Numerisk analyse

Mathematical modelling and computer simulations are playing a crucial role in the solution of the complex problems arising in the field of biomedical sciences and provide a support to clinical and experimental practices in an interdisciplinary framework.Indeed, the development of mathematical models and efficient numerical simulation tools is of key importance when dealing with such applications.Moreover, since the parameters in biomedical models have peculiar scientific interpretations and their values are often unknown, accurate estimation techniques need to be developed for parameter identification against the measured data of observed phenomena. In the light of the new challenges brought by the biomedical applications, computational mathematics paves the way for the validation of the mathematical models and the investigation of control problems.The volume hosts high-quality selected contributions containing original research results as well as comprehensive papers and survey articles including prospective discussion focusing on some topical biomedical problems. It is addressed, but not limited to: research institutes, academia, and pharmaceutical industries.

The book focuses on stability and approximation results concerning recent numerical methods for the numerical solution of hyperbolic conservation laws. The work begins with a detailed and thorough introduction of hyperbolic conservation/balance laws and their numerical treatment. In the main part, recent results in such context are presented focusing on the investigation of approximation properties of discontinuous Galerkin and flux reconstruction methods, the construction of (entropy) stable numerical methods and the extension of existing (entropy) stability results for both semidiscrete and fully discrete schemes, and development of new high-order methods.

This volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.

This book collects selected contributions presented at the INdAM Workshop "e;Geometric Challenges in Isogeometric Analysis"e;, held in Rome, Italy on January 27-31, 2020. It gives an overview of the forefront research on splines and their efficient use in isogeometric methods for the discretization of differential problems over complex and trimmed geometries. A variety of research topics in this context are covered, including (i) high-quality spline surfaces on complex and trimmed geometries, (ii) construction and analysis of smooth spline spaces on unstructured meshes, (iii) numerical aspects and benchmarking of isogeometric discretizations on unstructured meshes, meshing strategies and software. Given its scope, the book will be of interest to both researchers and graduate students working in the areas of approximation theory, geometric design and numerical simulation.Chapter 10 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

This book offers an in-depth verification of numerical solutions for differential equations modeling heat transfer phenomena, where the smoothed particle hydrodynamics (SPH) method is used to discretize the mathematical models. Techniques described in this book aim to speed up the convergence of numerical solutions and increase their accuracy by significantly reducing the discretization error.In their quest, the authors shed light on new sources of numerical error that are specific to the SPH method and, through them, they identify the characteristics of the solutions influenced by such errors. The accuracy of numerical solutions is also improved with the application of advanced tools like the repeated Richardson extrapolation (RRE) in quadruple precision, which was adapted to consider fixed or moving particles. The book finishes with the conclusion that the qualitative and quantitative verification of numerical solutions through coherence tests andmetrics are currently a methodology of excellence to treat computational heat transfer problems.Mathematicians in applied fields and engineers modelling and solving real physical phenomena can greatly benefit from this work, as well as any reader interested in numerical methods for differential equations.

Lisa Schneider entwickelt und implementiert ein Untersuchungsinstrument zur Analyse von Lösungsprozessen beim mathematischen Modellieren, das Modelling-Activity-Interaction-Tool (MAI-Tool). Das MAI-Tool zeichnet sich durch eine digitale Erfassung sowie eine automatisierte Darstellung und algorithmische Auswertung der Daten aus. Im Rahmen einer empirischen Studie wird das MAI-Tool angewendet, in der Modellierungsprozesse von Lernenden beim Lösen einer mathematischen Modellierungsaufgabe untersucht werden: Die Hälfte der Lernenden erhielt eine Unterweisung in idealtypische Modellierungsprozesse, die andere Hälfte nicht. Der Einfluss der Unterweisung auf die Struktur individueller Lösungsprozesse kann nachgewiesen werden und daraus ableitend Hürden während des Modellierens identifiziert werden. Außerdem werden Ergebnisse hinsichtlich des Zusammenhangs von Interaktionen und der Gruppenstruktur präsentiert. Die in der Studie erhobenen Daten werden zur Entwicklung eines Algorithmus mitMachine Learning verwendet, der individuelle Lösungsprozesse anhand von Strukturmerkmalen klassifiziert. Insgesamt leistet diese Forschungsarbeit einen Beitrag zur Grundlagenforschung in mathematischer Modellierung auf technologischer, empirischer und algorithmischer Ebene.

Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.

Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task, especially for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems, and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.

During the development of digital circuits, their functional correctness has to be ensured, for which formal verification methods have been established. However, the verification process using formal methods can have an exponential time or space complexity, causing the verification to fail. While exponential in general, recently it has been proven that the verification complexity of several circuits is polynomially bounded. Martha Schnieber proves the polynomial verifiability of several approximate circuits, which are beneficial in error-tolerant applications, where the circuit approximates the exact function in some cases, while having a lower delay or being more area-efficient. Here, upper bounds for the BDD size and the time and space complexity are provided for the verification of general approximate functions and several state-of-the-art approximate adders.

This book provides a mathematical and numerical analysis of many problems which lead to paradoxes in contemporary cosmology, in particular, the existence of dark matter and dark energy. It is shown that these hypothetical quantities arise from excessive extrapolations of simple mathematical models to the whole physical universe. Written in a completely different style to most books on General Relativity and cosmology, the important results take the form of mathematical theorems with precise assumptions and statements. All theorems are followed by a corresponding proof, or an exact reference to the proof.Some nonstandard topics are also covered, including violation of the causality principle in Newtonian mechanics, a critical mathematical and numerical analysis of Mercury's perihelion shift, inapplicability of Einstein's equations to the classical two-body problem due to computational complexity, non-uniqueness of the notion of universe, the topology of the universe, various descriptions of a hypersphere, regular tessellations of hyperbolic spaces, local Hubble expansion of the universe, neglected gravitational redshift in the detection of gravitational waves, and the possible distribution of mass inside a black hole. The book also dispels some myths appearing in the theory of relativity and in contemporary cosmology. For example, although the hidden assumption that Einstein's equations provide a good description of the evolution of the whole universe is considered to be obvious, it is just a null hypothesis which has not been verified by any experiment, and has only been postulated by excessive extrapolations of many orders of magnitude.

The NUMISHEET conference series is the most significant international conference on the area of the numerical simulation of sheet metal forming processes. It gathers the most prominent experts in numerical methods in sheet forming processes and is an outstanding forum for the exchange of ideas and for the discussion of technologies related to sheet metal forming processes. Topics covered in this volume include but are not limited to the following: Materials Modeling and Experimental Testing MethodsFriction and ContactFormability, Necking, and FractureInstabilities and Surface DefectsFracture and DamageNumerical MethodsSpringbackIncremental Sheet FormingRoll FormingInnovative Forming MethodsProduct and Process Design and Optimization

Using numerical examples to illustrate their concepts and results, this book examines recently developed fuzzy multi-criteria methods, such as Intuitionistic Fuzzy TOPSIS, Intuitionistic Fuzzy TOPSIS & DEA-AHP, Intuitionistic VIKOR, Pythagorean WASPAS, Pythagorean ENTROPI, Hesitant CBD, Hesitant MABAC, Triangular EDAS, Triangular PROMETHEE, q-Rung Orthopair COPRAS, and Fuzzy Type - 2 ELECTRE. Each chapter covers practical applications in addition to fresh developments and results.Given its structure and scope, the book can be used as a textbook in graduate courses on operations research and industrial engineering. It also offers a valuable resource for scientists working in a range of disciplines that require multi-criteria decision making.

