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Hypersingular Integral Equations In Fracture Analysis

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Hypersingular Integral Equations in Fracture Analysis

Hypersingular Integral Equations in Fracture Analysis Book
Author : Whye-Teong Ang
Publisher : Elsevier
Release : 2014-04-23
ISBN : 0857094807
Language : En, Es, Fr & De

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Book Description :

Hypersingular Integral Equations in Fracture Analysis explains how plane elastostatic crack problems may be formulated and solved in terms of hypersingular integral equations. The unknown functions in the hypersingular integral equations are the crack opening displacements. Once the hypersingular integral equations are solved, the crack tip stress intensity factors, which play an important role in fracture analysis, may be easily computed. This title consists of six chapters: Elastic crack problems, fracture mechanics, equations of elasticity and finite-part integrals; Hypersingular integral equations for coplanar cracks in anisotropic elastic media; Numerical methods for solving hypersingular integral equations; Hypersingular boundary integral equation method for planar cracks in an anisotropic elastic body; A numerical Green's function boundary integral approach for crack problems; and Edge and curved cracks and piezoelectric cracks. This book provides a clear account of the hypersingular integral approach for fracture analysis, gives in complete form the hypersingular integral equations for selected crack problems, and lists FORTRAN programs of numerical methods for solving hypersingular integral equations. Explains the hypersingular integral approach using specific and progressively more complex crack problems Gives hypersingular integral equations for selected crack problems in complete form Lists computer codes in FORTRAN for the numerical solution of hypersingular integral equations

Hypersingular Integral Equations in Fracture Analysis

Hypersingular Integral Equations in Fracture Analysis Book
Author : Whye-Teong Ang
Publisher : Woodhead Publishing
Release : 2017-11-13
ISBN : 9780081015926
Language : En, Es, Fr & De

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Book Description :

"Hypersingular Integral Equations in Fracture Analysis" explains how plane elastostatic crack problems may be formulated and solved in terms of hypersingular integral equations. The unknown functions in the hypersingular integral equations are the crack opening displacements. Once the hypersingular integral equations are solved, the crack tip stress intensity factors, which play an important role in fracture analysis, may be easily computed. This title consists of six chapters: Elastic crack problems, fracture mechanics, equations of elasticity and finite-part integrals; Hypersingular integral equations for coplanar cracks in anisotropic elastic media; Numerical methods for solving hypersingular integral equations; Hypersingular boundary integral equation method for planar cracks in an anisotropic elastic body; A numerical Green's function boundary integral approach for crack problems; and Edge and curved cracks and piezoelectric cracks. This book provides a clear account of the hypersingular integral approach for fracture analysis, gives in complete form the hypersingular integral equations for selected crack problems, and lists FORTRAN programs of numerical methods for solving hypersingular integral equations. Explains the hypersingular integral approach using specific and progressively more complex crack problemsGives hypersingular integral equations for selected crack problems in complete formLists computer codes in FORTRAN for the numerical solution of hypersingular integral equations

The Solution of Hypersingular Integral Equations with Applications in Acoustics and Fracture Mechanics

The Solution of Hypersingular Integral Equations with Applications in Acoustics and Fracture Mechanics Book
Author : Richard S. St. John
Publisher : Unknown
Release : 1998
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download The Solution of Hypersingular Integral Equations with Applications in Acoustics and Fracture Mechanics book written by Richard S. St. John, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Hypersingular Integrodifferential Equations and Applications to Fracture Mechanics of Homogeneous and Functionally Graded Materials with Strain gradient Effects

Hypersingular Integrodifferential Equations and Applications to Fracture Mechanics of Homogeneous and Functionally Graded Materials with Strain gradient Effects Book
Author : Youn-Sha Chan
Publisher : Unknown
Release : 2001
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Hypersingular Integrodifferential Equations and Applications to Fracture Mechanics of Homogeneous and Functionally Graded Materials with Strain gradient Effects book written by Youn-Sha Chan, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Application of the Hypersingular Boundary Integral Equation in Evaluating Stress Intensity Factors for 2D Elastostatic Fracture Mechanics Problems

