Kent-Andre Mardal - Böcker

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms.

This open access volume presents a novel computational framework for understanding how collections of excitable cells work. The approach allows for very detailed analysis of small collections of excitable cells, but computational challenges limit the applicability in the presence of large collections of cells.

This open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs.

This volume brings together a series of insightful chapters that highlight the latest trends in modeling microcirculation. It casts a spotlight on the vital role of microcirculation in brain function modeling and the innovative applications of microvascular models in oncology.

Microcirculation is a key area of interest within the realms of biology and medicine. As a vital discipline, microcirculatory biology forms a significant part of established medical fields like cardiovascular medicine and oncology, and is increasingly relevant in emerging fields such as neuroscience. With its multifaceted nature, the study of microcirculation has evolved from basic observations and experiments to embrace cutting-edge imaging technologies, quantitative methods, and the power of data science. This volume brings together a series of insightful chapters that highlight the latest trends in modeling microcirculation. It casts a spotlight on the vital role of microcirculation in brain function modeling and the innovative applications of microvascular models in oncology. Readers will be introduced to state-of-the-art methodologies of microcirculation modeling. A key focus is on mixed-dimensional models, mathematical methods adept at describing complex interactions within lower dimensional manifolds. Each chapter thoughtfully navigates the mathematical, computational, and practical challenges of these approaches, underscoring their effectiveness in capturing the essence of microcirculation. This book offers a window into the latest advancements and methodologies that are shaping the future of this vital field.

This open access book revolves around predictive mathematical modelling and simulation of brain multiphysics with an emphasis on cerebrospinal fluid flow and solute transport in and around the human brain.

The heart is a fantastic machine; during a normal lifetime it beats about 2.5 billion times and pumps 200.000 tons of blood through an enormous system of vessels extending 160.000 kilometres throughout the body. For centuries, man has tried to understand how the heart works, but there remain many unsolved problems, problems that have captured the attention of thousands of researchers worldwide. There is, for example, a huge amount of research being devoted to the analysis of single heart cells. Other areas of research include trying to understand how it works as a complete muscle, and how blood ows through the heart. The entire process is extremely complex. The history of bioelectricity can be traced back to the late eighteenth century and the experiments of Luigi Galvani. A century later, in 1887, Augustus Wallers managed to measure the electrical signal generated by the heart at the surface of the body [142]. His dog Jimmy earned a place in history by being the rst to have his heart measured in this way; see Figure 1.1. In 1903 Willem Einthoven [34] - veloped the rst commercial device for recording electrocardiograms (ECGs); see Figure 1.2.

The heart is a fantastic machine; during a normal lifetime it beats about 2.5 billion times and pumps 200.000 tons of blood through an enormous system of vessels extending 160.000 kilometres throughout the body. For centuries, man has tried to understand how the heart works, but there remain many unsolved problems, problems that have captured the attention of thousands of researchers worldwide. There is, for example, a huge amount of research being devoted to the analysis of single heart cells. Other areas of research include trying to understand how it works as a complete muscle, and how blood ows through the heart. The entire process is extremely complex. The history of bioelectricity can be traced back to the late eighteenth century and the experiments of Luigi Galvani. A century later, in 1887, Augustus Wallers managed to measure the electrical signal generated by the heart at the surface of the body [142]. His dog Jimmy earned a place in history by being the rst to have his heart measured in this way; see Figure 1.1. In 1903 Willem Einthoven [34] - veloped the rst commercial device for recording electrocardiograms (ECGs); see Figure 1.2.

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.