OF HETEROGENEOUS MATERIALS BY MEANS OF THE MESHLESS FINITE DIFFERENCE METHOD
International Journal for Multiscale Computational Engineering, 14 (2): 113-134 (2016)
ABSTRACT: The finite element (FE) method is the commonly applied engineering tool for numerical analysis of heterogeneous materials. The FE solution approach is successfully applied at all analysis levels, including the macro (material at large) and the micro (e.g., representative volume element) ones. However, this paper focuses on an alternative, perhaps more effective approach, based upon the meshless discretization and approximation. The aim of this paper is to present the formulation of the numerical homogenization in terms of the meshless finite difference method, as well as the results of the selected two-dimensional linear elasticity examples. Moreover, several benefits of the proposed approach are highlighted, especially toward analysis of more complex engineering problems.
AUTHOR KEYWORDS: meshless methods, numerical homogenization, MWLS approximation
LINK TO ARTICLE: link
Jaskowiec J., Milewski S.
The effective interface approach for coupling of the FE and meshless FD methods and applying essential boundary conditions
Computers & Mathematics with Applications, Volume 70 Issue 5, September 2015, Pages 962-979
ABSTRACT: The paper presents a new effective technique for coupling two computational methods with different types of discretization and approximation. It is based on a concept of two adjacent subdomains which are connected with each other by means of a thin layer of material. Each of the subdomain may have a different discretization structure and approximation base. The standard Finite Element Method (FEM) as well as the meshless Finite Difference Method (MFDM) are applied here to be coupled. However, the coupling can be used for any other methods. The same concept is used for applying the essential boundary conditions for both of the methods. The width of the interface layer, depending on discretization density, is evaluated by means of several heuristic assumptions. The paper is illustrated with selected two- and three- dimensional examples.
AUTHOR KEYWORDS: Meshless finite difference method, Finite element method, coupling method
LINK TO ARTICLE: link
Milewski S., Orkisz J.
In search of optimal acceleration approach to iterative solution methods of simultaneous algebraic equations
Computers & Mathematics with Applications, Volume 68, Issue 3, August, 2014, pp. 101-117
ABSTRACT: This paper presents several new proposals for acceleration of iterative solution methods of both linear and non-linear Simultaneous Algebraic Equations (SAE). The main concept is based on the successive over-relaxation technique (SOR). A new simple and effective way of evaluation of the relaxation parameter is based on either minimization or annihilation of the subsequent solution residuum. The other concept effectively uses features of the infinite geometrical progression. Its quotient is built using solution increments in several initial series of subsequent iterative steps. Both acceleration mechanisms were also combined in order to obtain the best acceleration of the solution process for Simultaneous Linear Algebraic Equations (SLAE). These concepts were tested on many 1D and 2D benchmark problems, with banded and/or sparse systems. For the relaxed GaussSeidel (GS) approach, the convergence rates were up to 200 times better when compared with the standard GS one. Significant convergence improvement was also reached while testing non-linear SAEs (with the relaxed NewtonRaphson method). The numerical models of the selected engineering problems were based on the meshless approach, due to their more sophisticated nature (when compared e.g. with the finite element analysis).
AUTHOR KEYWORDS: Iterative approach; Acceleration technique; Relaxation approach; Geometrical progression;Linear and non-linear SAE; Meshless methods
LINK TO ARTICLE: link
Milewski S., Orkisz J.
Numerical modelling of slumps under highways located on a mining damage area, based on experimental measurements
(2013) Inverse Problems in Science and Engineering, 21 (6), pp. 987-1006.
ABSTRACT: A system of ground movement measurements under a highway in an Upper Silesia (Poland, Europe) mining damage area has been presented. The objective of the research was to develop a numerical analysis of such slumps occurring under a highway, carried out by a reliable and fast method of converting the results of relevant experimental measurements into ground displacements under the road. For engineering purposes, the results of both monitoring and analysis should be proceeded online, in a fast, sufficiently accurate and reliable way.
AUTHOR KEYWORDS: error estimation; inverse problem; non-linear optimization; regularization; results reliability
LINK TO ARTICLE: link
Milewski S.
Selected computational aspects of the meshless finite difference method
(2013) Numerical Algorithms, 63 (1), pp. 107-126.
ABSTRACT: Meshless Finite Difference Method (MFDM) is nowadays a powerful engineering tool for numerical analysis of boundary value problems. Nowadays, its computational capabilities are not fully used mainly due to the lack of suitable commercial software. This paper briefly presents current state-of-the-art of the MFDM solution approach as well as deals with the selected computational aspects of the MFDM. A set of Matlab functions written by the author is attached to the paper. Techniques for generation of nodes, MFD stars, formulas, equations as well as local approximation technique and numerical integration schemes are discussed there.
AUTHOR KEYWORDS: Implementation in Matlab; Meshless finite difference method; Meshless methods; MWLS approximation
LINK TO ARTICLE: link
Milewski S.
Meshless Finite Difference Method with Higher Order Approximation-Applications in Mechanics