Application of the Hypersingular Boundary Integral Equation in Evaluating Stress Intensity Factors for 2D Elastostatic Fracture Mechanics Problems Book
Author : Anonim
Publisher : Unknown
Release : 2006
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Boundary element method is a numerical method that can be advantageously used for a wide range of engineering problems, including the stress concentration problems encountered in fracture mechanics. In linear elastic fracture mechanics (LEFM), the stress intensity factor (SIF) is an important parameter. Cracks, if present in the region experiencing the modes of deformation, increase the stress amplitude significantly and this high stress may lead to premature failure of the engineering components. Knowing the value of the SIF, one can predict if the crack will propagate or not. As the conventional boundary integral equation (CBIE) degenerates when a mathematical crack is modeled, dual boundary integral equation approach developed earlier has been adopted in the current work. It utilizes the hypersingular boundary integral equation (HBIE) along with the CBIE. Weakly singular form of HBIE is utilized in the current work to eliminate the hypersingularity analytically. SIFs are evaluated using the crack opening displacement (COD), displacement extrapolation (DE) and the J-integral approaches. A stand-alone code has been developed in C++ for calculating the SIFs of general 2D domains with cracks. The code has been validated by evaluating the SIFs for the standard components, for which the SIF values are available in the literature. Accurate and well converged results are obtained proving the robustness of the code. A linear combination of the CBIE and HBIE was applied at the crack and significant (87% - 97%) reduction in the condition numbers for the system of equations was observed for the examples studied. Again, the results obtained are accurate and well converged. To the best of author's knowledge this approach has not been reported in the literature for elastostatic crack problems.

Symmetric Galerkin Boundary Element Method

Symmetric Galerkin Boundary Element Method Book
Author : Alok Sutradhar,Glaucio Paulino,Leonard J. Gray
Publisher : Springer Science & Business Media
Release : 2008-09-26
ISBN : 3540687726
Language : En, Es, Fr & De

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Book Description :

Symmetric Galerkin Boundary Element Method presents an introduction as well as recent developments of this accurate, powerful, and versatile method. The formulation possesses the attractive feature of producing a symmetric coefficient matrix. In addition, the Galerkin approximation allows standard continuous elements to be used for evaluation of hypersingular integrals. FEATURES • Written in a form suitable for a graduate level textbook as well as a self-learning tutorial in the field. • Covers applications in two-dimensional and three-dimensional problems of potential theory and elasticity. Additional basic topics involve axisymmetry, multi-zone and interface formulations. More advanced topics include fluid flow (wave breaking over a sloping beach), non-homogeneous media, functionally graded materials (FGMs), anisotropic elasticity, error estimation, adaptivity, and fracture mechanics. • Presents integral equations as a basis for the formulation of general symmetric Galerkin boundary element methods and their corresponding numerical implementation. • Designed to convey effective unified procedures for the treatment of singular and hypersingular integrals that naturally arise in the method. Symbolic codes using Maple® for singular-type integrations are provided and discussed in detail. • The user-friendly adaptive computer code BEAN (Boundary Element ANalysis), fully written in Matlab®, is available as a companion to the text. The complete source code, including the graphical user-interface (GUI), can be downloaded from the web site http://www.ghpaulino.com/SGBEM_book. The source code can be used as the basis for building new applications, and should also function as an effective teaching tool. To facilitate the use of BEAN, a video tutorial and a library of practical examples are provided.

Topics in Integral and Integro Differential Equations

Topics in Integral and Integro Differential Equations Book
Author : Harendra Singh,Hemen Dutta,Marcelo M. Cavalcanti
Publisher : Springer Nature
Release : 2021-04-16
ISBN : 3030655091
Language : En, Es, Fr & De

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Book Description :

This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc. Key Features • New and advanced methods for solving integral and integro-differential equations • Contains comparison of various methods for accuracy • Demonstrates the applicability of integral and integro-differential equations in other scientific areas • Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations

Selected Topics in Boundary Integral Formulations for Solids and Fluids

Selected Topics in Boundary Integral Formulations for Solids and Fluids Book
Author : Vladimir Kompiš
Publisher : Springer
Release : 2014-05-04
ISBN : 3709125480
Language : En, Es, Fr & De

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Book Description :

The book outlines special approaches using singular and non-singular, multi-domain and meshless BEM formulations, hybrid- and reciprocity-based FEM for the solution of linear and non-linear problems of solid and fluid mechanics and for the acoustic fluid-structure interaction. Use of Trefftz functions and other regularization approaches to boundary integral equations (BIE), boundary contour and boundary node solution of BIE, sensitivity analysis, shape optimization, error analysis and adaptivity, stress and displacement derivatives in non-linear problems smoothing using Trefftz polynomials and other special numerical approaches are included. Applications to problems such as noise radiation from rolling bodies, acoustic radiation in closed and infinite domains, 3D dynamic piezoelectricity, Stefan problems and coupled problems are included.

Wavelet Based Approximation Schemes for Singular Integral Equations

Wavelet Based Approximation Schemes for Singular Integral Equations Book
Author : Madan Mohan Panja,Birendra Nath Mandal
Publisher : CRC Press
Release : 2020-09-25
ISBN : 0429534280
Language : En, Es, Fr & De

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Book Description :

Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It’s main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.

