The Boundary Element Method for Solving Improperly Posed Problems
Published on 31. March 1994
Book
Hardback
230 pages
978-1-85312-291-0 (ISBN)
Description
In recent years, an increasing amount of research work has been carried out on the application of the Boundary Element Method (BEM), to a growing variety of problems. The purpose of this book is to extend the range of applications of the BEM, with a view to establishing a sound basis on which to build new solution procedures with particular attention being paid to problems which arise in inverse heat conduction. The minimal energy technique has been introduced to modify the BEM for solving heat conduction problems which are improperly posed and the results indicate that excellent convergent and stable numerical approximate solutions may be obtained for various inverse heat conduction problems, which may be linear or nonlinear, steady or unsteady. Examples show that the agreement between the numerical results and the analytical solutions, where available, is excellent.
More details
Series
Language
English
Place of publication
Southampton
United Kingdom
Target group
College/higher education
Professional and scholarly
Illustrations
Ill.tabs.ch.
Dimensions
Height: 250 mm
ISBN-13
978-1-85312-291-0 (9781853122910)
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Schweitzer Classification
Content
General introduction - improperly posed problems; the boundary element method; steady inverse heat conduction problems; unsteady inverse heat conduction problems; the boundary element method - the formulation for the Laplace Equation; the formulation for nonlinear problems; the formulation of the time dependent problem; solution of the Laplace Equation with insufficient Dirichlet boundary conditions; mathematical models - direct method, least-squares method, minimization of energy method; numerical examples; existence of solution; a numerical investigation into the stability; conclusions; solution of the Laplace Equation with insufficient Dirichlet-Neuman mixed boundary conditions - mathematical model; numerical examples; determination of an unknown function in the boundary condition; conclusions; solution of the improperly posed nonlinear heat conduction problem with the thermal conductivity a given function of temperature - mathematical model; numerical examples; conclusions; solution of an improperly posed nonlinear heat conduction problem with an unknown thermal conductivity - mathematical model; Dirichlet problem - polynomial solutions, piecewise quadratic solutions, other boundary problems; conclusions; solution of the backward heat conduction problem - mathematical model - direct method, least-squares method, minimization of energy method; numerical results; solutions with Dirichlet-Neuman mixed boundary conditions; conclusions.