Radiation Boundary Conditions for the Two-Dimensional Wave Equation from a Variational Principle

• Published in: Mathematics of computation Vol. 58; no. 197; pp. 73 - 82
• Main Authors: Broeze, Jan, Edwin F. G. Van Daalen
• Format: Journal Article
• Language: English
• Published: Providence, RI American Mathematical Society 01-01-1992
• Subjects: Boundary conditions; Error rates; Exact sciences and technology; Mathematical analysis; Mathematical expressions; Mathematics; Momentum; Partial differential equations; Plane waves; Property lines; Sciences and techniques of general use; Velocity; Wave equations; Wave reflection; Wave equation; Two dimensional equation; Well posed problem; Absorption; Boundary condition; Variational principle
• ISSN: 0025-5718; 1088-6842
• DOI: 10.1090/S0025-5718-1992-1106959-5

A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary condition is analyzed by investigating the energy of the system. Results obtained with this (nonlinear) boundary condition are compared with those obtained with the (linear) first-order absorbing boundary condition suggested by Higdon. In an accompanying paper the underlying theory is presented.