Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume in the Elsevier Series in Electromagnetism presents a detailed, in-depth and self-contained treatment of the Fast Multipole Method and its applications to the solution of the Helmholtz equation in three dimensions. The Fast Multipole Method was pioneered by Rokhlin and Greengard in 1987 and has enjoyed a dramatic development and recognition during the past two decades. This method has been described as one of the best 10 algorithms of the 20th century. Thus, it is becoming increasingly important to give a detailed exposition of the Fast Multipole Method that will be accessible to a

Helmholtz equation --- Helmholtz, Equation d' --- Helmholtz equation. --- Wave equation. --- Differential equations, Partial --- Wave-motion, Theory of --- Reduced wave equation --- Wave equation, Reduced --- Differential equations, Elliptic --- Wave equation

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book gives a detailed overview of the theory of electromagnetic wave scattering on single, homogeneous, but nonspherical particles. A related Green’s function formalism is systematically developed which provides a powerful mathematical basis not only for the development of numerical approaches but also to discuss those general aspects like symmetry, unitarity, and the validity of Rayleigh’s hypothesis. Example simulations are performed in order to demonstrate the usefulness of the developed formalism as well as to introduce the simulation software which is provided on a CD-ROM with the book.

Electromagnetic waves --- Particles --- Green's functions --- Helmholtz equation --- Wave equation --- Separation of variables --- Electricity & Magnetism --- Light & Optics --- Physics --- Physical Sciences & Mathematics --- Mathematical models --- Scattering --- Optical properties --- Numerical solutions --- Electromagnetic theory. --- Scattering. --- Light, Electromagnetic theory of --- Physics. --- Optics. --- Electrodynamics. --- Engineering. --- Optics and Electrodynamics. --- Engineering, general. --- Electric fields --- Magnetic fields --- Scattering (Physics) --- Classical Electrodynamics. --- Construction --- Industrial arts --- Technology --- Dynamics --- Light

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book gives a comprehensive introduction to the Helmholtz Equation Least Squares (HELS) method and its use in diagnosing noise and vibration problems. In contrast to the traditional NAH technologies, the HELS method does not seek an exact solution to the acoustic field produced by an arbitrarily shaped structure. Rather, it attempts to obtain the best approximation of an acoustic field through the expansion of certain basis functions. Therefore, it significantly simplifies the complexities of the reconstruction process, yet still enables one to acquire an understanding of the root causes of different noise and vibration problems that involve arbitrarily shaped surfaces in non-free space using far fewer measurement points than either Fourier acoustics or BEM based NAH. The examples given in this book illustrate that the HELS method may potentially become a practical and versatile tool for engineers to tackle a variety of complex noise and vibration issues in engineering applications.

Engineering. --- Engineering Acoustics. --- Acoustics. --- Vibration, Dynamical Systems, Control. --- Mathematical Modeling and Industrial Mathematics. --- Vibration. --- Acoustics in engineering. --- Ingénierie --- Acoustique --- Vibration --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Sound-waves. --- Sound --- Radiation sources. --- Least squares. --- Helmholtz equation --- Transmission. --- Numerical solutions. --- Method of least squares --- Squares, Least --- Sources of radiation --- Transmission of sound --- Mathematical models. --- Dynamical systems. --- Dynamics. --- Acoustical engineering. --- Numerical analysis --- Curve fitting --- Geodesy --- Mathematical statistics --- Mathematics --- Probabilities --- Triangulation --- Quantum optics --- Radiation --- Architectural acoustics --- Sound-waves --- Soundproofing --- Waves --- Cycles --- Mechanics --- Acoustic engineering --- Sonic engineering --- Sonics --- Sound engineering --- Engineering --- Models, Mathematical --- Simulation methods --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Industrial applications

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The present book contains 14 articles that were accepted for publication in the Special Issue “Numerical Computation, Data Analysis and Software in Mathematics and Engineering” of the MDPI journal Mathematics. The topics of these articles include the aspects of the meshless method, numerical simulation, mathematical models, deep learning and data analysis. Meshless methods, such as the improved element-free Galerkin method, the dimension-splitting, interpolating, moving, least-squares method, the dimension-splitting, generalized, interpolating, element-free Galerkin method and the improved interpolating, complex variable, element-free Galerkin method, are presented. Some complicated problems, such as tge cold roll-forming process, ceramsite compound insulation block, crack propagation and heavy-haul railway tunnel with defects, are numerically analyzed. Mathematical models, such as the lattice hydrodynamic model, extended car-following model and smart helmet-based PLS-BPNN error compensation model, are proposed. The use of the deep learning approach to predict the mechanical properties of single-network hydrogel is presented, and data analysis for land leasing is discussed. This book will be interesting and useful for those working in the meshless method, numerical simulation, mathematical model, deep learning and data analysis fields.

