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Analysis and implementation of isogeometric boundary elements for electromagnetism / / Felix Wolf
Analysis and implementation of isogeometric boundary elements for electromagnetism / / Felix Wolf
Autore Wolf Felix
Edizione [1st ed. 2021.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (XX, 128 p. 38 illus., 25 illus. in color.)
Disciplina 537.0151
Collana Springer Theses
Soggetto topico Electromagnetism - Mathematics
Boundary element methods
ISBN 3-030-61939-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Foundations -- Isogeometric Boundary Elements -- Algorithmic Considerations for Matrix Assembly -- The Discrete Eigenvalue Problem.
Record Nr. UNINA-9910484267303321
Wolf Felix  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
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The boundary element method for engineers and scientists : theory and applications / / John T. Katsikadelis
The boundary element method for engineers and scientists : theory and applications / / John T. Katsikadelis
Autore Katsikadelis John T.
Edizione [Second edition.]
Pubbl/distr/stampa Amsterdam, [Netherlands] : , : Academic Press, , 2016
Descrizione fisica 1 online resource (466 pages) : illustrations
Disciplina 620.00151535
Soggetto topico Boundary element methods
ISBN 0-12-802010-5
0-12-804493-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910583034103321
Katsikadelis John T.  
Amsterdam, [Netherlands] : , : Academic Press, , 2016
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Boundary element methods in applied mechanics : proceedings of the First Joint Japan/US Symposium on Boundary Element Methods, University of Tokyo, Tokyo, Japan, 3-6 October 1988 / / editors, Masataka Tanaka, Thomas A. Cruse
Boundary element methods in applied mechanics : proceedings of the First Joint Japan/US Symposium on Boundary Element Methods, University of Tokyo, Tokyo, Japan, 3-6 October 1988 / / editors, Masataka Tanaka, Thomas A. Cruse
Edizione [First edition.]
Pubbl/distr/stampa Oxford, England : , : Pergamon Press plc, , 1988
Descrizione fisica 1 online resource (571 p.)
Disciplina 620.1001535
Soggetto topico Boundary element methods
Mechanics, Applied
ISBN 1-4832-8696-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front Cover; Boundary Element Methods in Applied Mechanics; Copyright Page; Table of Contents; Preface; COMMITTEES; ORGANIZING COMMITTEE; LOCAL ORGANIZING COMMITTEE; SCIENTIFIC ADVISORY COMMITTEE; PART 1: MATHEMATICAL ASPECTS; Chapter 1. Heat Conduction Analysis Using Single Layer Heat Potential; 1. INTRODUCTION; 2. DIRICHLET PROBLEM IN A NON-SMOOTH DOMAIN; 3. BOUNDARY INTEGRAL EQUATION OF THE FIRST KIND; 4. APPROXIMATION ON THE BOUNDARY; 5. APPROXIMATION IN TIME; ACKNOWLEDGEMENTS; REFERENCES; Chapter 2. A Variational Approach to Boundary Element Methods; INTRODUCTION
THE ELASTOSTATIC PROBLEMTHE ELASTODYNAMIC PROBLEM; CONCLUSION; Acknowledgement.; REFERENCES; APPENDIX; Chapter 3. BEM Formulations for Body Forces Using Particular Integrals; ABSTRACT; INTRODUCTION; CENTRIFUGAL FORCES AND SELF-WEIGHT; FREE-VIBRATION ANALYSIS; ACOOSTIC EKETFRBCUENCY ANALYSIS; THERMAL STRESS ANALYSIS; HLASTOPLASTIC ANALYSIS; CONCLUSIONS; REFERENCES; PART 2: NUMERICAL ASPECTS; Chapter 4. The Error Estimation of the Boundary Element Method on the Multi-regional and Non-linear Potential Problems; INTRODUCTION; THE METHOD OF THE ESTIMATING THE ERROR OF SOLUTION
THE EVALUATION OF THE DIFFERENCE ηu ON 3-DIMENSIONAL POTENTIAL PROBLEMSPOISSON EQUATION; NONLINEAR POISSON TYPE EQUATION; CONCLUSIONS; REFERENCES; Chapter 5. The Use of Continuous Finite Elements in Electron Optics; ABSTRACT; KEYWORDS; INTRODUCTION; THEORETICAL BACKGROUND; CONCLUSION; REFERENCES; Chapter 6. Comparison of the Boundary Collocation and the Boundary Element Methods; INTRODUCTION; TEST PROBLEMS WITH ANALYTICAL SOLUTIONS AND ERROR CRITERIA; THE BOUNDARY COLLOCATION METHOD; THE BOUNDARY ELEMENT METHOD; COMPARISON OF RESULTS AND CONCLUSIONS; REFERENCES
Chapter 7. Efficient Numerical Integration for Boundary Integral Methods in Two-dimensional and Axisymmetric Potential ProblemsINTRODUCTION; BOUNDARY INTEGRAL METHOD; NUMERICAL INTEGRATION; COMPUTATION PROCEDURE AND RESULTS; CONCLUSION; REFERENCES; Chapter 8. Improved Galerkin Methods for Integral Equations on Polygons and Polyhedral Surfaces; Acknowledgements; REFERENCES; Chapter 9. A Self-adaptive Boundary Element Technique for 2-D Potential Analysis; ABSTRACT; 1. INTRODUCTION; 2. ERROR ESTIVATION AND REFINEMENT ALGORITHM; 3. NUMERICAL APPLICATIONS; 4. CONCLUSIONS; 5. ACKNOWLEDGEMENTS
