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The investigation of the role of mechanical and mechano-chemical interactions in cellular processes and tissue development is a rapidly growing research field in the life sciences and in biomedical engineering. Quantitative understanding of this important area in the study of biological systems requires the development of adequate mathematical models for the simulation of the evolution of these systems in space and time. Since expertise in various fields is necessary, this calls for a multidisciplinary approach. This edited volume connects basic physical, biological, and physiological concepts to methods for the mathematical modeling of various materials by pursuing a multiscale approach, from subcellular to organ and system level. Written by active researchers, each chapter provides a detailed introduction to a given field, illustrates various approaches to creating models, and explores recent advances and future research perspectives. Topics covered include molecular dynamics simulations of lipid membranes, phenomenological continuum mechanics of tissue growth, and translational cardiovascular modeling. Modeling Biomaterials will be a valuable resource for both non-specialists and experienced researchers from various domains of science, such as applied mathematics, biophysics, computational physiology, and medicine. .

Biomedical materials --- Mathematical models. --- Simulation methods. --- Bioartificial materials --- Biocompatible materials --- Biomaterials (Biomedical materials) --- Hemocompatible materials --- Medical materials --- Medicine --- Biomedical engineering --- Materials --- Biocompatibility --- Prosthesis --- Materials biomèdics --- Models matemàtics --- Mètodes de simulació --- Biomaterials --- Materials biocompatibles --- Materials mèdics --- Materials en medicina --- Enginyeria biomèdica --- Biocompatibilitat --- Col·loides en medicina --- Materials dentals --- Polímers en medicina --- Pròtesis --- Tècniques de simulació --- Investigació operativa --- Biònica --- Intel·ligència artificial --- Jocs de simulació --- Jocs d'estratègia (Matemàtica) --- Optimització matemàtica --- Simulació per ordinador --- Models (Matemàtica) --- Models experimentals --- Models teòrics --- Anàlisi de sistemes --- Mètode de Montecarlo --- Modelització multiescala --- Models economètrics --- Models lineals (Estadística) --- Models multinivell (Estadística) --- Models no lineals (Estadística) --- Programació (Ordinadors) --- Teoria de màquines --- Models biològics --- Stochastic models. --- Markov processes. --- Numerical analysis. --- Continuum mechanics. --- Biomaterials. --- Mathematical Modeling and Industrial Mathematics. --- Stochastic Modelling. --- Markov Process. --- Numerical Analysis. --- Continuum Mechanics. --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Mathematical analysis --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Models, Stochastic --- Mathematical models --- Models, Mathematical --- Simulation methods

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Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book's central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.

Boundary value problems --- Numerical solutions. --- Numerical solution of partial differential equations --- Operator and algebraic preconditioning in link with discretization --- Matching moments model reduction --- Conjugate gradient method --- Computational efficiency