cold-roll forming --- longitudinal strain --- cubic spline function --- cumulative chord --- elastic–plastic problem --- complex variable meshless method --- interpolating shape function --- singular weight function --- complete basis function --- mathematical model --- leased price --- total leased area --- data analysis --- residential land --- Beijing --- meshless method --- dimension splitting–interpolating moving least squares (DS-IMLS) method --- improved interpolating element-free Galerkin (IEFG) method --- potential problem --- traffic flow --- two-dimensional lattice hydrodynamic model --- driver’s predictive effect --- finite element method --- alkali-activated slag ceramsite compound insulation block --- ANSYS CFX --- thermal and mechanical performances --- indoor thermal environment --- dimension splitting method --- dimension splitting generalized interpolating element-free Galerkin method --- convection–diffusion–reaction problem --- deep learning --- hydrogel network --- mechanical property --- convolutional neural network --- self-avoiding walk --- personnel health monitoring --- construction site management --- smart helmet --- infrared temperature measurement --- temperature error compensation --- BP neural network --- COVID-19 --- peridynamics --- dual-horizon --- crack propagation --- variable horizon --- multi-grid --- car-following model --- visual angle model --- electronic throttle angle --- stability analysis --- heavy haul --- railway tunnel --- basement structure --- dynamic response characteristics --- defects --- the lattice hydrodynamic model --- control signal --- strong wind --- optimal estimation of flux difference integral --- improved element-free Galerkin method --- Helmholtz equation --- penalty method --- improved moving least-squares approximation --- n/a --- elastic-plastic problem --- dimension splitting-interpolating moving least squares (DS-IMLS) method --- driver's predictive effect --- convection-diffusion-reaction problem

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Modelling and simulation in acoustics is currently gaining importance. In fact, with the development and improvement of innovative computational techniques and with the growing need for predictive models, an impressive boost has been observed in several research and application areas, such as noise control, indoor acoustics, and industrial applications. This led us to the proposal of a special issue about “Modelling, Simulation and Data Analysis in Acoustical Problems”, as we believe in the importance of these topics in modern acoustics’ studies. In total, 81 papers were submitted and 33 of them were published, with an acceptance rate of 37.5%. According to the number of papers submitted, it can be affirmed that this is a trending topic in the scientific and academic community and this special issue will try to provide a future reference for the research that will be developed in coming years.

noise barrier --- insertion loss --- vehicle frequencies --- diffraction --- flow speed --- Analytical solutions --- FDTD --- EMATs --- beam directivity --- perforate tube silencer --- transmission loss (TL) --- pressure loss --- computational fluid dynamics (CFD) --- temperature --- air flow velocity --- graphical bilinear method --- seismic survey --- dynamic cone penetration test --- soil depth --- time-distance curve --- KZK equation --- fractional order derivative --- ultrasound hyperthermia --- HIFU --- acoustic simulation --- Kramers–Kronig relation --- stereo audio coding --- Principal Component Analysis (PCA) --- multi-frame --- Pyramid Vector Quantization (PVQ) --- bowel sound --- bowel motility --- automatic detection/evaluation --- power-normalized cepstral coefficients --- noncontact instrumentation --- acoustic localization --- cross array --- moving sound source --- discrete sampling --- error analysis --- open-air theatres --- acoustical measurements --- prediction models --- historical acoustics --- Direction of Arrival (DOA) --- time-frequency (TF) mask --- speech sparsity --- speech enhancement (SE) --- acoustic vector sensor (AVS) --- intelligent service robot --- voice generation --- multichannel electroglottograph --- larynx acoustics --- fingerprinting acoustic localization --- iterative interpolation --- K-Means clustering --- Two-stage matching --- Adjacent RPs --- dynamic tissue property --- Westervelt equation --- thermal damage zone --- submerged floating tunnel (SFT) --- mooring line --- coupled dynamics --- hydro-elastic responses --- wet natural frequencies --- mooring tension --- seismic excitation --- wave excitation --- seaquake --- thick annular circular plate --- Rayleigh integral --- finite element modeling --- rectangular and concentric stiffener patches --- taper ratio --- thickness variation --- MRI --- Zone Plates --- ultrasonic lenses --- piano playing --- vibrotactile feedback --- interaction --- musical performance --- auditory perception --- sensors --- actuators --- crack growth --- acoustic echo --- COSMO --- p-value --- l1-regularized RLS --- sparsity --- room impulse response --- total least squares --- regularization factor --- fluid-filled polyethylene (PE) pipeline --- noise control --- acoustic propagation --- cutoff phenomenon --- UWA communication --- channel modelling --- OFDM --- channel estimation --- simulation platform --- minimum variance distortionless response --- signal self-cancellation --- direction estimation --- underwater acoustic source --- spatial power spectrum --- cochlear implant --- coding strategy --- Fixed-Channel --- Channel-Picking --- vocoder simulation --- normal-hearing --- point mass --- parabolic thickness variation --- landmine detection --- lumped parameter model --- prodder --- resonance frequency --- noised-induced hearing loss --- powered surgical instruments --- ultrasonic aspirator --- transcanal endoscopic ear surgery --- balanced armature receiver --- lumped parameter method --- finite element method and Boundary element method --- focused transducer --- acoustic field --- nonuniform radiation distribution --- Bessel radiation distribution --- spherically curved uniform radiator --- rim radiation --- Lamb waves --- wooden constructions --- acoustics --- low frequency noise --- modelling --- ultrasonic guided waves --- SAFE --- rail defect detection --- mode excitation --- solid dielectrics --- acoustic emission --- artificial neural networks --- electrical treeing --- wavelets --- non-destructive testing --- high-voltage insulating systems --- boundary element method --- Helmholtz equation --- structural health monitoring --- mooring chain --- fatigue crack growth --- structural integrity --- n/a --- Kramers-Kronig relation