Boundary Element Advances in Solid Mechanics

Boundary Element Advances in Solid Mechanics Book
Author : Dimitri Beskos,Giulio Maier
Publisher : Springer
Release : 2014-05-04
ISBN : 3709127904
Language : En, Es, Fr & De

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Book Description :

This volume presents and discusses recent advances in boundary element methods and their solid mechanics applications. It illustrates these methods in their latest forms, developed during the last five to ten years, and demonstrates their advantages in solving a wide range of solid mechanics problems.

Fracture Mechanics in Layered and Graded Solids

Fracture Mechanics in Layered and Graded Solids Book
Author : Tian Xiaohong,Quentin Zhong Qi Yue
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2014-06-23
ISBN : 3110297973
Language : En, Es, Fr & De

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Book Description :

Mechanical responses of solid materials are governed by their material properties. The solutions for estimating and predicting the mechanical responses are extremely difficult, in particular for non-homogeneous materials. Among these, there is a special type of materials whose properties are variable only along one direction, defined as graded materials or functionally graded materials (FGMs). Examples are plant stems and bones. Artificial graded materials are widely used in mechanical engineering, chemical engineering, biological engineering, and electronic engineering. This work covers and develops boundary element methods (BEM) to investigate the properties of realistic graded materials.It is a must have for practitioners and researchers in materials science, both academic and in industry. Covers analysis of properties of graded materials. Presents solutions based methods for analysis of fracture mechanics. Presents two types of boundary element methods for layered isotropic materials and transversely isotropic materials. Written by two authors with extensive international experience in academic and private research and engineering.

Damage and Fracture Mechanics

Damage and Fracture Mechanics Book
Author : Taoufik Boukharouba,Mimoun Elboujdaini,Guy Pluvinage
Publisher : Springer Science & Business Media
Release : 2009-08-09
ISBN : 904812669X
Language : En, Es, Fr & De

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Book Description :

The First African InterQuadrennial ICF Conference “AIQ-ICF2008” on Damage and Fracture Mechanics – Failure Analysis of Engineering Materials and Structures”, Algiers, Algeria, June 1–5, 2008 is the first in the series of InterQuadrennial Conferences on Fracture to be held in the continent of Africa. During the conference, African researchers have shown that they merit a strong reputation in international circles and continue to make substantial contributions to the field of fracture mechanics. As in most countries, the research effort in Africa is und- taken at the industrial, academic, private sector and governmental levels, and covers the whole spectrum of fracture and fatigue. The AIQ-ICF2008 has brought together researchers and engineers to review and discuss advances in the development of methods and approaches on Damage and Fracture Mechanics. By bringing together the leading international experts in the field, AIQ-ICF promotes technology transfer and provides a forum for industry and researchers of the host nation to present their accomplishments and to develop new ideas at the highest level. International Conferences have an important role to play in the technology transfer process, especially in terms of the relationships to be established between the participants and the informal exchange of ideas that this ICF offers.

Recent Advances in Fracture Mechanics

Recent Advances in Fracture Mechanics Book
Author : W.G. Knauss,R.A. Schapery
Publisher : Springer Science & Business Media
Release : 2013-06-29
ISBN : 9401728542
Language : En, Es, Fr & De

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Book Description :

The papers in this volume represent a considerable cross-section of the field of fracture mechanics, a testimony to the breadth of interest that Mel and Max Williams' friends share with them. Several are expanded versions of papers that were given in special sessions honoring them at the 1997 Ninth International Conference on Fracture Mechanics in Sydney, Australia. The subjects treated in this volume can be classified as follows: dynamic fracture problems as viewed primarily from a classical continuum point of view; analysis of relatively general crack geometrics; fracture problems of polymers and other relatively ductile materials; scaling rules that allow extension of results obtained at one size to be translated into behavior at different size scales; problems dealing with interactions that produce complex stress fields; fracture problems directly appropriate to composite materials; analysis of stress concentrations in anisotropic, elastic solids; and the problem of cracks in thin plates bending. This volume will be of interest to engineers and scientists working on all aspects of the physics and mechanics of fracture.

Applied Mechanics Reviews

Applied Mechanics Reviews Book
Author : Anonim
Publisher : Unknown
Release : 2000
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Applied Mechanics Reviews book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Introduction to Boundary Elements

Introduction to Boundary Elements Book
Author : Friedel Hartmann
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 3642488730
Language : En, Es, Fr & De

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Book Description :

to Boundary Elements Theory and Applications With 194 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Dr.-Ing. Friedel Hartmann University of Dortmund Department of Civil Engineering 4600 Dortmund 50 FRG ISBN-13: 978-3-642-48875-7 e-ISBN-13: 978-3-642-48873-3 001: 10.1007/978-3-642-48873-3 Library of Congress Cataloging-in-Publication Data Hartmann, F. (Friedel) Introduction to boundary elements: theory and applications/Friedel Hartmann. ISBN-13: 978-3-642-48875-7 1. Boundary value problems. I. Title. TA347.B69H371989 515.3'5--dc19 89-4160 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provision of the German Copyright Law of September 9,1965, in its version of June 24,1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1989 Softcover reprint of the hardcover 1 st edition 1989 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Contemporary Computational Mathematics A Celebration of the 80th Birthday of Ian Sloan

Contemporary Computational Mathematics   A Celebration of the 80th Birthday of Ian Sloan Book
Author : Josef Dick,Frances Y. Kuo,Henryk Woźniakowski
Publisher : Springer
Release : 2018-05-23
ISBN : 3319724568
Language : En, Es, Fr & De

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Book Description :

This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.

On Wave Propagation in Elastic Solids with Cracks

On Wave Propagation in Elastic Solids with Cracks Book
Author : Ch Zhang,Dietmar Gross
Publisher : Computational Mechanics
Release : 1998
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Begins with both a non-hypersingular time-domain traction boundary integral equation formulation for transient elastodynamic crack analysis and a time-stepping scheme for solving the boundary integral equations. The scheme is applied to analyze three-dimensional rectangular and penny-shaped cracks, and to investigate pulse shape effects on the dynamic stress intensity factor. The corresponding frequency-domain boundary integral equation is given, and time- harmonic wave propagation in randomly cracked solids is treated. The second half of the book deals with the elastodynamic analysis of a periodic array of cracks in plane strain and of anti-plane interface cracks between two different materials, and the effect of the material anistrophy on the near-tip quantities, the scattered far-field, and wave attenuation and dispersion. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Recent Advances in Mathematics for Engineering

Recent Advances in Mathematics for Engineering Book
Author : Mangey Ram
Publisher : CRC Press
Release : 2020-03-17
ISBN : 0429577915
Language : En, Es, Fr & De

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Book Description :

In recent years, mathematics has experienced amazing growth in the engineering sciences. Mathematics forms the common foundation of all engineering disciplines. This book provides a comprehensive range of mathematics applied in various fields of engineering for different tasks such as civil engineering, structural engineering, computer science, and electrical engineering, among others. It offers chapters that develop the applications of mathematics in engineering sciences, conveys the innovative research ideas, offers real-world utility of mathematics, and has a significance in the life of academics, practitioners, researchers, and industry leaders. Features Focuses on the latest research in the field of engineering applications Includes recent findings from various institutions Identifies the gaps in the knowledge in the field and provides the latest approaches Presents international studies and findings in modeling and simulation Offers various mathematical tools, techniques, strategies, and methods across different engineering fields

Functional Thin Films and Functional Materials

Functional Thin Films and Functional Materials Book
Author : 时东陆
Publisher : 清华大学出版社有限公司
Release : 2003
ISBN : 9787302059035
Language : En, Es, Fr & De

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Book Description :

This book provides an up-to-date introduction to the field of functional thin films and materials, encompassing newly developed technologies and fundamental new concepts. The focus is on the critical areas of novel thin films such as sol gel synthesis of membrane, ferroelectric thin films and devices, functional nanostructured thin films, micromechanical analysis of fiber-reinforced composites, and novel applications. An important aspect of the book lies in its wide coverage of practical applications. It introduces not only the cutting-edge technologies in modern industry, but also unique applications in many rapidly advancing fields. This book is written for a wide readership including university students and researchers from diverse backgrounds such as physics, materials science, engineering and chemistry. Both undergraduate and graduate students will find it a valuable reference book on key topics related to solid state and materials science.

Boundary Elements and Other Mesh Reduction Methods XXX

Boundary Elements and Other Mesh Reduction Methods XXX Book
Author : L. Škerget,C. A. Brebbia
Publisher : WIT Press
Release : 2008
ISBN : 1845641213
Language : En, Es, Fr & De

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Book Description :

The major motivation behind the Boundary Element Method (BEM) was to reduce the dependency of analysis on the definition of meshes. This has allowed the method to expand naturally into new techniques such as Dual Reciprocity and all other Mesh reduction Methods (MRM). MRM and BEM continue to be very active areas of research with many of the resulting techniques applied to solve increasingly complex problems. This book contains papers presented at the much-acclaimed thirtieth International Conference on Boundary Elements and other Mesh Reductions Methods . The proceedings contain papers on practically all major developments in Boundary Elements, including the most recent MRM techniques, grouped under the following topics: Fluid Flow; Heat Transfer; Electrical Engineering and Electromagnetics; Damage Mechanics and Fracture; Mesh Reduction Techniques; Advanced Computational Techniques