6. REFERENCESChapter 10. BEASY - An Advanced Boundary Element Analysis System; 1. INTRODUCTION; 2. IMPROVED ELEMENT PERFORMANCE; 3. VOLUME INTEGRALS AND POINT SOURCES; 4. PRE AND POST PROCESSING FOR BEM; 5. CONCLUSIONS; REFERENCES; PART 3: POTENTIAL PROBLEMS; Chapter 11. An Analysis of the Axisymmetric Modified Heimholte Equation by Using the Boundary Element Method; INTRODUCTION; FUNDAMENTAL SOLUTION; INTEGRAL EQUATION METHOD; NUMERICAL PROPERTIES; NUMERICAL RESULTS; CONCLUSIONS; REFERENCES; PART4: ELASTICITY
Chapter 12. Application of Advanced BEM Code to Three-dimensional Stress Analysis and Fracture Mechanics Analysis
Record Nr. UNINA-9910789590703321
Oxford, England : , : Pergamon Press plc, , 1988
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Boundary element methods in applied mechanics : proceedings of the First Joint Japan/US Symposium on Boundary Element Methods, University of Tokyo, Tokyo, Japan, 3-6 October 1988 / / editors, Masataka Tanaka, Thomas A. Cruse
Boundary element methods in applied mechanics : proceedings of the First Joint Japan/US Symposium on Boundary Element Methods, University of Tokyo, Tokyo, Japan, 3-6 October 1988 / / editors, Masataka Tanaka, Thomas A. Cruse
Edizione [First edition.]
Pubbl/distr/stampa Oxford, England : , : Pergamon Press plc, , 1988
Descrizione fisica 1 online resource (571 p.)
Disciplina 620.1001535
Soggetto topico Boundary element methods
Mechanics, Applied
ISBN 1-4832-8696-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front Cover; Boundary Element Methods in Applied Mechanics; Copyright Page; Table of Contents; Preface; COMMITTEES; ORGANIZING COMMITTEE; LOCAL ORGANIZING COMMITTEE; SCIENTIFIC ADVISORY COMMITTEE; PART 1: MATHEMATICAL ASPECTS; Chapter 1. Heat Conduction Analysis Using Single Layer Heat Potential; 1. INTRODUCTION; 2. DIRICHLET PROBLEM IN A NON-SMOOTH DOMAIN; 3. BOUNDARY INTEGRAL EQUATION OF THE FIRST KIND; 4. APPROXIMATION ON THE BOUNDARY; 5. APPROXIMATION IN TIME; ACKNOWLEDGEMENTS; REFERENCES; Chapter 2. A Variational Approach to Boundary Element Methods; INTRODUCTION
THE ELASTOSTATIC PROBLEMTHE ELASTODYNAMIC PROBLEM; CONCLUSION; Acknowledgement.; REFERENCES; APPENDIX; Chapter 3. BEM Formulations for Body Forces Using Particular Integrals; ABSTRACT; INTRODUCTION; CENTRIFUGAL FORCES AND SELF-WEIGHT; FREE-VIBRATION ANALYSIS; ACOOSTIC EKETFRBCUENCY ANALYSIS; THERMAL STRESS ANALYSIS; HLASTOPLASTIC ANALYSIS; CONCLUSIONS; REFERENCES; PART 2: NUMERICAL ASPECTS; Chapter 4. The Error Estimation of the Boundary Element Method on the Multi-regional and Non-linear Potential Problems; INTRODUCTION; THE METHOD OF THE ESTIMATING THE ERROR OF SOLUTION
THE EVALUATION OF THE DIFFERENCE ηu ON 3-DIMENSIONAL POTENTIAL PROBLEMSPOISSON EQUATION; NONLINEAR POISSON TYPE EQUATION; CONCLUSIONS; REFERENCES; Chapter 5. The Use of Continuous Finite Elements in Electron Optics; ABSTRACT; KEYWORDS; INTRODUCTION; THEORETICAL BACKGROUND; CONCLUSION; REFERENCES; Chapter 6. Comparison of the Boundary Collocation and the Boundary Element Methods; INTRODUCTION; TEST PROBLEMS WITH ANALYTICAL SOLUTIONS AND ERROR CRITERIA; THE BOUNDARY COLLOCATION METHOD; THE BOUNDARY ELEMENT METHOD; COMPARISON OF RESULTS AND CONCLUSIONS; REFERENCES
Chapter 7. Efficient Numerical Integration for Boundary Integral Methods in Two-dimensional and Axisymmetric Potential ProblemsINTRODUCTION; BOUNDARY INTEGRAL METHOD; NUMERICAL INTEGRATION; COMPUTATION PROCEDURE AND RESULTS; CONCLUSION; REFERENCES; Chapter 8. Improved Galerkin Methods for Integral Equations on Polygons and Polyhedral Surfaces; Acknowledgements; REFERENCES; Chapter 9. A Self-adaptive Boundary Element Technique for 2-D Potential Analysis; ABSTRACT; 1. INTRODUCTION; 2. ERROR ESTIVATION AND REFINEMENT ALGORITHM; 3. NUMERICAL APPLICATIONS; 4. CONCLUSIONS; 5. ACKNOWLEDGEMENTS
6. REFERENCESChapter 10. BEASY - An Advanced Boundary Element Analysis System; 1. INTRODUCTION; 2. IMPROVED ELEMENT PERFORMANCE; 3. VOLUME INTEGRALS AND POINT SOURCES; 4. PRE AND POST PROCESSING FOR BEM; 5. CONCLUSIONS; REFERENCES; PART 3: POTENTIAL PROBLEMS; Chapter 11. An Analysis of the Axisymmetric Modified Heimholte Equation by Using the Boundary Element Method; INTRODUCTION; FUNDAMENTAL SOLUTION; INTEGRAL EQUATION METHOD; NUMERICAL PROPERTIES; NUMERICAL RESULTS; CONCLUSIONS; REFERENCES; PART4: ELASTICITY
Chapter 12. Application of Advanced BEM Code to Three-dimensional Stress Analysis and Fracture Mechanics Analysis
Record Nr. UNINA-9910820716803321
Oxford, England : , : Pergamon Press plc, , 1988
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Boundary element methods in engineering and sciences [[electronic resource] /] / M.H. Aliabadi, P.H. Wen
Boundary element methods in engineering and sciences [[electronic resource] /] / M.H. Aliabadi, P.H. Wen
Autore Aliabadi M. H
Pubbl/distr/stampa London, : Imperial College Press, 2011
Descrizione fisica 1 online resource (450 p.)
Disciplina 620.00151535
Altri autori (Persone) WenP. H
Collana Computational and experimental methods in structures
Soggetto topico Boundary element methods
Engineering mathematics
Soggetto genere / forma Electronic books.
ISBN 1-283-14342-9
9786613143426
1-84816-580-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto PREFACE; CONTENTS; Chapter 1 THE BOUNDARY ELEMENT METHOD FOR GEOMETRICALLY NON-LINEAR ANALYSES OF PLATES AND SHELLS; Chapter 2 TIME-DOMAIN BEM TECHNIQUES; Chapter 3 THE BOUNDARY ELEMENT METHOD FOR THE FRACTURE ANALYSIS OF THE GENERAL PIEZOELECTRIC SOLIDS; Chapter 4 BOUNDARY INTEGRAL ANALYSIS FOR THREE-DIMENSIONAL EXPONENTIALLY GRADED ELASTICITY; Chapter 5 FAST HIERARCHICAL BOUNDARY ELEMENT METHOD FOR LARGE-SCALE 3-D ELASTIC PROBLEMS; Chapter 6 MODELLING OF PLATES AND SHALLOW SHELLS BY MESHLESS LOCAL INTEGRAL EQUATION METHOD
Chapter 7 BOUNDARY ELEMENT TECHNIQUE FOR SLOW VISCOUS FLOWS ABOUT PARTICLES Chapter 8 BIT FOR FREE SURFACE FLOWS; Chapter 9 SIMULATION OF CAVITATING AND FREE SURFACE FLOWS USING BEM; Chapter 10 CONDITION NUMBERS AND LOCAL ERRORS IN THE BOUNDARY ELEMENT METHOD
Record Nr. UNINA-9910463925503321
Aliabadi M. H  
London, : Imperial College Press, 2011
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Boundary element methods in engineering and sciences [[electronic resource] /] / M.H. Aliabadi, P.H. Wen
Boundary element methods in engineering and sciences [[electronic resource] /] / M.H. Aliabadi, P.H. Wen
Autore Aliabadi M. H
Pubbl/distr/stampa London, : Imperial College Press, 2011
Descrizione fisica 1 online resource (450 p.)
Disciplina 620.00151535
Altri autori (Persone) WenP. H
Collana Computational and experimental methods in structures
Soggetto topico Boundary element methods
Engineering mathematics
ISBN 1-283-14342-9
9786613143426
1-84816-580-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto PREFACE; CONTENTS; Chapter 1 THE BOUNDARY ELEMENT METHOD FOR GEOMETRICALLY NON-LINEAR ANALYSES OF PLATES AND SHELLS; Chapter 2 TIME-DOMAIN BEM TECHNIQUES; Chapter 3 THE BOUNDARY ELEMENT METHOD FOR THE FRACTURE ANALYSIS OF THE GENERAL PIEZOELECTRIC SOLIDS; Chapter 4 BOUNDARY INTEGRAL ANALYSIS FOR THREE-DIMENSIONAL EXPONENTIALLY GRADED ELASTICITY; Chapter 5 FAST HIERARCHICAL BOUNDARY ELEMENT METHOD FOR LARGE-SCALE 3-D ELASTIC PROBLEMS; Chapter 6 MODELLING OF PLATES AND SHALLOW SHELLS BY MESHLESS LOCAL INTEGRAL EQUATION METHOD
Chapter 7 BOUNDARY ELEMENT TECHNIQUE FOR SLOW VISCOUS FLOWS ABOUT PARTICLES Chapter 8 BIT FOR FREE SURFACE FLOWS; Chapter 9 SIMULATION OF CAVITATING AND FREE SURFACE FLOWS USING BEM; Chapter 10 CONDITION NUMBERS AND LOCAL ERRORS IN THE BOUNDARY ELEMENT METHOD
Record Nr. UNINA-9910788566103321
Aliabadi M. H  
London, : Imperial College Press, 2011
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Boundary element methods in engineering and sciences [[electronic resource] /] / M.H. Aliabadi, P.H. Wen
Boundary element methods in engineering and sciences [[electronic resource] /] / M.H. Aliabadi, P.H. Wen
Autore Aliabadi M. H
Pubbl/distr/stampa London, : Imperial College Press, 2011
Descrizione fisica 1 online resource (450 p.)