(2012) Archives of Computational Methods in Engineering, 19 (1), pp. 1-49. Cited 2 times.
ABSTRACT: This work is devoted to some recent developments in the Higher Order Approximation introduced to the Meshless Finite Difference Method (MFDM), and its application to the solution of boundary value problems in mechanics. In the MFDM, approximation of the sought function is described in terms of nodes rather than by means of any imposed structure like elements, regular meshes etc. Therefore, the MFDM, using arbitrarily irregular clouds of nodes using the Moving Weighted Least Squares (MWLS) approximation falls into the category of the Meshless Methods (MM). The MFDM, dating to early seventies, is one of the oldest and possibly the most developed one. In this paper considered are some techniques which lead to improvement of the MFDM solution's quality. The main objective of this paper is the presentation and overview of new ideas and the development of the Higher Order solution approach in the MFDM provided by correction terms, preceded by a brief information about the current state-of-the art of this method. The main concept of the Higher Order Approximation (HOA) used here, is based on consideration of additional terms in the local Taylor expansion of the sought function. It shall be demonstrated that such a move may essentially improve, in many ways, efficiency and solution quality of the Higher Order MFDM. The Higher Order correction terms may be applied in many aspects of the MFDM solution approach. Among them one may distinguish the a-posteriori error estimation as well as adaptive solution process with multigrid strategy. Moreover, in the present work considered are: computational implementation of the Higher Order MFDM algorithms, examination of the above mentioned aspects using 1D and 2D benchmark tests, as well as an application of the Higher Order MFDM solution approach to selected boundary value problems in mechanics.
LINK TO ARTICLE: link
Milewski S., Orkisz J.
Improvements in the global A-posteriori error estimation of the fem and MFDM solutions
(2011) Computing and Informatics, 30 (3), pp. 639-653. Cited 1 time.
ABSTRACT: The present paper deals with the estimation of the solution error of the boundary value problems of mechanics science. The well-known ideas of error estimators are presented, as well as new original ones, which use the concept of the improved HO reference solution, obtained using the Meshless Finite Difference Method analysis. Such HO estimators may be applied not only in the MFDM, but also in the Finite Element Method error analysis. This issue is presented here for the first time ever. The approach is tested on chosen 2D benchmark problems. The results are very encouraging.
AUTHOR KEYWORDS: A-posteriori error analysis; Correction terms; Finite Element Method; Higher order approximation; Meshless Finite Difference Method
LINK TO ARTICLE: link
Milewski S., Orkisz J.
Global-local petrov-galerkin formulations in the meshless finite difference method
(2011) Lecture Notes in Computational Science and Engineering, 79 LNCSE, pp. 1-26.
ABSTRACT: The paper presents the recent developments in both the Local Petrov-Galerkin (LPG) formulations of the boundary value problems of mechanics, and the Meshless Finite Difference Method MFDM of numerical analysis. The MLPG formulations use the well-known concept of the Petrov-Galerkin weak approach, where the test function may be different from the trial function. The support of such test function is limited to chosen subdomains, usually of regular shape, rather than to the whole domain. This significantly simplifies the numerical integration. MLPG discretization is performed here for the first time ever, in combination with the MFDM, the oldest and possibly the most developed meshless method. It is based on arbitrarily irregular clouds of nodes and moving weighted least squares approximation (MWLS), using here additional Higher Order correction terms. These Higher Order terms, originated from the Taylor series expansion, are considered in order to raise the local approximation rank in the most efficient manner, as well as to estimate both the a-posteriori solution and residual errors. Some new concepts of development of the original MLPG formulations are proposed as well. Several benchmark problems are analysed. Results of preliminary tests are very encouraging.
AUTHOR KEYWORDS: Higher order approximation; Meshless Finite Difference Method; Meshless Local Petrov Galerkin
LINK TO ARTICLE: link
Milewski S., Orkisz J.
A'posteriori error estimation based on higher order approximation in the meshless finite difference method
(2008) Lecture Notes in Computational Science and Engineering, 65, pp. 189-213. Cited 2 times.
ABSTRACT: The paper presents recent developments in the Higher Order Approximation applied to the Meshless Finite Difference Method MFDM [13]. The concept of the Higher Order Approximation (HOA) [14] is based on considering additional terms in the Taylor expansion of the searched function. Those terms may consist of HO derivatives as well as their jumps and/or singularities. They are used as correction terms to the standard meshless FD operator. Among many applications of the HOA, special emphasis is focused on a'posteriori estimation of the solution and the residual error in both the local and global forms. Thus the HOA approach provides results which may be also used as a high quality reference solution in global or local error estimators. A variety of 1D and 2D tests done indicate clear superiority of such estimation approach over those currently used in the other discrete methods [1].
AUTHOR KEYWORDS: A'posteriori error estimation; Correction terms; Higher order approximation; Meshless Finite Difference Method
LINK TO ARTICLE: link

