Bücher der Reihe MS&A

The book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. This book is addressed to all scientists interested in the mathematical modeling and numerical simulation of the human cardiocirculatory system.

The book provides a pedagogic and comprehensive introduction to homogenization theory with a special focus on problems set for non-periodic media. The presentation encompasses both deterministic and probabilistic settings. It also mixes the most abstract aspects with some more practical aspects regarding the numerical approaches necessary to simulate such multiscale problems. Based on lecture courses of the authors, the book is suitable for graduate students of mathematics and engineering.

The text is aimed at graduate students in mathematics and fluid dynamics, researchers in applied mathematics, numerical analysis and scientific computing, and engineers and physicists.The book contains original theoretical material based on a new approach to generalized solutions (dissipative or measure-valued solutions).

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems.The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effort, carried out over the last 12 years, to build a growing research community in this field.Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).

Mathematical models and numerical simulations can aid the understanding of physiological and pathological processes. This book offers a mathematically sound and up-to-date foundation to the training of researchers and serves as a useful reference for the development of mathematical models and numerical simulation codes.

Mathematics forms bridges between knowledge, tradition, and contemporary life. The continuous development and growth of its many branches, both classical and modern, permeates and fertilizes all aspects of applied science and technology, and so has a vital impact on our modern society.

This book illustrates applications of mathematics to various processes (physiological or artificial) involving flowing blood, including hemorheology, microcirculation, coagulation, kidney filtration and dialysis, offering a historical overview of each topic.

The book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. This book is addressed to all scientists interested in the mathematical modeling and numerical simulation of the human cardiocirculatory system.

This book details advances and developments in reduced order methods for modeling and computational reduction of complex parametrized systems held by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques.

This book introduces the basic concepts for the numerical modelling of partial differential equations. It details algorithmic and computer implementation aspects and provides a number of easy-to-use programs.

This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions.

Here is essential coverage of modeling, simulation, analysis and applications dealing with biological cellular control systems. Shows how to use data to estimate parameters, and use MATLAB for simulations, predictions and stability and sensitivity analysis.

This book offers a mathematical update of the state of the art of the research in the field of mathematical and numerical models of the circulatory system.

This book deals with the mathematical analysis and the numerical approximation of eddy current problems in the time-harmonic case. It takes into account all the most used formulations, placing the problem in a rigorous functional framework.

Reduced Order Methods for modeling and computational reduction

This book presents mathematical models and numerical simulations of crowd dynamics. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one.

This book describes theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, including diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems.

This advanced textbook offers a user friendly and systematic introduction to mathematical models in speech and hearing sciences. It features step-by-step analysis of models and computational methods from numerical analysis, signal processing and statistics.

This book introduces concepts and techniques for mathematical modeling of the respiratory system, using differential equations, resistive networks and other mathematical tools. Offers state-of-the-art modeling techniques, and several detailed exercises.

This book offers a mathematical update of the state of the art of the research in the field of mathematical and numerical models of the circulatory system.

Mathematics forms bridges between knowledge, tradition, and contemporary life. The continuous development and growth of its many branches, both classical and modern, permeates and fertilizes all aspects of applied science and technology, and so has a vital impact on our modern society.

This book covers the main mathematical and numerical models in computational electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal models and cardiac source representations.

We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems.