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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 | ||
| ||
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] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||