This book revises and expands upon the prior edition, The Navier-Stokes Problem. The focus of this book is to provide a mathematical analysis of the Navier-Stokes Problem (NSP) in R^3 without boundaries. Before delving into analysis, the author begins by explaining the background and history of the Navier-Stokes Problem. This edition includes new analysis and an a priori estimate of the solution. The estimate proves the contradictory nature of the Navier-Stokes Problem. The author reaches the conclusion that the solution to the NSP with smooth and rapidly decaying data cannot exist for all positive times. By proving the NSP paradox, this book provides a solution to the millennium problem concerning the Navier-Stokes Equations and shows that they are physically and mathematically contradictive.

This book collects a selection of papers presented at ELECTRIMACS 2021, the 14th international conference of the IMACS TC1 Committee, held in Nancy, France, on 16th-19th May 2022. The conference papers deal with modelling, simulation, analysis, control, power management, design optimization, identification and diagnostics in electrical power engineering. The main application fields include electric machines and electromagnetic devices, power electronics, transportation systems, smart grids, renewable energy systems, energy storage like batteries and supercapacitors, fuel cells, and wireless power transfer. The contributions included in Volume 1 will be particularly focused on electrical engineering simulation aspects and innovative applications.

This book reports on the latest scientific achievements on robot kinematics provided by the prominent researchers participating in the 18th International Symposium on Advances in Robot Kinematics ARK2022, organized in the University of the Basque Country, Bilbao, Spain. It is of interest to researchers wanting to know more about the latest topics and methods in the fields of the kinematics, control and design of robotic systems. The book brings together 53 peer-reviewed papers. These cover the full range of robotic systems, including serial, parallel, flexible mechanisms, and cable-driven manipulators, and tackle problems such as: kinematic analysis of robots, robot modelling and simulation, theories and methods in kinematics, singularity analysis, kinematic problems in parallel robots, redundant robots, cable robots, kinematics in biological systems, flexible parallel manipulators, humanoid robots and humanoid subsystems.

This book ¿offers step-by-step descriptions of various random systems and explores the world of computer simulations. In addition, this book offers a working introduction to those who want to learn how to create and run Monte Carlo simulations. Monte Carlo simulation has been a powerful computational tool for physics models, and when combined with the programming language Excel, this book is a valuable resource for readers who wish to acquire knowledge that can be applied to more complex systems. Visualization of the simulation results via the Visual Basic built in Microsoft EXCEL is presented as the first step towards the subject. Prior experience with the Excel add-in VBA is kept to a minimum. In addition, a chapter on quantum optimization simulation utilizing Python is added to explore the quantum computation. Readers will gain a fundamental knowledge and techniques of simulation physics, which can be extended to STEM projects and other research projects.

This book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications. 

Machine learning heavily relies on optimization algorithms to solve its learning models. Constrained problems constitute a major type of optimization problem, and the alternating direction method of multipliers (ADMM) is a commonly used algorithm to solve constrained problems, especially linearly constrained ones. Written by experts in machine learning and optimization, this is the first book providing a state-of-the-art review on ADMM under various scenarios, including deterministic and convex optimization, nonconvex optimization, stochastic optimization, and distributed optimization. Offering a rich blend of ideas, theories and proofs, the book is up-to-date and self-contained. It is an excellent reference book for users who are seeking a relatively universal algorithm for constrained problems. Graduate students or researchers can read it to grasp the frontiers of ADMM in machine learning in a short period of time.

This monograph is devoted to the study of multiscale model reduction methods from the point of view of multiscale finite element methods. Multiscale numerical methods have become popular tools for modeling processes with multiple scales. These methods allow reducing the degrees of freedom based on local offline computations. Moreover, these methods allow deriving rigorous macroscopic equations for multiscale problems without scale separation and high contrast. Multiscale methods are also used to design efficient solvers. This book offers a combination of analytical and numerical methods designed for solving multiscale problems. The book mostly focuses on methods that are based on multiscale finite element methods. Both applications and theoretical developments in this field are presented. The book is suitable for graduate students and researchers, who are interested in this topic.