Disciplina 620.00151535
Altri autori (Persone) WenP. H
Collana Computational and experimental methods in structures
Soggetto topico Boundary element methods
Engineering mathematics
ISBN 1-283-14342-9
9786613143426
1-84816-580-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto PREFACE; CONTENTS; Chapter 1 THE BOUNDARY ELEMENT METHOD FOR GEOMETRICALLY NON-LINEAR ANALYSES OF PLATES AND SHELLS; Chapter 2 TIME-DOMAIN BEM TECHNIQUES; Chapter 3 THE BOUNDARY ELEMENT METHOD FOR THE FRACTURE ANALYSIS OF THE GENERAL PIEZOELECTRIC SOLIDS; Chapter 4 BOUNDARY INTEGRAL ANALYSIS FOR THREE-DIMENSIONAL EXPONENTIALLY GRADED ELASTICITY; Chapter 5 FAST HIERARCHICAL BOUNDARY ELEMENT METHOD FOR LARGE-SCALE 3-D ELASTIC PROBLEMS; Chapter 6 MODELLING OF PLATES AND SHALLOW SHELLS BY MESHLESS LOCAL INTEGRAL EQUATION METHOD
Chapter 7 BOUNDARY ELEMENT TECHNIQUE FOR SLOW VISCOUS FLOWS ABOUT PARTICLES Chapter 8 BIT FOR FREE SURFACE FLOWS; Chapter 9 SIMULATION OF CAVITATING AND FREE SURFACE FLOWS USING BEM; Chapter 10 CONDITION NUMBERS AND LOCAL ERRORS IN THE BOUNDARY ELEMENT METHOD
Record Nr. UNINA-9910816856503321
Aliabadi M. H  
London, : Imperial College Press, 2011
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Boundary elements [e-book] : theory and applications / John T. Katsikadelis.
Boundary elements [e-book] : theory and applications / John T. Katsikadelis.
Autore Katsikadelis, John T.
Edizione [1st ed.]
Pubbl/distr/stampa Amsterdam ; New York : Elsevier, 2002
Descrizione fisica xiv, 336 p. : ill. ; 25 cm. + 1 CD-ROM (4 3/4 in.)
Disciplina 620/.001/51535
Soggetto topico Boundary element methods
Soggetto genere / forma Electronic books.
ISBN 9780080441078
0080441076
Formato Risorse elettroniche
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Introduction. Preliminary mathematical concepts. The BEM for potential problems in two dimensions. Numerical implementation of the BEM. Boundary element technology. Applications. The BEM for two-dimensional elastostatic problems.
Record Nr. UNISALENTO-991003231459707536
Katsikadelis, John T.  
Amsterdam ; New York : Elsevier, 2002
Risorse elettroniche
Lo trovi qui: Univ. del Salento
Opac: Controlla la disponibilità qui
Boundary integral equations / / George C. Hsiao, Wolfgang L. Wendland
Boundary integral equations / / George C. Hsiao, Wolfgang L. Wendland
Autore Hsiao G. C (George C.)
Edizione [Second edition.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (xx, 783 pages) : illustrations
Disciplina 620.00151535
Collana Applied mathematical sciences
Soggetto topico Boundary element methods
Integral equations
Problemes de contorn
Equacions integrals
Soggetto genere / forma Llibres electrònics
ISBN 3-030-71127-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface to the Second Edition -- Preface to the First Edition -- Acknowledgements -- Table of Contents -- 1. Introduction -- 1.1 The Green Representation Formula -- 1.2 Boundary Potentials and Calderón's Projector -- 1.3 Boundary Integral Equations -- 1.3.1 The Dirichlet Problem -- 1.3.2 The Neumann Problem -- 1.4 Exterior Problems -- 1.4.1 The Exterior Dirichlet Problem -- 1.4.2 The Exterior Neumann Problem -- 1.5 Remarks -- 2. Boundary Integral Equations -- 2.1 The Helmholtz Equation -- 2.1.1 Low Frequency Behaviour -- 2.2 The Lamé System -- 2.2.1 The Interior Displacement Problem -- 2.2.2 The Interior Traction Problem -- 2.2.3 Some Exterior Fundamental Problems -- 2.2.4 The Incompressible Material -- 2.3 The Stokes Equations -- 2.3.1 Hydrodynamic Potentials -- 2.3.2 The Stokes Boundary Value Problems -- 2.3.3 The Incompressible Material - Revisited -- 2.4 The Biharmonic Equation -- 2.4.1 Calderón's Projector -- 2.4.2 Boundary Value Problems and Boundary Integral Equations -- 2.5 Remarks -- 3. Representation Formulae, Local Coordinates and Direct Boundary Integral Equations -- 3.1 Classical Function Spaces and Distributions -- 3.2 Hadamard's Finite Part Integrals -- 3.3 Local Coordinates -- 3.4 Short Excursion to Elementary Differential Geometry -- 3.4.1 Second Order Differential Operators in Divergence Form -- 3.5 Distributional Derivatives and Abstract Green's Second Formula -- 3.6 The Green Representation Formula -- 3.7 Green's Representation Formulae in Local Coordinates -- 3.8 Multilayer Potentials -- 3.9 Direct Boundary Integral Equations -- 3.9.1 Boundary Value Problems -- 3.9.2 Transmission Problems -- 3.10 Remarks -- 4. Sobolev Spaces -- 4.1 The Spaces Hs(Ω) -- 4.2 The Trace Spaces Hs(Γ) -- 4.2.1 Trace Spaces for Periodic Functions on a Smooth Curve in IR -- 4.2.2 Trace Spaces on Curved Polygons in IR.
