Finite element method for solving Helmholtz type equations in waveguides and other unbounded domains

Journal Article · Fri Oct 01 04:00:00 EDT 1982 · Math. Comput.; (United States)

DOI:https://doi.org/10.1090/S0025-5718-1982-0669632-7· OSTI ID:6788525

Goldstein, C I

A finite element method is described for solving Helmholtz type boundary value problems in unbounded regions, including those with infinite boundaries. Typical examples include the propagation of acoustic or electromagnetic waves in waveguides. The radiation condition at infinity is based on separation of variables and differs from the classical Sommerfeld radiation condition. It is shown that the problem may be replaced by a boundary value problem on a fixed bounded domain. The behavior of the solution near infinity is incorporated in a nonlocal boundary condition. This problem is given a weak or variational formulation, and the finite element method is then applied. It is proved that optimal error estimates hold.

• DOE Contract Number: AC02-76CH00016
• OSTI ID: 6788525
• Journal Information: Math. Comput.; (United States), Journal Name: Math. Comput.; (United States) Vol. 39:160; ISSN MCMPA
• Country of Publication: United States
• Language: English

Related Subjects

658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
BOUNDARY-VALUE PROBLEMS
CONFIGURATION
CYLINDRICAL CONFIGURATION
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC RADIATION
EQUATIONS
FINITE ELEMENT METHOD
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
RADIATIONS
SOUND WAVES
VARIATIONAL METHODS
WAVE PROPAGATION
WAVEGUIDES