The book "Finite Element Analysis of Acoustic Scattering" by Frank Ihlenburg provides a comprehensive overview of the mathematical and computational methods used in solving scattering problems involving waves. It focuses on the Helmholtz equation, which describes wave propagation and scattering in various physical systems, including acoustic and elastic waves. The book is aimed at mathematicians, physicists, and computational engineers working on scattering problems, and it is written in a self-contained manner to be accessible to a mixed audience. The text begins with an introduction to the governing equations of time-harmonic wave propagation, covering acoustic, elastic, and electromagnetic waves. It then discusses analytical and variational solutions of Helmholtz problems, including separation of variables, functional analysis, and variational formulations. The book addresses the challenges of applying finite element methods (FEM) to Helmholtz problems, particularly in unbounded domains, where domain decomposition and artificial boundaries are used. It reviews various coupling methods, such as Dirichlet-to-Neumann operators, absorbing boundary conditions, and perfectly matched layers. The book also discusses the numerical analysis of FEM for Helmholtz problems, focusing on the stability and error estimates. It presents new estimates that characterize the error behavior in the range of engineering computations, distinguishing them from asymptotic error estimates. The text emphasizes the advantages of the hp-version of FEM over piecewise linear approximation and explores generalized FEM and a posteriori error estimation for Helmholtz problems. The book includes computational results for three-dimensional scattering problems and discusses the application of FEM to elastic scattering, such as scattering from a sphere and a cylinder with spherical endcaps. It concludes with a summary of the results and a bibliography of relevant references. The book is a valuable resource for researchers and practitioners in the field of wave propagation and scattering, providing both theoretical insights and practical computational methods.The book "Finite Element Analysis of Acoustic Scattering" by Frank Ihlenburg provides a comprehensive overview of the mathematical and computational methods used in solving scattering problems involving waves. It focuses on the Helmholtz equation, which describes wave propagation and scattering in various physical systems, including acoustic and elastic waves. The book is aimed at mathematicians, physicists, and computational engineers working on scattering problems, and it is written in a self-contained manner to be accessible to a mixed audience. The text begins with an introduction to the governing equations of time-harmonic wave propagation, covering acoustic, elastic, and electromagnetic waves. It then discusses analytical and variational solutions of Helmholtz problems, including separation of variables, functional analysis, and variational formulations. The book addresses the challenges of applying finite element methods (FEM) to Helmholtz problems, particularly in unbounded domains, where domain decomposition and artificial boundaries are used. It reviews various coupling methods, such as Dirichlet-to-Neumann operators, absorbing boundary conditions, and perfectly matched layers. The book also discusses the numerical analysis of FEM for Helmholtz problems, focusing on the stability and error estimates. It presents new estimates that characterize the error behavior in the range of engineering computations, distinguishing them from asymptotic error estimates. The text emphasizes the advantages of the hp-version of FEM over piecewise linear approximation and explores generalized FEM and a posteriori error estimation for Helmholtz problems. The book includes computational results for three-dimensional scattering problems and discusses the application of FEM to elastic scattering, such as scattering from a sphere and a cylinder with spherical endcaps. It concludes with a summary of the results and a bibliography of relevant references. The book is a valuable resource for researchers and practitioners in the field of wave propagation and scattering, providing both theoretical insights and practical computational methods.