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Boundary element methods are very important for solving boundary value problems in PDEs. Many boundary value problems of partial differential equations can be reduced into boundary integral equations by the natural boundary reduction. In this book the natural boundary integral method, suggested and developed by Feng and Yu, is introduced systematically. It is quite different from popular boundary element methods and has many distinctive advantages. The variational principle is conserved after the natural boundary reduction, and some useful properties are also preserved faithfully. Moreover, it can be applied directly and naturally in the coupling method and the domain decomposition method of finite and boundary elements. Most of the material in this book has only appeared in the author's previous papers. Compared with its Chinese edition (Science Press, Beijing, 1993), many new research results such as the domain decomposition methods based on the natural boundary reduction are added.
List of contents
Preface.- I. General Principle of the Natural Boundary Integral Method.- II. Boundary Value Problem for the Harmonic Equation.- III. Boundary Value Problem of the Biharmonic Equation.- IV. Plane Elasticity Problem.- V. Stokes' Problem.- VI. The Coupling of Natural Boundary Elements and Finite Elements.- VII. Domain Decomposition Methods Based On Natural Boundary Reduction.- References.- Index.
Summary
Boundary element methods are very important for solving boundary value problems in PDEs. Many boundary value problems of partial differential equations can be reduced into boundary integral equations by the natural boundary reduction. In this book the natural boundary integral method, suggested and developed by Feng and Yu, is introduced systematically. It is quite different from popular boundary element methods and has many distinctive advantages. The variational principle is conserved after the natural boundary reduction, and some useful properties are also preserved faithfully. Moreover, it can be applied directly and naturally in the coupling method and the domain decomposition method of finite and boundary elements. Most of the material in this book has only appeared in the author's previous papers. Compared with its Chinese edition (Science Press, Beijing, 1993), many new research results such as the domain decomposition methods based on the natural boundary reduction are added.
Additional text
Natural Boundary Integral Method and Its Applications
"The book includes many useful formulas as well as entries on stiffness matrices for many examples in the aforementioned class of applications and it outlines many existence results and error estimates in scales of Sobolev spaces from the Chinese literature."
(D.H.Yu, MATHEMATICAL REVIEWS)
Report
Natural Boundary Integral Method and Its Applications
"The book includes many useful formulas as well as entries on stiffness matrices for many examples in the aforementioned class of applications and it outlines many existence results and error estimates in scales of Sobolev spaces from the Chinese literature."
(D.H.Yu, MATHEMATICAL REVIEWS)