4.3 The Trace Spaces on an Open Surface -- 4.4 The Weighted Sobolev Spaces Hm(Ωc -- λ) and Hm(IRn -- λ) -- 4.5 Function Spaces H( div ,Ω) and H( curl,Ω) -- 5. Variational Formulations -- 5.1 Partial Differential Equations of Second Order -- 5.1.1 Interior Problems -- 5.1.2 Exterior Problems -- 5.1.3 Transmission Problems -- 5.2 Abstract Existence Theorems for Variational Problems -- 5.2.1 The Lax-Milgram Theorem -- 5.3 The Fredholm-Nikolski Theorems -- 5.3.1 Fredholm's Alternative -- 5.3.2 The Riesz-Schauder and the Nikolski Theorems -- 5.3.3 Fredholm's Alternative for Sesquilinear Forms -- 5.3.4 Fredholm Operators -- 5.4 Gårding's Inequality for Boundary Value Problems -- 5.4.1 Gårding's Inequality for Second Order Strongly Elliptic Equations in Ω -- 5.4.2 The Stokes System -- 5.4.3 Gårding's Inequality for Exterior Second Order Problems -- 5.4.4 Gårding's Inequality for Second Order Transmission Problems -- 5.5 Existence of Solutions to Strongly Elliptic Boundary Value Problems -- 5.5.1 Interior Boundary Value Problems -- 5.5.2 Exterior Boundary Value Problems -- 5.5.3 Transmission Problems -- 5.6 Solutions of Certain Boundary Integral Equations and Associated Boundary Value Problems -- 5.6.1 The Generalized Representation Formula for Second Order Systems -- 5.6.2 Continuity of Some Boundary Integral Operators -- 5.6.3 Continuity Based on Finite Regions -- 5.6.4 Continuity of Hydrodynamic Potentials -- 5.6.5 The Equivalence Between Boundary Value Problems and Integral Equations -- 5.6.6 Variational Formulation of Direct Boundary Integral Equations -- 5.6.7 Positivity and Contraction of Boundary Integral Operators -- 5.6.8 The Solvability of Direct Boundary Integral Equations -- 5.6.9 Positivity of the Boundary Integral Operators of the Stokes System -- 5.7 Partial Differential Equations of Higher Order -- 5.8 Remarks -- 5.8.1 Assumptions on Γ.
5.8.2 Higher Regularity of Solutions -- 5.8.3 Mixed Boundary Conditions and Crack Problem -- 6. Electromagnetic Fields -- 6.1 Introduction -- 6.2 Maxwell Equations -- 6.3 Constitutive Equations -- 6.4 Time Harmonic Fields -- 6.4.1 Plane waves -- 6.5 Electromagnetic potentials -- 6.6 Transmission and Boundary Conditions -- 6.7 Boundary Value Problems -- 6.7.1 Scattering problems -- 6.7.2 Eddy current problems -- 6.8 Uniqueness -- 6.8.1 The cavity problem -- 6.8.2 Exterior problems -- 6.8.3 The transmission problem -- 6.9 Representation Formulae -- 6.10 Boundary Integral Equations for Electromagnetic fields -- 6.10.1 The Calderon projector and the capacity operators -- 6.10.2 Weak solutions for a fundamental problem -- 6.10.2.1 Interior Dirichlet problem in Ω. -- 6.10.2.2 A reduction to boundary integral equations. -- 6.11 Application of the Electromagnetic Potentials to Eddy Current Problems -- 6.11.1 The '(A, ϕ) − (A) − (ψ)' formulation in the bounded domain -- 6.11.2 The '(A, ϕ) − (ψ)' formulation in an unbounded domain -- 6.11.3 Electric field in the dielectric domain ΩD. -- 6.11.4 Vector potentials - revisited -- 6.12 Applications of boundary integral equations to scattering problems -- 6.12.1 Scattering by a perfect electric conductor, EFIE and MFIE -- 6.12.2 Scattering by a dielectric body -- 6.12.3 Scattering by objects with impedance boundary conditions -- 7. Introduction to Pseudodifferential Operators -- 7.1 Basic Theory of Pseudodifferential Operators -- 7.2 Elliptic Pseudodifferential Operators on Ω ⊂ IRn -- 7.2.1 Systems of Pseudodifferential Operators -- 7.2.2 Parametrix and Fundamental Solution -- 7.2.3 Levi Functions for Scalar Elliptic Equations -- 7.2.4 Levi Functions for Elliptic Systems -- 7.2.5 Strong Ellipticity and Gårding's Inequality -- 7.3 Review on Fundamental Solutions -- 7.3.1 Local Fundamental Solutions.
