Periodic Integral and Pseudodifferential Equations with Numerical Approximation

Beschreibung

Classical boundary integral equations arising from the potential theory and acoustics (Laplace and Helmholtz equations) are derived. Using the parametrization of the boundary these equations take a form of periodic pseudodifferential equations. A general theory of periodic pseudodifferential equations and methods of solving are developed, including trigonometric Galerkin and collocation methods, their fully discrete versions with fast solvers, quadrature and spline based methods. The theory of periodic pseudodifferential operators is presented in details, with preliminaries (Fredholm operators, periodic distributions, periodic Sobolev spaces) and full proofs. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.
Classical boundary integral equations arising from the potential theory and acoustics (Laplace and Helmholtz equations) are derived. Using the parametrization of the boundary these equations take a form of periodic pseudodifferential equations. A general theory of periodic pseudodifferential equations and methods of solving are developed, including trigonometric Galerkin and collocation methods, their fully discrete versions with fast solvers, quadrature and spline based methods. The theory of periodic pseudodifferential operators is presented in details, with preliminaries (Fredholm operators, periodic distributions, periodic Sobolev spaces) and full proofs. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.
An attractive book in the intersection of analysis and numerical analysis Includes supplementary material: sn.pub/extras

Autor*in

Jukka Saranen

Themen in »Periodic Integral and Pseudodifferential Equations with Numerical Approximation«

Boundary value problem Helmholtz equation Periodic pseudodifferential equations Sobolev space boundary integral equations fast solvers fully discrete methods numerical analysis periodic integral equations

Stimmen zu »Periodic Integral and Pseudodifferential Equations with Numerical Approximation«

Details

Link teilen