Fast Direct Solvers For Elliptic Pdes
DOWNLOAD
Download Fast Direct Solvers For Elliptic Pdes PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Fast Direct Solvers For Elliptic Pdes book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Fast Direct Solvers For Elliptic Pdes
DOWNLOAD
Author : Per-Gunnar Martinsson
language : en
Publisher: SIAM
Release Date : 2019-12-16
Fast Direct Solvers For Elliptic Pdes written by Per-Gunnar Martinsson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-16 with Mathematics categories.
Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.
Computational Methods In Optimal Control
DOWNLOAD
Author : William H. Hager
language : en
Publisher: SIAM
Release Date : 2025-02-13
Computational Methods In Optimal Control written by William H. Hager and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-13 with Mathematics categories.
Using material from many different sources in a systematic and unified way, this self-contained book provides both rigorous mathematical theory and practical numerical insights while developing a framework for determining the convergence rate of discrete approximations to optimal control problems. Elements of the framework include the reference point, the truncation error, and a stability theory for the linearized first-order optimality conditions. Within this framework, the discretized control problem has a stationary point whose distance to the reference point is bounded in terms of the truncation error. The theory applies to a broad range of discretizations and provides completely new insights into the convergence theory for discrete approximations in optimal control, including the relationship between orthogonal collocation and Runge–Kutta methods. Throughout the book, derivatives associated with the discretized control problem are expressed in terms of a back-propagated costate. In particular, the objective derivative of a bang-bang or singular control problem with respect to a switch point of the control are obtained, which leads to the efficient solution of a class of nonsmooth control problems using a gradient-based optimizer. Computational Methods in Optimal Control: Theory and Practice is intended for numerical analysts and computational scientists. Users of the software package GPOPS may find the book useful since the theoretical basis for the GPOPS algorithm is developed within the book. It is appropriate for courses in variational analysis, numerical optimization, and the calculus of variations.
Inverse Scattering Theory And Transmission Eigenvalues
DOWNLOAD
Author : Fioralba Cakoni
language : en
Publisher: SIAM
Release Date : 2022-12-07
Inverse Scattering Theory And Transmission Eigenvalues written by Fioralba Cakoni and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-07 with Mathematics categories.
Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.
Numerical Linear Algebra
DOWNLOAD
Author : Lloyd N. Trefethen
language : en
Publisher: SIAM
Release Date : 2022-06-17
Numerical Linear Algebra written by Lloyd N. Trefethen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-17 with Mathematics categories.
Since its original appearance in 1997, Numerical Linear Algebra has been a leading textbook in its field, used in universities around the world. It is noted for its 40 lecture-sized short chapters and its clear and inviting style. It is reissued here with a new foreword by James Nagy and a new afterword by Yuji Nakatsukasa about subsequent developments.
Siam Journal On Scientific Computing
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 2006
Siam Journal On Scientific Computing written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematical statistics categories.
Optimization Discrete Mathematics And Applications To Data Sciences
DOWNLOAD
Author : Ashkan Nikeghbali
language : en
Publisher: Springer Nature
Release Date : 2025-01-08
Optimization Discrete Mathematics And Applications To Data Sciences written by Ashkan Nikeghbali and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-08 with Mathematics categories.
This book delves into the dynamic intersection of optimization and discrete mathematics, offering a comprehensive exploration of their applications in data sciences. Through a collection of high-quality papers, readers will gain insights into cutting-edge research and methodologies that address complex problems across a wide array of topics. The chapters cover an impressive range of subjects, including advances in the study of polynomials, combinatorial identities, and global optimization algorithms. Readers will encounter innovative approaches to predictive models for non-performing loans, rainbow greedy matching algorithms, and the cost of detection in interaction testing. The book also examines critical issues such as demand aggregation, mid-term energy planning, and minimum-cost energy flow. Contributions from expert authors provide a deep dive into multilevel low-rank matrices, the protection of medical image authenticity, and the mathematical intricacies of the Braess paradox. This volume invites readers to explore diverse perspectives and theoretical insights that are both practical and forward-thinking. This publication is an invaluable resource for graduate students and advanced researchers in the fields of optimization and discrete mathematics. It is particularly beneficial for those interested in their applications within data sciences. Academics across these disciplines will find the book's content relevant to their work, while practitioners seeking to apply these concepts in industry will appreciate its practical case studies. Whether you are a scholar or a professional, this book offers a wealth of knowledge that bridges theory with real-world applications.
A Tutorial On Elliptic Pde Solvers And Their Parallelization
DOWNLOAD
Author : Craig C. Douglas
language : en
Publisher: SIAM
Release Date : 2003-01-01
A Tutorial On Elliptic Pde Solvers And Their Parallelization written by Craig C. Douglas and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Technology & Engineering categories.
This compact yet thorough tutorial is the perfect introduction to the basic concepts of solving partial differential equations (PDEs) using parallel numerical methods. In just eight short chapters, the authors provide readers with enough basic knowledge of PDEs, discretization methods, solution techniques, parallel computers, parallel programming, and the run-time behavior of parallel algorithms to allow them to understand, develop, and implement parallel PDE solvers. Examples throughout the book are intentionally kept simple so that the parallelization strategies are not dominated by technical details.
Petsc For Partial Differential Equations Numerical Solutions In C And Python
DOWNLOAD
Author : Ed Bueler
language : en
Publisher: SIAM
Release Date : 2020-10-22
Petsc For Partial Differential Equations Numerical Solutions In C And Python written by Ed Bueler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-22 with Mathematics categories.
The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.
Nasa Technical Paper
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 1986
Nasa Technical Paper written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Science categories.
Nasa Technical Note
DOWNLOAD
Author : United States. National Aeronautics and Space Administration
language : en
Publisher:
Release Date : 1975
Nasa Technical Note written by United States. National Aeronautics and Space Administration and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Aeronautics categories.