7.3.2 Fundamental Solutions in IRn for Operators with Constant Coefficients -- 7.3.3 Existing Fundamental Solutions in Applications -- 8. Pseudodifferential Operators as Integral Operators -- 8.1 Pseudohomogeneous Kernels -- 8.1.1 Integral Operators as Pseudodifferential Operators of Negative Order -- 8.1.2 Non-Negative Order Pseudodifferential Operators as Hadamard Finite Part Integral Operators -- 8.1.3 Parity Conditions -- 8.1.4 A Summary of the Relations between Kernels and Symbols -- 8.2 Coordinate Changes and Pseudohomogeneous Kernels -- 8.2.1 The Transformation of General Hadamard Finite Part Integral Operators under Change of Coordinates -- 8.2.2 The Class of Invariant Hadamard Finite Part Integral Operators under Change of Coordinates -- 9. Pseudodifferential and Boundary Integral Operators -- 9.1 Pseudodifferential Operators on Boundary Manifolds -- 9.1.1 Ellipticity on Boundary Manifolds -- 9.1.2 Schwartz Kernels on Boundary Manifolds -- 9.2 Boundary Operators Generated by Domain Pseudodifferential Operators -- 9.3 Surface Potentials on the Plane IRn−1 -- 9.4 Pseudodifferential Operators with Symbols of Rational Type -- 9.5 Surface Potentials on the Boundary Manifold Γ -- 9.6 Volume Potentials -- 9.7 Strong Ellipticity and Fredholm Properties -- 9.8 Strong Ellipticity of Boundary Value Problems and Associated Boundary Integral Equations -- 9.8.1 The Boundary Value and Transmission Problems -- 9.8.2 The Associated Boundary Integral Equations of the First Kind -- 9.8.3 The Transmission Problem and Gårding's inequality -- 9.9 Remarks -- 10. Integral Equations on Γ ⊂ IR3 Recast as Pseudodifferential Equations -- 10.1 Newton Potential Operators for Elliptic Partial Differential Equations and Systems -- 10.1.1 Generalized Newton Potentials for the Helmholtz Equation -- 10.1.2 The Newton Potential for the Lamé System.
10.1.3 The Newton Potential for the Stokes System -- 10.2 Surface Potentials for Second Order Equations -- 10.2.1 Strongly Elliptic Differential Equations -- 10.2.2 Surface Potentials for the Helmholtz Equation -- 10.2.3 Surface Potentials for the Lamé System -- 10.2.4 Surface Potentials for the Stokes System -- 10.3 Invariance of Boundary Pseudodifferential Operators -- 10.3.1 The Hypersingular Boundary Integral Operators for the Helmholtz Equation -- 10.3.2 The Hypersingular Operator for the Lamé System -- 10.3.3 The Hypersingular Operator for the Stokes System -- 10.4 Derivatives of Boundary Potentials -- 10.4.1 Derivatives of the Solution to the Helmholtz Equation -- 10.4.2 Computation of Stress and Strain on the Boundary for the Lamé System -- 10.5 Remarks -- 11. Boundary Integral Equations on Curves in IR2 -- 11.1 Representation of the basic operators for the 2D-Laplacian in terms of Fourier series -- 11.2 The Fourier Series Representation of Periodic Operators A ∈ L m cl(Γ) -- 11.3 Ellipticity Conditions for Periodic Operators on Γ -- 11.3.1 Scalar Equations -- 11.3.2 Systems of Equations -- 11.3.3 Multiply Connected Domains -- 11.4 Fourier Series Representation of some Particular Operators -- 11.4.1 The Helmholtz Equation -- 11.4.2 The Lamé System -- 11.4.3 The Stokes System -- 11.4.4 The Biharmonic Equation -- 11.5 Remarks -- 12. Remarks on Pseudodifferential Operators Related to the Time Harmonic Maxwell Equations -- 12.1 Introduction -- 12.2 Symbols of P and the corresponding Newton potentials -- 12.3 Representation formulae -- 12.4 Symbols of the Electromagnetic Boundary Potentials -- 12.5 Symbols of boundary integral operators -- 12.6 Symbols of the Capacity Operators -- 12.7 Boundary Integral Operators for the Fundamental Boundary Value Problems -- 12.8 Coerciveness and Strong Ellipticity.
12.9 Gårding's inequality for the sesquilinear form A in (6.12.23).
Record Nr. UNISA-996466567503316
Hsiao G. C (George C.)  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Boundary integral equations / / George C. Hsiao, Wolfgang L. Wendland
Boundary integral equations / / George C. Hsiao, Wolfgang L. Wendland
Autore Hsiao G. C (George C.)
