Integral Methods in Science and Engineering
* Good reference text; clusters well with other Birkhauser integral equations & integral methods books (Estrada and Kanwal, Kythe/Puri, Constanda, et al).\ * Includes many practical applications/techniques for applied mathematicians, physicists, engineers, grad students.\ * The contributors to the volume draw from a number of physical domains and propose diverse treatments for various mathematical models through the use of integration as an essential solution tool.\ * Physically...
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An outgrowth of The Seventh International Conference on Integral Methods in Science and Engineering, this book focuses on applications of integration-based analytic and numerical techniques. The contributors to the volume draw from a number of physical domains and propose diverse treatments for various mathematical models through the use of integration as an essential solution tool.Physically meaningful problems in areas related to finite and boundary element techniques, conservation laws, hybrid approaches, ordinary and partial differential equations, and vortex methods are explored in a rigorous, accessible manner. The new results provided are a good starting point for future exploitation of the interdisciplinary potential of integration as a unifying methodology for the investigation of mathematical models.Features:* Detailed, clear illustrations of efficient solution methods* Rigorous numerical results developed and justified* Application of integral methods to a wide variety of mathematical and physical problems* New results gleaned from various physical and mechanical models* Examination of an entire class of methodologies rather than narrow, specific fields of studyIntegral Methods in Science and Engineering is a practical resource for a broad audience of practitioners, researchers, and graduate students in applied mathematics, physics, and mechanical engineering.
PrefaceContributors1Use of Elastodynamic Reciprocity Theorems for Field Calculations12Linear Solvers for the Galerkin Boundary Element Method153Reciprocity of Hopf's and Feautrier's Operators in Radiation Transport Theory214Spectral Approximation of Weakly Singular Integrable Kernels Using Projections275Effect of Imperfect Interface on Thermal Inclusion with an Interior Radial Crack336An Integrodifferential Equation of Atomic Diffusion397Nonradiating Dislocations in Uniform Supersonic Motion in Anisotropic Linear Elastic Solids458On the Use of the Conjugate Gradient Method for the Numerical Solution of First-Kind Integral Equations in Two Variables519On the Stopping Criteria for Conjugate Gradient Solutions of First-Kind Integral Equations in Two Variables5710An Initial-Boundary Value Problem for Thermoelastic Plates6311A Global Existence Result for Functional Differential Equations with Causal Operators6912Direct Stiffness-Modification Route to Linear Consistency Between Incompatible Finite Element Meshes7513Nonlinear Dynamic Analysis of a Curved Beam Structure Using a Finite Element Method8114Seminal Ideas in Integral Methods8715Mixed Boundary Value Problem with Two Displacement Boundaries for Thin Plate Bending9916Use of Cross-Referencing for Solving the Parameter Choice Problem in Generalized CLS10517Numerical Technique for Solving an Ordinary Differential Equation by Picard's Method11118On a Class of Boundary Conditions Splitting Coupled Thermoelasticity Problems11719Recent Mathematical Developments for Functionally Graded Linearly Elastic Materials12320Ground Vibration Dynamics During Pile Hammering13121Connection Between Liquid Crystal Theory and Plate Theory13722Product Integration Quadratures for the Radiative Transfer Problem with Hopf's Kernel14323A Numerical Scheme for Determining Diffraction Coefficients in Anisotropic Materials14924Effect of Imperfect Inclusion/Matrix Interaction Between a Circular Inclusion and a Radial Matrix Crack15525Neutral Equations with Causal Operators16126Computation of Free-Surface Flows Under the Influence of Pressure Distribution16727Solution of Eigenvalue Problems for Rectangular Plates by Differential Transformation17328Free Vibrations of Structural Hyperbolic Paraboloid Networks17929Sharp Invertibility Results for Layer Potentials in 2D18530An Enhanced Theory of Bending of Plates19131Comparison of Zonal, Spectral Solutions for Compressible Boundary Layer and Navier-Stokes Equations19732Hybrid Laplace and Poisson Solvers I: Dirichlet Boundary Conditions20333Estimation of Boundary Conditions for Different Experimental Data Using the LTS[subscript N] Method and Tikhonov Regularization20934Analytical-Numerical Treatment of the One-Phase Stefan Problem with Constant Applied Heat Flux21535Integral Equations Arising in Boundary Value Problems at Resonance22136Thermal Stress Analysis of an Elliptic Inclusion with Imperfect Interface Embedded in an Infinite Elastic Medium22737Three-Dimensional Elasticity Solutions for Anisotropic and Inhomogeneous Plates and Shells23338A Circular Inclusion with Homogeneous Interface24539Multiwavelets for Geometrically Complicated Domains and Their Application to Boundary Element Methods25140Mathematical Investigation of Contact Problems with Friction in Fracture Dynamics257Index263