This book contains reports made at the International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, held in Belgorod, Russia, in October 2021 and is devoted to various aspects of the theory of differential equations and their applications in various branches of science. Theoretical papers devoted to the qualitative analysis of emerging mathematical objects, theorems of the existence and uniqueness of solutions to the boundary value problems under study are presented, and numerical algorithms for their solution are described. Some issues of mathematical modeling are also covered; in particular, in problems of economics, computational aspects of the theory of differential equations and boundary value problems are studied. The articles are written by well-known experts and are interesting and useful to a wide audience: mathematicians, representatives of applied sciences and students and postgraduates of universities engaged in applied mathematics.

Modern complex multi-domain systems require increased efficiency, reliability, and availability combined with reduced cost. This book contains papers on mathematical modeling and simulation of processes in various areas: ecology and the environment, production and energy, information technology, samples of special-purpose equipment, and cyber-physical systems. The outcomes presented in the book are useful to specialists involved in the modeling and simulation of real-world system, management and decision-making models, production models, and software products. Scientists have the opportunity to familiarize themselves with the latest research in a variety of solutions proposed by leading scientists and to determine promising directions for solving complex scientific and practical tasks. Chapters of this book contain papers presented at the 17th MODS International Conference, November 14¿16, 2022, Chernihiv, Ukraine.

This book contains a selection of the best papers presented at the Computational Urban Planning and Urban Management (CUPUM) conference, held in June 2023 at McGill University in Montreal, Quebec. Major themes of this book are smart cities, urban big data, and shared mobility. This book also contains chapters with cutting-edge research on urban modeling, walkability and bikeability analysis, and planning support systems (PSS).

A broad range of phenomena in science and technology can be described by non-linear partial differential equations characterized by systems of conservation laws with source terms. Well known examples are hyperbolic systems with source terms, kinetic equations, and convection-reaction-diffusion equations. This book collects research advances in numerical methods for hyperbolic balance laws and kinetic equations together with related modelling aspects. All the contributions are based on the talks of the speakers of the Young Researchers¿ Conference ¿Numerical Aspects of Hyperbolic Balance Laws and Related Problems¿, hosted at the University of Verona, Italy, in December 2021.

This book presents and discusses the fundamental topic of classification of musical objects, such as chords, motifs, and gestures. Their classification deals with the exhibition of isomorphism classes. Our structure types include local and global constructions, the latter being similar to global structures in geometry, such as differentiable manifolds.The discussion extends to the role, which classification plays for the creative construction of musical compositions. Our examples include references to classical compositions, such as Beethoven¿s sonatas, and some of the author¿s own compositions of classical and jazz styles.We also discuss software that enables the application of classification to musical creativity.The volume is addressed to an audience that would apply classification to programming and creative musical construction.

This book constitutes the refereed proceedings of the 6th International Conference on Optimization and Learning, OLA 2023, held in Malaga, Spain, during May 3¿5, 2023. The 32 full papers included in this book were carefully reviewed and selected from 78 submissions. They were organized in topical sections as follows: advanced optimization; learning; learning methods to enhance optimization tools; optimization applied to learning methods; and real-world applications.

The developments in mesh generation are usually driven by the needs of new applications and/or novel algorithms. The last decade has seen a renewed interest in mesh generation and adaptation by the computational engineering community, due to the challenges introduced by complex industrial problems.Another common challenge is the need to handle complex geometries. Nowadays, it is becoming obvious that geometry should be persistent throughout the whole simulation process. Several methodologies that can carry the geometric information throughout the simulation stage are available, but due to the novelty of these methods, the generation of suitable meshes for these techniques is still the main obstacle for the industrial uptake of this technology.This book will cover different aspects of mesh generation and adaptation, with particular emphasis on cutting-edge mesh generation techniques for advanced discretisation methods and complex geometries.