Edizione [Second edition.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (xx, 783 pages) : illustrations
Disciplina 620.00151535
Collana Applied mathematical sciences
Soggetto topico Boundary element methods
Integral equations
Problemes de contorn
Equacions integrals
Soggetto genere / forma Llibres electrònics
ISBN 3-030-71127-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface to the Second Edition -- Preface to the First Edition -- Acknowledgements -- Table of Contents -- 1. Introduction -- 1.1 The Green Representation Formula -- 1.2 Boundary Potentials and Calderón's Projector -- 1.3 Boundary Integral Equations -- 1.3.1 The Dirichlet Problem -- 1.3.2 The Neumann Problem -- 1.4 Exterior Problems -- 1.4.1 The Exterior Dirichlet Problem -- 1.4.2 The Exterior Neumann Problem -- 1.5 Remarks -- 2. Boundary Integral Equations -- 2.1 The Helmholtz Equation -- 2.1.1 Low Frequency Behaviour -- 2.2 The Lamé System -- 2.2.1 The Interior Displacement Problem -- 2.2.2 The Interior Traction Problem -- 2.2.3 Some Exterior Fundamental Problems -- 2.2.4 The Incompressible Material -- 2.3 The Stokes Equations -- 2.3.1 Hydrodynamic Potentials -- 2.3.2 The Stokes Boundary Value Problems -- 2.3.3 The Incompressible Material - Revisited -- 2.4 The Biharmonic Equation -- 2.4.1 Calderón's Projector -- 2.4.2 Boundary Value Problems and Boundary Integral Equations -- 2.5 Remarks -- 3. Representation Formulae, Local Coordinates and Direct Boundary Integral Equations -- 3.1 Classical Function Spaces and Distributions -- 3.2 Hadamard's Finite Part Integrals -- 3.3 Local Coordinates -- 3.4 Short Excursion to Elementary Differential Geometry -- 3.4.1 Second Order Differential Operators in Divergence Form -- 3.5 Distributional Derivatives and Abstract Green's Second Formula -- 3.6 The Green Representation Formula -- 3.7 Green's Representation Formulae in Local Coordinates -- 3.8 Multilayer Potentials -- 3.9 Direct Boundary Integral Equations -- 3.9.1 Boundary Value Problems -- 3.9.2 Transmission Problems -- 3.10 Remarks -- 4. Sobolev Spaces -- 4.1 The Spaces Hs(Ω) -- 4.2 The Trace Spaces Hs(Γ) -- 4.2.1 Trace Spaces for Periodic Functions on a Smooth Curve in IR -- 4.2.2 Trace Spaces on Curved Polygons in IR.
4.3 The Trace Spaces on an Open Surface -- 4.4 The Weighted Sobolev Spaces Hm(Ωc -- λ) and Hm(IRn -- λ) -- 4.5 Function Spaces H( div ,Ω) and H( curl,Ω) -- 5. Variational Formulations -- 5.1 Partial Differential Equations of Second Order -- 5.1.1 Interior Problems -- 5.1.2 Exterior Problems -- 5.1.3 Transmission Problems -- 5.2 Abstract Existence Theorems for Variational Problems -- 5.2.1 The Lax-Milgram Theorem -- 5.3 The Fredholm-Nikolski Theorems -- 5.3.1 Fredholm's Alternative -- 5.3.2 The Riesz-Schauder and the Nikolski Theorems -- 5.3.3 Fredholm's Alternative for Sesquilinear Forms -- 5.3.4 Fredholm Operators -- 5.4 Gårding's Inequality for Boundary Value Problems -- 5.4.1 Gårding's Inequality for Second Order Strongly Elliptic Equations in Ω -- 5.4.2 The Stokes System -- 5.4.3 Gårding's Inequality for Exterior Second Order Problems -- 5.4.4 Gårding's Inequality for Second Order Transmission Problems -- 5.5 Existence of Solutions to Strongly Elliptic Boundary Value Problems -- 5.5.1 Interior Boundary Value Problems -- 5.5.2 Exterior Boundary Value Problems -- 5.5.3 Transmission Problems -- 5.6 Solutions of Certain Boundary Integral Equations and Associated Boundary Value Problems -- 5.6.1 The Generalized Representation Formula for Second Order Systems -- 5.6.2 Continuity of Some Boundary Integral Operators -- 5.6.3 Continuity Based on Finite Regions -- 5.6.4 Continuity of Hydrodynamic Potentials -- 5.6.5 The Equivalence Between Boundary Value Problems and Integral Equations -- 5.6.6 Variational Formulation of Direct Boundary Integral Equations -- 5.6.7 Positivity and Contraction of Boundary Integral Operators -- 5.6.8 The Solvability of Direct Boundary Integral Equations -- 5.6.9 Positivity of the Boundary Integral Operators of the Stokes System -- 5.7 Partial Differential Equations of Higher Order -- 5.8 Remarks -- 5.8.1 Assumptions on Γ.
5.8.2 Higher Regularity of Solutions -- 5.8.3 Mixed Boundary Conditions and Crack Problem -- 6. Electromagnetic Fields -- 6.1 Introduction -- 6.2 Maxwell Equations -- 6.3 Constitutive Equations -- 6.4 Time Harmonic Fields -- 6.4.1 Plane waves -- 6.5 Electromagnetic potentials -- 6.6 Transmission and Boundary Conditions -- 6.7 Boundary Value Problems -- 6.7.1 Scattering problems -- 6.7.2 Eddy current problems -- 6.8 Uniqueness -- 6.8.1 The cavity problem -- 6.8.2 Exterior problems -- 6.8.3 The transmission problem -- 6.9 Representation Formulae -- 6.10 Boundary Integral Equations for Electromagnetic fields -- 6.10.1 The Calderon projector and the capacity operators -- 6.10.2 Weak solutions for a fundamental problem -- 6.10.2.1 Interior Dirichlet problem in Ω. -- 6.10.2.2 A reduction to boundary integral equations. -- 6.11 Application of the Electromagnetic Potentials to Eddy Current Problems -- 6.11.1 The '(A, ϕ) − (A) − (ψ)' formulation in the bounded domain -- 6.11.2 The '(A, ϕ) − (ψ)' formulation in an unbounded domain -- 6.11.3 Electric field in the dielectric domain ΩD. -- 6.11.4 Vector potentials - revisited -- 6.12 Applications of boundary integral equations to scattering problems -- 6.12.1 Scattering by a perfect electric conductor, EFIE and MFIE -- 6.12.2 Scattering by a dielectric body -- 6.12.3 Scattering by objects with impedance boundary conditions -- 7. Introduction to Pseudodifferential Operators -- 7.1 Basic Theory of Pseudodifferential Operators -- 7.2 Elliptic Pseudodifferential Operators on Ω ⊂ IRn -- 7.2.1 Systems of Pseudodifferential Operators -- 7.2.2 Parametrix and Fundamental Solution -- 7.2.3 Levi Functions for Scalar Elliptic Equations -- 7.2.4 Levi Functions for Elliptic Systems -- 7.2.5 Strong Ellipticity and Gårding's Inequality -- 7.3 Review on Fundamental Solutions -- 7.3.1 Local Fundamental Solutions.