CONFERENCE ARTICLES , ABSTRACTS AND PRESENTATIONS

Sławomir Milewski, Janusz Orkisz, On HO MFDM in 1D boundary value problems, 14th Inter-Institute Seminar for Young Researchers, Zakopane, Poland, 16 - 19 October, 2003 (book of abstracts)
Sławomir Milewski, Janusz Orkisz, Selected problems of the higher order MFDM approach, 15th Inter-Institute Seminar for Young Researchers, Budapest, Hungary, 21 - 24 April, 2005 (book of abstracts)
Janusz Orkisz, Sławomir Milewski, On higher order approximation in the MFDM metod, Elsevier (editor: K.J. Bathe), Proceedings Third MIT Conference on Computational Fluid and Solid Mechanics, Cambridge, Ma, USA, June 14-17, 2005, pages: 419 - 422
Janusz Orkisz, Sławomir Milewski, Higher order approximation approach in meshless finite difference analysis of boundary value problems, the 16th International Conference on Computer Methods in Mechanics CMM-2005, June 21 - 24, 2005, Częstochowa, Poland (on CD-ROM: cp147)
Janusz Orkisz, Sławomir Milewski, Higher Order approximation multigrid approach in the Meshless Finite Difference Method, CMM-2007 - Computer Methods in Mechanics, Łódz - Spała, Poland, June 19-22, 2007
Janusz Orkisz, Irena Jaworska, Sławomir Milewski, Meshless finite difference method for higher order approximation, Third International Workshop Meshfree Methods for Partial Differential Equations, September 12-15, 2005, Bonn, Germany (book of abstracts)
Janusz Orkisz, Sławomir Milewski, On a-posteriori error analysis in Higher Order approximation in the Meshless Finite Difference Method, ICCES Special Symposium On Meshless Methods, 14-16 June 2006, Dubrovnik, Croatia, (book of abstracts)
Janusz Orkisz, Sławomir Milewski, Recent advances in the Higher Order Approximation in the Meshless Finite Difference Method, 7th World Congress on Computational Mechanics, Los Angeles, California, July 16 - 22, 2006 (book of abstracts)
Janusz Orkisz, Sławomir Milewski, Recent advances in a-posteriori error estimation based on the Higher Order correction terms in the Meshless Finite Difference Method, ICCES Special Symposium, On Meshless Methods ICCES MM 2007, Patras, Greece, 15 - 17 June, 2007 (book of abstracts)
Janusz Orkisz, Sławomir Milewski, Aproksymacja wyższego rzędu w Bezsiatkowej Metodzie Różnic Skończonych oparta na członach korekcyjnych, I Kongres Mechaniki Polskiej, Warszawa, Polska, 28-31 sierpień, 2007 (artykuł na prawach rękopisu)
Janusz Orkisz, Sławomir Milewski, Higher order a-posteriori error estimation in the Meshless Finite Difference Method, 4th International Workshop Meshfree Methods for Partial Differential Equations, Bonn, Sept. 17-20, 2007 (book of abstracts)
Janusz Orkisz, Sławomir Milewski, Higher Order Approximation in the Meshless Finite Difference Method - state of the art, 8th World Congress on Computational Mechanics WCCM8, Venice, Italy, 30 June - 4 July, 2008
