A parallel hp‐FEM infrastructure for three‐dimensional structural acoustics

This paper describes a parallel three-dimensional numerical infrastructure for the solution of a wide range of time-harmonic problems in structural acoustics and vibration. High accuracy and rate of error-convergence, in the mid-frequency regime,is achieved by the use of hp-finite and infinite element approximations. The infrastructure supports parallel computation in both single and multi-frequency settings. Multi-frequency solves utilize concurrent factoring of the frequency-dependent linear algebraic systems and are naturally scalable. Scalability of large-scale single-frequency problems is realized by using FETI-DP—an iterative domain-decomposition scheme. Numerical examples are presented to cover applications in vibratory response of fluid-filled elastic structures as well as radiation and scattering from elastic structures submerged in an infinite acoustic medium. We demonstrate both the numerical accuracy as well as parallel scalability of the infrastructure in terms of problem parameters that include wavenumber and number of frequencies, polynomial degree of finite/infinite element approximations as well as the number of processors. Scalability and accuracy is evaluated for both single and multiple frequency sweeps on four high-performance parallel computing platforms: SGI Altix, SGI Origin, IBM p690 SP and Linux-cluster. Results show good performance on shared as well as distributed-memory architecture. Copyright © 2006 John Wiley & Sons, Ltd.

[1]  Joseph JáJá,et al.  An Introduction to Parallel Algorithms , 1992 .

[2]  C. Farhat,et al.  FETI-DPH: A DUAL-PRIMAL DOMAIN DECOMPOSITION METHOD FOR ACOUSTIC SCATTERING , 2005 .

[3]  Christian Soize,et al.  Structural Acoustics and Vibration , 2001 .

[4]  S. Dey.  Evaluation of p-FEM Approximations for Mid-Frequency Elasto-Acoustics , 2003 .

[5]  C. Farhat,et al.  A fast method for solving acoustic scattering problems in frequency bands , 2001 .

[6]  M. Shephard,et al.  Geometry representation issues associated with p-version finite element computations , 1997 .

[7]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[8]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[9]  Olof B. Widlund,et al.  DUAL-PRIMAL FETI METHODS FOR THREE-DIMENSIONAL ELLIPTIC PROBLEMS WITH HETEROGENEOUS COEFFICIENTS , 2022 .

[10]  D. Rixen,et al.  FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method , 2001 .

[11]  Saikat Dey,et al.  Mid-frequency structural acoustic and vibration analysis in arbitrary, curved three-dimensional domains , 2001 .

[12]  C. Farhat,et al.  A method of finite element tearing and interconnecting and its parallel solution algorithm , 1991 .

[13]  I. Babuska,et al.  Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation , 1995 .

[14]  Saikat Dey,et al.  Scalable Three-Dimensional Acoustics Using hp-finite/infinite Elements and FETI-DP , 2007 .

[15]  Saikat Dey,et al.  Acoustic infinite elements for non-separable geometries , 2002 .

[16]  Joseph W. H. Liu,et al.  The Multifrontal Method for Sparse Matrix Solution: Theory and Practice , 1992, SIAM Rev..

[17]  Carlos A. Felippa,et al.  Partitioned formulation of internal fluid–structure interaction problems by localized Lagrange multipliers , 2001 .

[18]  M. Shephard,et al.  p-Version FEM for structural acoustics with a posteriori error estimation ☆ , 2006 .

[19]  Vipin Kumar,et al.  Highly Scalable Parallel Algorithms for Sparse Matrix Factorization , 1997, IEEE Trans. Parallel Distributed Syst..

[20]  M. Shephard,et al.  A straightforward structure to construct shape functions for variable p-order meshes , 1997 .

[21]  Patrick R. Amestoy,et al.  Multifrontal parallel distributed symmetric and unsymmetric solvers , 2000 .

[22]  Jing Li,et al.  An iterative domain decomposition method for the solution of a class of indefinite problems in computational structural dynamics , 2005 .

[23]  Barry F. Smith,et al.  Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations , 1996 .

[24]  Patrick Amestoy,et al.  A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling , 2001, SIAM J. Matrix Anal. Appl..

[25]  Patrick Joly,et al.  Domain Decomposition Method for Harmonic Wave Propagation : A General Presentation , 2000 .