This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros, the extrema, and the integrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete and appealing, the programming environments Matlab and Octave are adopted as faithful companions. The book contains...
This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of ...
The book comprises the contribution of several authors who are among the most renowned scientists working in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. The contributions cover a wide range of topics, from the pre processing of clinical data, to the set up of mathematical equations, their numerical solution, both in-vivo and in-vitro validation. They address the flow in the systemic arterial tree and the complex electro- fluid-mechanical coupling in the human heart. Many examples of patient-specific simulations are addressed. This book is...
The book comprises the contribution of several authors who are among the most renowned scientists working in the field of mathematical modeling and nu...
Spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of their 1988 book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since then.
This second new treatment, Evolution to Complex Geometries and Applications to Fluid Dynamics, provides an extensive overview of the essential...
Spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering com...
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization.
The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures.
More specifically, the authors discuss alternative...
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equation...
In questo testo si introducono i concetti di base per la modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes e le leggi di conservazione; si forniscono inoltre numerosi esempi fisici che stanno alla base di tali equazioni. Quindi si analizzano metodi di risoluzione numerica basati su elementi finiti (continui e discontinui), differenze finite, volumi finiti, metodi spettrali (continui e discontinui), nonche...
In questo testo si introducono i concetti di base per la modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le cla...
This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros, the extrema, and the integrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete and appealing, the programming environments Matlab and Octave are adopted as faithful companions. The book contains...
This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of ...
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 book introduces the basic concepts for the numerical modelling of partial differential equations. It details algorithmic and computer implementa...
This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.
Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in...
This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, gover...
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 comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human ...
In this text, we introduce the basic concepts for the numerical modeling of partial differential equations. 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. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and...
In this text, we introduce the basic concepts for the numerical modeling of partial differential equations. We consider the classical elliptic, parabo...
