Discontinuous Galerkin (DG) methods for solving partial differential equations, developed in the late 1990s, have become popular among computational scientists. This book covers both theory and computation as it focus...
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ISBN:
(数字)9780898717440
ISBN:
(纸本)089871656X
Discontinuous Galerkin (DG) methods for solving partial differential equations, developed in the late 1990s, have become popular among computational scientists. This book covers both theory and computation as it focuses on three primal DG methods--the symmetric interior penalty Galerkin, incomplete interior penalty Galerkin, and nonsymmetric interior penalty Galerkin which are variations of interior penalty methods. The author provides the basic tools for analysis and discusses coding issues, including data structure, construction of local matrices, and assembling of the global matrix. Computational examples and applications to important engineering problems are also included. Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation is divided into three parts: Part I focuses on the application of DG methods to second order elliptic problems in one dimension and in higher dimensions. Part II presents the time-dependent parabolic problems without and with convection. Part III contains applications of DG methods to solid mechanics (linear elasticity), fluid dynamics (Stokes and Navier Stokes), and porous media flow (two-phase and miscible displacement). Appendices contain proofs and MATLAB code for one-dimensional problems for elliptic equations and routines written in C that correspond to algorithms for the implementation of DG methods in two or three dimensions. Audience: This book is intended for numerical analysts, computational and applied mathematicians interested in numerical methods for partial differential equations or who study the applications discussed in the book, and engineers who work in fluid dynamics and solid mechanics and want to use DG methods for their numerical results. The book is appropriate for graduate courses in finite element methods, numerical methods for partial differential equations, numerical analysis, and scientific computing. Chapter 1 is suitable for a senior undergraduate class in scien
Bioconsensus is a rapidly evolving scientific field in which consensus methods, often developed for use in social choice theory, are adapted for such areas of the biological sciences as taxonomy, systematics, and evol...
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ISBN:
(数字)9780898717501
ISBN:
(纸本)9780898715514
Bioconsensus is a rapidly evolving scientific field in which consensus methods, often developed for use in social choice theory, are adapted for such areas of the biological sciences as taxonomy, systematics, and evolutionary and molecular biology. Typically, after several alternatives are produced using different data sets, methods or algorithms, one needs to find a consensus solution.
The axiomatic approach of this book explores the existence or nonexistence of consensus rules that satisfy particular sets of desirable well-defined properties. The axiomatic research reviewed here focuses first on the area of group choice, then in areas of biomathematics where the objects of interest represent partitions of a set, hierarchical structures, phylogenetic trees, or molecular sequences.
Axiomatic Consensus Theory in Group Choice and Biomathematics provides a unique comprehensive review of axiomatic consensus theory in biomathematics as it has developed over the past 30 years. Established here are the theory's basic results using standard terminology and notation and with uniform attention to rigor and detail. This book cites both traditional and current literature and poses open problems that remain to be solved. The bibliographic notes in each chapter place the described work within a general context while providing useful pointers to relevant research. The bibliographic references are a valuable resource for both students and experts in the field.
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