7.3.2 Fundamental Solutions in IRn for Operators with Constant Coefficients -- 7.3.3 Existing Fundamental Solutions in Applications -- 8. Pseudodifferential Operators as Integral Operators -- 8.1 Pseudohomogeneous Kernels -- 8.1.1 Integral Operators as Pseudodifferential Operators of Negative Order -- 8.1.2 Non-Negative Order Pseudodifferential Operators as Hadamard Finite Part Integral Operators -- 8.1.3 Parity Conditions -- 8.1.4 A Summary of the Relations between Kernels and Symbols -- 8.2 Coordinate Changes and Pseudohomogeneous Kernels -- 8.2.1 The Transformation of General Hadamard Finite Part Integral Operators under Change of Coordinates -- 8.2.2 The Class of Invariant Hadamard Finite Part Integral Operators under Change of Coordinates -- 9. Pseudodifferential and Boundary Integral Operators -- 9.1 Pseudodifferential Operators on Boundary Manifolds -- 9.1.1 Ellipticity on Boundary Manifolds -- 9.1.2 Schwartz Kernels on Boundary Manifolds -- 9.2 Boundary Operators Generated by Domain Pseudodifferential Operators -- 9.3 Surface Potentials on the Plane IRn−1 -- 9.4 Pseudodifferential Operators with Symbols of Rational Type -- 9.5 Surface Potentials on the Boundary Manifold Γ -- 9.6 Volume Potentials -- 9.7 Strong Ellipticity and Fredholm Properties -- 9.8 Strong Ellipticity of Boundary Value Problems and Associated Boundary Integral Equations -- 9.8.1 The Boundary Value and Transmission Problems -- 9.8.2 The Associated Boundary Integral Equations of the First Kind -- 9.8.3 The Transmission Problem and Gårding's inequality -- 9.9 Remarks -- 10. Integral Equations on Γ ⊂ IR3 Recast as Pseudodifferential Equations -- 10.1 Newton Potential Operators for Elliptic Partial Differential Equations and Systems -- 10.1.1 Generalized Newton Potentials for the Helmholtz Equation -- 10.1.2 The Newton Potential for the Lamé System.
10.1.3 The Newton Potential for the Stokes System -- 10.2 Surface Potentials for Second Order Equations -- 10.2.1 Strongly Elliptic Differential Equations -- 10.2.2 Surface Potentials for the Helmholtz Equation -- 10.2.3 Surface Potentials for the Lamé System -- 10.2.4 Surface Potentials for the Stokes System -- 10.3 Invariance of Boundary Pseudodifferential Operators -- 10.3.1 The Hypersingular Boundary Integral Operators for the Helmholtz Equation -- 10.3.2 The Hypersingular Operator for the Lamé System -- 10.3.3 The Hypersingular Operator for the Stokes System -- 10.4 Derivatives of Boundary Potentials -- 10.4.1 Derivatives of the Solution to the Helmholtz Equation -- 10.4.2 Computation of Stress and Strain on the Boundary for the Lamé System -- 10.5 Remarks -- 11. Boundary Integral Equations on Curves in IR2 -- 11.1 Representation of the basic operators for the 2D-Laplacian in terms of Fourier series -- 11.2 The Fourier Series Representation of Periodic Operators A ∈ L m cl(Γ) -- 11.3 Ellipticity Conditions for Periodic Operators on Γ -- 11.3.1 Scalar Equations -- 11.3.2 Systems of Equations -- 11.3.3 Multiply Connected Domains -- 11.4 Fourier Series Representation of some Particular Operators -- 11.4.1 The Helmholtz Equation -- 11.4.2 The Lamé System -- 11.4.3 The Stokes System -- 11.4.4 The Biharmonic Equation -- 11.5 Remarks -- 12. Remarks on Pseudodifferential Operators Related to the Time Harmonic Maxwell Equations -- 12.1 Introduction -- 12.2 Symbols of P and the corresponding Newton potentials -- 12.3 Representation formulae -- 12.4 Symbols of the Electromagnetic Boundary Potentials -- 12.5 Symbols of boundary integral operators -- 12.6 Symbols of the Capacity Operators -- 12.7 Boundary Integral Operators for the Fundamental Boundary Value Problems -- 12.8 Coerciveness and Strong Ellipticity.
12.9 Gårding's inequality for the sesquilinear form A in (6.12.23).
Record Nr. UNINA-9910483092503321
Hsiao G. C (George C.)  
Cham, Switzerland : , : Springer, , [2021]
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