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W S HALL School of Computing and Mathematics, University of Teesside, Middlesbrough, TS1 3BA UK G OLIVETO Division of Structural Engineering, Department of Civil and Environmental Engineering, University of Catania, Viale A. Doria 6, 95125 Catania, Italy Soil-Structure Interaction is a challenging multidisciplinary subject which covers several areas of Civil Engineering. Virtually every construction is connected to the ground and the interaction between the artefact and the foundation medium may affect considerably both the superstructure and the foundation soil. The Soil-Structure Interaction problem has become an important feature of Structural Engineering with the advent of massive constructions on soft soils such as nuclear power plants, concrete and earth dams. Buildings, bridges, tunnels and underground structures may also require particular attention to be given to the problems of Soil-Structure Interaction. Dynamic Soil-Structure Interaction is prominent in Earthquake Engineering problems. The complexity of the problem, due also to its multidisciplinary nature and to the fact of having to consider bounded and unbounded media of different mechanical characteristics, requires a numerical treatment for any application of engineering significance. The Boundary Element Method appears to be well suited to solve problems of Soil- Structure Interaction through its ability to discretize only the boundaries of complex and often unbounded geometries. Non-linear problems which often arise in Soil-Structure Interaction may also be treated advantageously by a judicious mix of Boundary and Finite Element discretizations.

Soil-structure interaction. --- Mechanics. --- Boundary element methods

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The purpose of this book is to give a comprehensive exposition of the theory of boundary integral equations for single and double layer potentials on curves with exterior and interior cusps. The theory was developed by the authors during the last twenty years and the present volume is based on their results. The first three chapters are devoted to harmonic potentials, and in the final chapter elastic potentials are treated. Theorems on solvability in various function spaces and asymptotic representations for solutions near the cusps are obtained. Kernels and cokernels of the integral operators

Boundary element methods -- Congresses. --- Boundary element methods. --- Nonlinear theories -- Congresses. --- Nonlinear theories. --- Boundary value problems --- Boundary element methods --- Dirichlet problem --- Neumann problem --- Elasticity --- Integral equations --- Civil & Environmental Engineering --- Mathematics --- Calculus --- Operations Research --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Integral equations. --- Equations, Integral --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Mathematics. --- Integral Equations. --- Functional equations --- Functional analysis --- Numerical analysis

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This book constructs a non-Bloch band theory and studies physics described by non-Hermitian Hamiltonian in terms of the theory proposed here. In non-Hermitian crystals, the author introduces the non-Bloch band theory which produces an energy spectrum in the limit of a large system size. The energy spectrum is then calculated from a generalized Brillouin zone for a complex Bloch wave number. While a generalized Brillouin zone becomes a unit circle on a complex plane in Hermitian systems, it becomes a circle with cusps in non-Hermitian systems. Such unique features of the generalized Brillouin zone realize remarkable phenomena peculiar in non-Hermitian systems. Further the author reveals rich aspects of non-Hermitian physics in terms of the non-Bloch band theory. First, a topological invariant defined by a generalized Brillouin zone implies the appearance of topological edge states. Second, a topological semimetal phase with exceptional points appears, The topological semimetal phase is unique to non-Hermitian systems because it is caused by the deformation of the generalized Brillouin zone by changes of system parameters. Third, the author reveals a certain relationship between the non-Bloch waves and non-Hermitian topology.

Mathematical physics --- Quantum mechanics. Quantumfield theory --- Statistical physics --- Solid state physics --- Matter physics --- EMI (electromagnetic interference) --- materie (fysica) --- quantummechanica --- theoretische fysica --- wiskunde --- fysica --- Boundary element methods. --- Condensed matter.

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Boundary Element Methods have become a major numerical tool in scientific and engineering problem-solving, with particular applications to numerical computations and simulations of partial differential equations in engineering. Boundary Element Methods provides a rigorous and systematic account of the modern mathematical theory of Boundary Element Methods, including the requisite background on general partial, differential equation methods, Sobolev spaces, pseudo-differential and Fredholm operators and finite elements. It aims at the computation of many types of elliptic boundary value problems in potential theory, elasticity, wave propagation, and structural mechanics. Also presented are various methods and algorithms for nonlinear partial differential equations. This second edition has been fully revised and combines the mathematical rigour necessary for a full understanding of the subject, with extensive examples of applications illustrated with computer graphics. This book is intended as a textbook and reference for applied mathematicians, physical scientists and engineers at graduate and research level. It will be an invaluable sourcebook for all concerned with numerical modeling and the solution of partial differential equations.

Boundary element methods. --- Nonlinear theories. --- Numerical analysis. --- Operator theory. --- Boundary element methods --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Mathematics. --- Operator Theory. --- Numerical Analysis. --- Mathematical analysis --- Functional analysis --- Math --- Science --- Numerical analysis

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Finite element method --- Galerkin methods --- Boundary element methods --- Boundary value problems --- Méthode des éléments finis --- Galerkin, Méthode de --- Equations intégrales de frontière, Méthodes des --- Problèmes aux limites --- Numerical solutions --- Solutions numériques