Bücher der Reihe SEMA SIMAI Springer Series

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.

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.

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.

This book contains plenary lectures given at the International Conference on Mathematical and Computational Modeling, Approximation and Simulation, dealing with three very different problems: reduction of Runge and Gibbs phenomena, difficulties arising when studying models that depend on the highly nonlinear behaviour of a system of PDEs, and data fitting with truncated hierarchical B-splines for the adaptive reconstruction of industrial models. The book includes nine contributions, mostly related to quasi-interpolation. This is a topic that continues to register a high level of interest, both for those working in the field of approximation theory and for those interested in its use in a practical context. Two chapters address the construction of quasi-interpolants, and three others focus on the use of quasi-interpolation in solving integral equations. The remaining four concern a problem related to the heat diffusion equation, new results on the notion of convexity in probabilistic metric spaces (which are applied to the study of the existence and uniqueness of the solution of a Volterra equation), the use of smoothing splines to address an economic problem and, finally, the analysis of poverty measures, which is a topic of increased interest to society. The book is addressed to researchers interested in Applied Mathematics, with particular reference to the aforementioned topics.

In this book we gather recent mathematical developments and engineering applications of Trefftz methods, with particular emphasis on the Method of Fundamental Solutions (MFS).

This book contains some of the results presented at the mini-symposium titled Emerging Problems in the Homogenization of Partial Differential Equations, held during the ICIAM2019 conference in Valencia in July 2019. The papers cover a large range of topics, problems with weak regularity data involving renormalized solutions, eigenvalue problems for complicated shapes of the domain, homogenization of partial differential problems with strongly alternating boundary conditions of Robin type with large parameters, multiscale analysis of the potential action along a neuron with a myelinated axon, and multi-scale model of magnetorheological suspensions. The volume is addressed to scientists who deal with complex systems that presents several elements (characteristics, constituents...) of very different scales, very heterogeneous, and search for homogenized models providing an effective (macroscopic) description of their behaviors.

This book collects the latest results and new trends in the application of mathematics to some problems in control theory, numerical simulation and differential equations. Problems in control theory, as in most engineering problems, are modeled by differential equations, for which standard solving procedures may be insufficient.

Many problems coming from engineering, physics or biology are characterized by both the presence of different temporal and spatial scales and the presence of contacts among different components through (irregular) interfaces that often connect media with different characteristics.

This book contains some contributions presented at the Applied Mathematics for Environmental Problems minisymposium during the International Congress on Industrial and Applied Mathematics (ICIAM) held July 15-19, 2019 in Valencia, Spain.

This volume collects the most important contributions from four minisymposia from ICIAM 2019. The papers highlight cutting-edge applications of Cartesian CFD methods and describe the employed algorithms and numerical schemes. finite difference, finite volume, multiresolution or lattice Boltzmann CFD schemes.

This volume aims at bringing together contributions on stabilizing control design for different classes of dynamical systems described by partial differential equations, functional-differential equations, delay equations, and dynamical systems in abstract spaces.

This book disseminates the latest results and envisages new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology.

Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography.

In this book we gather recent mathematical developments and engineering applications of Trefftz methods, with particular emphasis on the Method of Fundamental Solutions (MFS).

This book disseminates the latest results and envisages new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology.

This book presents generalized heat-conduction laws which, from a mesoscopic perspective, are relevant to new applications (especially in nanoscale heat transfer, nanoscale thermoelectric phenomena, and in diffusive-to-ballistic regime) and at the same time keep up with the pace of current microscopic research.

This book book explores the ways that elaborate flux functions can be constructed, mainly in a one-dimensional context for hyperbolic systems admitting shock-type solutions and also for kinetic equations in the discrete-ordinate approximation.

This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields.

The methods described include, among others, partition of unity methods (meshfree, XFEM, GFEM), virtual element methods, fictitious domain methods, and special techniques for static and evolving interfaces.

This book presents lecture notes from the XVI 'Jacques-Louis Lions' Spanish-French School on Numerical Simulation in Physics and Engineering, held in Pamplona (Navarra, Spain) in September 2014.

This work collects the most important results presented at the Congress on Differential Equations and Applications/Congress on Applied Mathematics (CEDYA/CMA) in Cádiz (Spain) in 2015. It supports further research in differential equations, numerical analysis, mechanics, control and optimization. In particular, it helps readers gain an overview of specific problems of interest in the current mathematical research related to different branches of applied mathematics. This includes the analysis of nonlinear partial differential equations, exact solutions techniques for ordinary differential equations, numerical analysis and numerical simulation of some models arising in experimental sciences and engineering, control and optimization, and also trending topics on numerical linear Algebra, dynamical systems, and applied mathematics for Industry. This volume is mainly addressed to any researcher interested in the applications of mathematics, especially in any subject mentioned above. It may be also useful to PhD students in applied mathematics, engineering or experimental sciences.

This book focuses on the approximation of nonlinear equations using iterative methods. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation.

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods.

This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure.