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Analysis Of The Robin Dirichlet Iterative Procedure For Solving The Cauchy Problem For Elliptic Equations With Extension To Unbounded Domains
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Book Synopsis Analysis of the Robin-Dirichlet iterative procedure for solving the Cauchy problem for elliptic equations with extension to unbounded domains by : Pauline Achieng
Download or read book Analysis of the Robin-Dirichlet iterative procedure for solving the Cauchy problem for elliptic equations with extension to unbounded domains written by Pauline Achieng and published by Linköping University Electronic Press. This book was released on 2020-10-26 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we study the Cauchy problem for elliptic equations. It arises in many areas of application in science and engineering as a problem of reconstruction of solutions to elliptic equations in a domain from boundary measurements taken on a part of the boundary of this domain. The Cauchy problem for elliptic equations is known to be ill-posed. We use an iterative regularization method based on alternatively solving a sequence of well-posed mixed boundary value problems for the same elliptic equation. This method, based on iterations between Dirichlet-Neumann and Neumann-Dirichlet mixed boundary value problems was first proposed by Kozlov and Maz’ya [13] for Laplace equation and Lame’ system but not Helmholtz-type equations. As a result different modifications of this original regularization method have been proposed in literature. We consider the Robin-Dirichlet iterative method proposed by Mpinganzima et.al [3] for the Cauchy problem for the Helmholtz equation in bounded domains. We demonstrate that the Robin-Dirichlet iterative procedure is convergent for second order elliptic equations with variable coefficients provided the parameter in the Robin condition is appropriately chosen. We further investigate the convergence of the Robin-Dirichlet iterative procedure for the Cauchy problem for the Helmholtz equation in a an unbounded domain. We derive and analyse the necessary conditions needed for the convergence of the procedure. In the numerical experiments, the precise behaviour of the procedure for different values of k2 in the Helmholtz equation is investigated and the results show that the speed of convergence depends on the choice of the Robin parameters, ?0 and ?1. In the unbounded domain case, the numerical experiments demonstrate that the procedure is convergent provided that the domain is truncated appropriately and the Robin parameters, ?0 and ?1 are also chosen appropriately.
Book Synopsis Reconstruction of Solutions of Cauchy Problems for Elliptic Equations in Bounded and Unbounded Domains Using Iterative Regularization Methods by : Pauline Achieng
Download or read book Reconstruction of Solutions of Cauchy Problems for Elliptic Equations in Bounded and Unbounded Domains Using Iterative Regularization Methods written by Pauline Achieng and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Cauchy Problem for Solutions of Elliptic Equations by : Nikolaĭ Nikolaevich Tarkhanov
Download or read book The Cauchy Problem for Solutions of Elliptic Equations written by Nikolaĭ Nikolaevich Tarkhanov and published by De Gruyter Akademie Forschung. This book was released on 1995 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an attempt to bring together various topics in partial differential equations related to the Cauchy problem for solutions of an elliptic equation. Ever since Hadamard, the Cauchy problem for solutions of elliptic equations has been known to be ill-posed.
Book Synopsis The Dirichlet Problem with L2-Boundary Data for Elliptic Linear Equations by : Jan Chabrowski
Download or read book The Dirichlet Problem with L2-Boundary Data for Elliptic Linear Equations written by Jan Chabrowski and published by Springer. This book was released on 2006-11-14 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dirichlet problem has a very long history in mathematics and its importance in partial differential equations, harmonic analysis, potential theory and the applied sciences is well-known. In the last decade the Dirichlet problem with L2-boundary data has attracted the attention of several mathematicians. The significant features of this recent research are the use of weighted Sobolev spaces, existence results for elliptic equations under very weak regularity assumptions on coefficients, energy estimates involving L2-norm of a boundary data and the construction of a space larger than the usual Sobolev space W1,2 such that every L2-function on the boundary of a given set is the trace of a suitable element of this space. The book gives a concise account of main aspects of these recent developments and is intended for researchers and graduate students. Some basic knowledge of Sobolev spaces and measure theory is required.
