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Nonlocal Boundary Conditions for Higher–Order Parabolic Equations
Author(s) -
Ehrhardt Matthias,
Zisowsky Andrea
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610347
Subject(s) - helmholtz equation , domain (mathematical analysis) , boundary (topology) , mathematics , helmholtz free energy , parabolic partial differential equation , mathematical analysis , transformation (genetics) , work (physics) , boundary value problem , construct (python library) , order (exchange) , partial differential equation , computer science , physics , biochemistry , chemistry , quantum mechanics , programming language , gene , thermodynamics , finance , economics
This work deals with the efficient numerical solution of the two–dimensional one–way Helmholtz equation posed on an unbounded domain. In this case one has to introduce artificial boundary conditions to confine the computational domain. Here we construct with the Z –transformation so–called discrete transparent boundary conditions for higher–order parabolic equations schemes. These methods are Padé “Parabolic” approximations of the one–way Helmholtz equation and frequently used in integrated optics and (underwater) acoustics. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)