Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons

2011 ◽  
Vol 89 (4) ◽  
pp. 403-417 ◽  
Author(s):  
Dalei Wang ◽  
Radek Tezaur ◽  
Jari Toivanen ◽  
Charbel Farhat
Keyword(s):  
Variational Formulation ◽  
Acoustic Scattering ◽  
Partition Of Unity ◽  
Partition Of Unity Method ◽  
Medium Frequency ◽  
Enrichment Method ◽  
Discontinuous Enrichment ◽  
Frequency Regime ◽  
And Performance ◽  
Performance Comparisons

Recent Developments in High-Performance Computational Vibro-Acoustics in the Medium Frequency Regime

2012 ◽  
Author(s):  
Charbel Farhat ◽  
Radek Tezaur ◽  
Ulrich Hetmaniuk
Keyword(s):  
High Performance ◽  
Computational Cost ◽  
Medium Frequency ◽  
Time Frequency ◽  
Additional Information ◽  
Reduction Techniques ◽  
Discontinuous Enrichment ◽  
Recent Developments ◽  
Frequency Regime ◽  
Frequency Sweeps

Structural acoustics applications in the medium frequency regime are computationally challenging. One avenue of research pursues higher-order discretization methods that can deliver both accuracy and computational efficiency at smaller mesh resolutions. The Discontinuous Enrichment Method (DEM) is one example which distinguishes itself from competing approaches in the additional information it incorporates in the approximation method. It has shown a significant promise for acoustic and structural acoustic applications and therefore is reviewed here, together with new applications to shell problems. Frequency sweeps, which are almost inevitable in many vibro-acoustic engineering problems, present an additional challenge as they significantly increase the already high computational cost. Therefore, interpolatory model reduction techniques that successfully address this challenge and enable real-time frequency sweep analyses are also discussed in this paper.

A parallel partition of unity method for the unsteady Stokes equations

2017 ◽  
Vol 27 (9) ◽  
pp. 2105-2114
Author(s):  
Xiaoying Zhao ◽  
Yanren Hou ◽  
Guangzhi Du
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Partition Of Unity ◽  
Time Dependent ◽  
The Finite Element Method ◽  
Partition Of Unity Method ◽  
Content Type ◽  
Standard Galerkin Method ◽  
Unsteady Stokes Equations

Purpose The purpose of this paper is to propose a parallel partition of unity method to solve the time-dependent Stokes problems. Design/methodology/approach This paper solved the time-dependent Stokes equations using the finite element method and the partition of unity method. Findings The proposed method in this paper obtained the same accuracy as the standard Galerkin method, but it, in general, saves time. Originality/value Based on a combination of the partition of unity method and the finite element method, the authors, in this paper, propose a new parallel partition of unity method to solve the unsteady Stokes equations. The idea is that, at each time step, one need to only solve a series of independent local sub-problems in parallel instead of one global problem. Numerical tests show that the proposed method not only reaches the same convergence orders as the fully discrete standard Galerkin method but also saves ample computing time.

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