The approximate component mode synthesis special finite element method in two dimensions: Parallel implementation and numerical results

A. Heinlein ^[1] ; U. Hetmaniuk ^[2] ; A. Klawonn ^[1] ; O. Rheinbach ^[3]
1. [1] University of Cologne
  
  University of Cologne
  
  Kreisfreie Stadt Köln, Alemania
2. [2] University of Washington
  
  University of Washington
  
  Estados Unidos
3. [3] Freiberg University Of Mining And Technology
  
  Freiberg University Of Mining And Technology
  
  Landkreis Mittelsachsen, Alemania
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Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 289, Nº 1 (1 December 2015), 2015, págs. 116-133
Idioma: inglés
DOI: 10.1016/j.cam.2015.02.053
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Resumen
- A special finite element method based on approximate component mode synthesis (ACMS) was introduced in Hetmaniuk and Lehoucq (2010). ACMS was developed for second order elliptic partial differential equations with rough or highly varying coefficients. Here, a parallel implementation of ACMS is presented and parallel scalability issues are discussed for representative examples. Additionally, a parallel domain decomposition preconditioner (FETI-DP) is applied to solve the ACMS finite element system. Weak parallel scalability results for ACMS are presented for up to 1024 cores. Our numerical results also suggest a quadratic–logarithmic condition number bound for the preconditioned FETI-DP method applied to ACMS discretizations.