A symmetric PML formulation that is suitable for finite element computation of time-harmonic acoustic waves in exterior domains is analyzed. Dispersion analysis displays the dependence of the discrete representation of the PML parameters on mesh refinement. Stabilization by modification of the coefficients is employed to improve PML performance, in conjunction with standard stabilized finite elements in the Helmholtz region. Numerical results validate the good performance of this finite element PML approach.

A novel approach to the development of infinite element formulations for exterior problems of time‐harmonic acoustics is presented. This approach is based on a functional which provides a general framework for domain‐based computation of exterior problems. Special cases include non‐reflecting boundary conditions (such as the DtN method). A prominent feature of this formulation is the lack of integration over the unbounded domain, simplifying the task of discretization. The original formulation is generalized to account for derivative discontinuities across infinite element boundaries, typical of standard infinite element approximations. Continuity between finite elements and infinite elements is enforced weakly, precluding compatibility requirements. Various infinite element approximations for two‐dimensional configurations with circular interfaces are presented. Implementation requirements are relatively simple. Numerical results demonstrate the good performance of this scheme. © 1998 John Wiley & Sons, Ltd.

A novel approach to the development of inÿnite element formulations for exterior problems of time-harmonic acoustics is presented. This approach is based on a functional which provides a general framework for domainbased computation of exterior problems. Special cases include non-re ecting boundary conditions (such as the DtN method). A prominent feature of this formulation is the lack of integration over the unbounded domain, simplifying the task of discretization. The original formulation is generalized to account for derivative discontinuities across inÿnite element boundaries, typical of standard inÿnite element approximations. Continuity between ÿnite elements and inÿnite elements is enforced weakly, precluding compatibility requirements. Various inÿnite element approximations for two-dimensional conÿgurations with circular interfaces are presented. Implementation requirements are relatively simple. Numerical results demonstrate the good performance of this scheme. ?

Three-dimensional infinite elements for exterior problems of time-harmonic acoustics are developed. The infinite elements mesh only the outer boundary of the finite element domain and need not match the finite elements on the interface. A four-noded infinite element, based on separation of variables in spherical coordinates, is presented. Singular behavior of associated Legendre functions at the poles is circumvented. Numerical results validate the good performance of this approach.

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