Book Synopsis Accelerated Dirichlet-Robin Alternating Algorithm for Solving the Cauchy Problem for an Elliptic Equation Using Krylov Subspaces by :
Download or read book Accelerated Dirichlet-Robin Alternating Algorithm for Solving the Cauchy Problem for an Elliptic Equation Using Krylov Subspaces written by and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of Elliptic Problems by : Garrett Birkhoff
Download or read book Numerical Solution of Elliptic Problems written by Garrett Birkhoff and published by Soc for Industrial & Applied Math. This book was released on 1984 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Book Synopsis Iterative Methods and Preconditioners for Systems of Linear Equations by : Gabriele Ciaramella
Download or read book Iterative Methods and Preconditioners for Systems of Linear Equations written by Gabriele Ciaramella and published by SIAM. This book was released on 2022-02-08 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative methods use successive approximations to obtain more accurate solutions. This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations and optimal control problems governed by the Laplace equation, for which the use of matrix-free procedures is crucial. All methods are explained and analyzed starting from the historical ideas of the inventors, which are often quoted from their seminal works. Iterative Methods and Preconditioners for Systems of Linear Equations grew out of a set of lecture notes that were improved and enriched over time, resulting in a clear focus for the teaching methodology, which derives complete convergence estimates for all methods, illustrates and provides MATLAB codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students who want an overview or deeper understanding of iterative methods. Its focus on both analysis and numerical experiments allows the material to be taught with very little preparation, since all the arguments are self-contained, and makes it appropriate for self-study as well. It can be used in courses on iterative methods, Krylov methods and preconditioners, and numerical optimal control. Scientists and engineers interested in new topics and applications will also find the text useful.
Book Synopsis Direct and Inverse Imbedding Theorems by : Lev Dmitrievich Kudri͡avt͡sev
Download or read book Direct and Inverse Imbedding Theorems written by Lev Dmitrievich Kudri͡avt͡sev and published by American Mathematical Soc.. This book was released on 1959 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic Problems in Nonsmooth Domains by : Pierre Grisvard
Download or read book Elliptic Problems in Nonsmooth Domains written by Pierre Grisvard and published by Pitman Advanced Publishing Program. This book was released on 1985 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Partial Differential Equations by : Walter A. Strauss
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Book Synopsis Singular and Degenerate Cauchy Problems by :
Download or read book Singular and Degenerate Cauchy Problems written by and published by Academic Press. This book was released on 1977-01-13 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Book Synopsis The Dirichlet Problem for the Laplacian in Bounded and Unbounded Domains by : Christian G Simader
Download or read book The Dirichlet Problem for the Laplacian in Bounded and Unbounded Domains written by Christian G Simader and published by CRC Press. This book was released on 1996-11-07 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dirichlet Problem -?u=ƒ in G, u|?G=0 for the Laplacian in a domain GÌRn with boundary ?G is one of the basic problems in the theory of partial differential equations and it plays a fundamental role in mathematical physics and engineering.
Book Synopsis A Parallel Multigrid Method for Solving Elliptic Partial Differential Equations by : Theodore E. Ferretta
Download or read book A Parallel Multigrid Method for Solving Elliptic Partial Differential Equations written by Theodore E. Ferretta and published by . This book was released on 1989 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Approximation Methods for Elliptic Boundary Value Problems by : Olaf Steinbach
Download or read book Numerical Approximation Methods for Elliptic Boundary Value Problems written by Olaf Steinbach and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.
Book Synopsis On a Priori Estimates of the First Derivatives of Solutions of the Dirichlet Problem for Quasilinear Elliptic Equations in an Unbounded Domain by : A. P. Oskolkov
Download or read book On a Priori Estimates of the First Derivatives of Solutions of the Dirichlet Problem for Quasilinear Elliptic Equations in an Unbounded Domain written by A. P. Oskolkov and published by . This book was released on 1966 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Cauchy's Problem in Linear Partial Differential Equations by : Jacques Hadamard
Download or read book Lectures on Cauchy's Problem in Linear Partial Differential Equations written by Jacques Hadamard and published by . This book was released on 1923 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