Janusz Orkisz, Sławomir Milewski, On optimal acceleration of iterative solution methods of Simultaneous Algebraic Equations, KU KDM Conference, 6-7 March, 2008, Zakopane, Poland
Janusz Orkisz, Sławomir Milewski, In search of optimal acceleration approach to iterative solution methods of Simultaneous Algebraic Equations, 5th M.I.T. Conference on Computational Fluid and Solid Mechanics, Advances in CFD, June 17-19, 2009, Massachusetts Institute of Technology, Cambridge, USA
Janusz Orkisz, Sławomir Milewski, Higher Order discretization of the Meshless Local Petrov Galerkin formulations, CMM-2009 - Computer Methods in Mechanics, 18-21 May 2009, Zielona Góra, Poland
Janusz Orkisz, Sławomir Milewski, Higher Order a-posteriori error analysis in the Meshless Finite Difference Method - State of the art, 17th Inter Institute Seminar for Young Researchers, 22-23 May 2009, Cracow, Poland
Janusz Orkisz, Sławomir Milewski, Global-local Petrov-Galerkin formulations in the MFDM, 5th International Workshop Meshfree Methods for Partial Differential Equations, August 17-19, 2009, Bonn, Germany
Janusz Orkisz, Sławomir Milewski, Metody bezsiatkowe - narzędzie analizy inżynierskiej alternatywne dla MES, XI Konferencja Naukowo-Technicznna Programy MES We Wspomaganiu Analizy, Projektowania i Wytwarzania MES-2009, Pisz, 21-23 October, 2009, Poland
Sławomir Milewski, Janusz Orkisz, Improvements in the global a-posteriori error estimation of the FEM and MFDM solutions, Konferencja Użytkowników Komputerów Dużej Mocy, Zakopane, 18-19 March, 2010, Poland
Janusz Orkisz, Sławomir Milewski, Non-linear analysis by the MFDM using HO approximation, ECCM 2010, Paris, May 16-21, 2010, France
Janusz Orkisz, Sławomir Milewski, Meshless Methods - a solution tool of engineering analysis alternative to the FEM, X Międzynarodowa Konferencja Naukowa Computer Aided Engineering, Szklarska Poręba, 23-26 June, 2010, Poland

CLASSES

applied mathematics and numerical methods
computational methods
foundamentals of informatics
engineering graphics
object-oriented programming
informatics

FILES FOR STUDENTS (in Polish)

- APPLIED MATHEMATICS AND NUMERICAL METHODS

- COMPUTATIONAL METHODS

HEATMRS 2016 (ACTUAL SOFTWARE FOR STATIONARY HEAT FLOW ANALYSIS BY FDM)

ARCHIVE - HEATMIL 2012 (CURRENT UNSOLVED PROBLEMS UNDER NEW WIN/MATLAB)

PERSONAL INTERESTS

worldwide rock music (60's, 70's, 80's, 90's): listening to, collecting, reading and writing about
My old music blog
My blog devoted to old MTV Europe channel
Blog devoted to old MTV Europe channel, created together with my friend, Piotrek
modelling and simulating of railroad tracks and trains (see part one of : Piastow-Warszawa Zachodnia line as well as Kraków Mydlniki-Kraków Płaszów line created in Auran Trainz 2006)
collecting rare and obscure music videos from the 70's, 80's and 90's
collecting videos from the old MTV EUROPE

LAST UPDATE: 2017.03.13