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

Journal Article · Fri Oct 01 00:00:00 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), Vol. 39:160
• Country of Publication: United States
• Language: English

Related Subjects

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