Mathematical Modeling and Simulation

This textbook is relevant to BSc/MSc students interested in mathematical modeling and simulation. It brings together analysis, calculus and numerical methods presented in a single coherent volume.
Particular attention is given to engineering mathematics, addressing modeling, analysis, method development, implementation and testing of algorithms, as well as application to actual problems and critical interpretation of the results. The book can be used throughout bachelor programs and parts of masters programs, presenting a comprehensive suite of courses that link formal abstract thinking on the one hand to intuitive model formulation, critical algorithm development and interpretation of results on the other hand. The books contains numerous examples of practical applications from physics, technology, biology and chemistry. It also contains an introduction to Matlab and C for algorithm development and computational analysis. Software and solutions to selected problems are included.

Bernard Geurts is the Chair of the Multiscale Modeling and Simulation (MMS) group at the University of Twente, The Netherlands. The big dream behind their work is to help open entirely new worlds of understanding and application in science and technology, by creating advanced computational methods. The impact of their work is increased by close collaboration with other disciplines.The main research focus is on the mathematical development of computational methods forsystems of nonlinear differential equations. The models studied at MMS represent complexphysical mechanisms acting simultaneously at micro- and macro scales. Much of the workis motivated by fluid-mechanical problems, from nano- and micro fluidics to macroscopicturbulence.The three directions of MMS expertise, i.e., (i) mathematical models, (ii) numerical methods and (iii) advanced reduction and regularisation techniques, are exploited in multi-disciplinary research. The work is characterised by balancing fundamental orientation and application perspective. Specific targets are derived from unresolved issues in science and technology.Main application areas are in fluid technology, health and energy such as: - multi-phase turbulence and heat transfer, - aerosol formation and phase transitions, - biomedical flows in complex domains, - nano-engineered materials for energy systemsSpecific challenges range from understanding the physics of boiling and turbulence modulation, to novel methods of controlled respiratory drug delivery. Moreover, new methods are forgedfor the prediction and mitigation of cerebral haemorrhages and the optimisation of nanostructured inclusions for new materials in energy harvesting.While these applications and research fields appear diverse, the binding element is his interest in mathematical elegance and abstraction to discover and exploit the simplicity behind apparent complexity in physical systems.
Ruud van Damme is associate professor in numerical analysis in the Multiscale Modeling and Simulation. This group is part of the Department of Applied Mathematics at the University of Twente.

His research interests are in mathematics, physics and numerics. The main topics lie in fields such as fluid mechanics, quantum mechanics, graph theory and stochastic processes. His recent research concentrates on advanced numerical techniques and their application, such as splines and wavelets, adaptive grid methods and high dimensional integration.